Evolutionary Multi-Objective Optimization.ipynb

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   "source": [
    "# Multi-Objective Optimization with Estimation of Distribution Algorithms"
   ]
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   "metadata": {},
   "source": [
    "## [Luis Martí](http://lmarti.com)/[IC](http://www.ic.uff.br)/[UFF](http://www.uff.br)"
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   "source": [
    "[http://lmarti.com](http://lmarti.com); [lmarti@ic.uff.br](mailto:lmarti@ic.uff.br) "
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "# Why we need *artificial intelligence*?"
   ]
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    "What does **intelligence** implies:\n",
    "* **infer**, **deduct**, **learn**, **create** and **adapt**;\n",
    "* to be able to deal with **NP-hard** problems $\\rightarrow$ **search and optimization problems**;\n",
    "* handle uncertainly, contradiction and noise.\n",
    "<br/><p/><br/>\n",
    "<div align='center'>\n",
    "AI is the how computer science attempts to answer the question 'What are we?'\n",
    "</div>"
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    "# In this talk\n",
    "\n",
    "* Multi-objective optimization problems (MOPs).\n",
    "* Multi-objective evolutionary algorithms (MOEAs/EMOAs).\n",
    "* Many-objective problems and the need for better MOEAs.\n",
    "* Multi-objective estimation of distribution algorithms.\n",
    "* Experiment design and comparing results.\n",
    "* Salient issues and research directions."
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    "# About the slides\n",
    "\n",
    "<img src='http://jupyter.org/assets/nav_logo.svg' width='38%'>\n",
    "\n",
    "* You may notice that I will be running some code inside the slides.\n",
    "* That is because the slides are _programmed_ as a Jupyter (IPython) notebook.\n",
    "* If you are viewing this as a \"plain\" notebook, be warned that the slide version is the best way of viewing it.\n",
    "* You can get them from **https://github.com/lmarti/scalable-moedas-talk**.\n",
    "* You are free to try them and experiment on your own."
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   "source": [
    "import time, array, random, copy, math\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
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   "source": [
    "# How we handle multiple -and conflictive- objectives?\n",
    "\n",
    "It's _\"easy\"_: we do it all the time.\n",
    "<br/>\n",
    "<div align='center'><img src='http://imgs.xkcd.com/comics/fuck_grapefruit.png' width='65%' align='center'/>\n",
    "taken from http://xkcd.com/388/</div>"
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    "# [Multi-objective optimization](http://en.wikipedia.org/wiki/Multi-objective_optimization)\n",
    "\n",
    "* Most -*if not all*- optimization problems involve more than one objective function to be optimized simultaneously.\n",
    "* Sometimes those other objectives are converted to constraints or fixed to default values, but they are still there.\n",
    "* Multi-objective optimization has been applied in [many fields of science](http://en.wikipedia.org/wiki/Multi-objective_optimization#Examples_of_multi-objective_optimization_applications) where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives."
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    "## A Multi-objective Optimization Problem (MOP)\n",
    "\n",
    "$$\n",
    "\\begin{array}{rl}\n",
    "\\mathrm{minimize}             & \\mathbf{F}(\\mathbf{x})=\\langle f_1(\\mathbf{x}),\\ldots,f_M(\\mathbf{x})\\rangle\\,,\\\\ \n",
    "\\mathrm{subject}\\ \\mathrm{to} & c_1(\\mathbf{x}),\\ldots,c_C(\\mathbf{x})\\le 0\\,,\\\\\n",
    "\t\t\t\t\t\t\t  & d_1(\\mathbf{x}),\\ldots,d_D(\\mathbf{x})= 0\\,,\\\\\n",
    "& \\text{with}\\ \\mathbf{x}\\in\\mathcal{D}\\,,\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "* $\\mathcal{D}$ is known as the *decision set* or *search set*.\n",
    "* functions $f_1(\\mathbf{x}),\\ldots,f_M(\\mathbf{x})$ are the *objective functions*.\n",
    "* Image set, $\\mathcal{O}$, result of the projection of $\\mathcal{D}$ via $f_1(\\mathbf{x}),\\ldots,f_M(\\mathbf{x})$ is called *objective set* ($\\mathbf{F}:\\mathcal{D}\\rightarrow\\mathcal{O}$).\n",
    "* $c_1(\\mathbf{x}),\\ldots,c_C(\\mathbf{x})\\le 0$ and $d_1(\\mathbf{x}),\\ldots,d_D(\\mathbf{x})= 0$  express the constraints imposed on the values of $\\mathbf{x}$."
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    "*Note 1:* In case you are -still- wondering, a maximization problem can be posed as the minimization one: $\\min\\ -\\mathbf{F}(\\mathbf{x})$.\n",
    "\n",
    "*Note 2:* If $M=1$ the problem reduces to a single-objective optimization problem. "
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   "source": [
    "## Example: A two variables and two objectives MOP\n",
    "<div align='center'><img src='static/mop-2d.jpg' height='56%' align='center'/></div>"
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    "## MOP (optimal) solutions\n",
    "\n",
    "Usually, there is not a unique solution that minimizes all objective functions simultaneously, but, instead, a set of equally good *trade-off* solutions.\n",
    "\n",
    "*Optimality* can be defined in terms of the [*Pareto dominance*](https://en.wikipedia.org/wiki/Pareto_efficiency) relation: \n",
    "* having $\\mathbf{x},\\mathbf{y}\\in\\mathcal{D}$, $\\mathbf{x}$ **is said to dominate** $\\mathbf{y}$ (expressed as $\\mathbf{x}\\preccurlyeq\\mathbf{y}$) iff $\\forall f_j$, $f_j(\\mathbf{x})\\leq f_j(\\mathbf{y})$ and $\\exists f_i$ such that $f_i(\\mathbf{x})< f_i(\\mathbf{y})$.\n",
    "* Having the set $\\mathcal{A}$. $\\mathcal{A}^\\ast$, the *non-dominated subset* of $\\mathcal{A}$, is defined as\n",
    "\n",
    "$$\n",
    "\\mathcal{A}^\\ast=\\left\\{ \\mathbf{x}\\in\\mathcal{A} \\left|\\not\\exists\\mathbf{y}\\in\\mathcal{A}:\\mathbf{y}\\preccurlyeq\\mathbf{x}\\right.\\right\\}.\n",
    "$$"
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    "* The *Pareto-optimal set*, $\\mathcal{D}^{\\ast}$, is the solution of the problem. It is the subset of non-dominated elements of $\\mathcal{D}$. It is also known as the *efficient set*.\n",
    "* It consists of solutions that cannot be improved in any of the objectives without degrading at least one of the other objectives.\n",
    "* Its image in objective set is called the *Pareto-optimal front*, $\\mathcal{O}^\\ast$.\n",
    "* Evolutionary algorithms generally yield a set of non-dominated solutions, $\\mathcal{P}^\\ast$, that approximates $\\mathcal{D}^{\\ast}$."
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    "## Visualizing the Pareto dominance relation\n",
    "\n",
    "We will be using DEAP, a python module for evolutionary computing."
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   "source": [
    "from deap import algorithms, base, benchmarks, tools, creator"
   ]
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   "source": [
    "Planting a constant seed to always have the same results (and avoid surprises in class). -*you should not do this in a real-world case!*"
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    "random.seed(a=42)"
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    "* To start, lets have a visual example of the Pareto dominance relationship in action.\n",
    "* In this notebook we will deal with two-objective problems in order to simplify visualization. \n",
    "* Therefore, we can create:"
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    "creator.create(\"FitnessMin\", base.Fitness, weights=(-1.0,-1.0))\n",
    "creator.create(\"Individual\", array.array, typecode='d', \n",
    "               fitness=creator.FitnessMin)"
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   "source": [
    "## An illustrative MOP: Dent\n",
    "\n",
    "$$\n",
    "\\begin{array}{rl}\n",
    "\\text{minimize} & f_1(\\mathbf{x}),f_2(\\mathbf{x}) \\\\\n",
    "\\text{such that} & f_1(\\mathbf{x}) = \\frac{1}{2}\\left( \\sqrt{1 + (x_1 + x_2)^2} \\sqrt{1 + (x_1 - x_2)^2} + x_1 -x_2\\right) + d,\\\\\n",
    " & f_2(\\mathbf{x}) = \\frac{1}{2}\\left( \\sqrt{1 + (x_1 + x_2)^2} \\sqrt{1 + (x_1 - x_2)^2} - x_1 -x_2\\right) + d,\\\\\n",
    "\\text{with}& d = \\lambda e^{-\\left(x_1-x_2\\right)^2}\\ (\\text{generally }\\lambda=0.85) \\text{ and }\\\\\n",
    "& \\mathbf{x}\\in \\left[-1.5,1.5\\right]^2.\n",
    "\\end{array}\n",
    "$$"
   ]
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   "source": [
    "Implementing the Dent problem"
   ]
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    "def dent(individual, lbda = 0.85):\n",
    "    \"\"\" Implements the test problem Dent\n",
    "    Num. variables = 2; bounds in [-1.5, 1.5]; num. objetives = 2.\n",
    "    @author Cesar Revelo\"\"\"\n",
    "    d  = lbda * math.exp(-(individual[0] - individual[1]) ** 2)  \n",
    "    f1 = 0.5 * (math.sqrt(1 + (individual[0] + individual[1]) ** 2) + \\\n",
    "                math.sqrt(1 + (individual[0] - individual[1]) ** 2) + \\\n",
    "                individual[0] - individual[1]) + d\n",
    "    f2 = 0.5 * (math.sqrt(1 + (individual[0] + individual[1]) ** 2) + \\\n",
    "                math.sqrt(1 + (individual[0] - individual[1]) ** 2) - \\\n",
    "                individual[0] + individual[1]) + d\n",
    "    return f1, f2"
   ]
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   "source": [
    "Preparing a DEAP `toolbox` with Dent."
   ]
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   "source": [
    "toolbox = base.Toolbox()"
   ]
  },
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   "execution_count": 10,
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    "BOUND_LOW, BOUND_UP = -1.5, 1.5\n",
    "NDIM = 2\n",
    "toolbox.register(\"evaluate\", dent)"
   ]
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   "source": [
    "Defining attributes, individuals and population."
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   "source": [
    "def uniform(low, up, size=None):\n",
    "    try:\n",
    "        return [random.uniform(a, b) for a, b in zip(low, up)]\n",
    "    except TypeError:\n",
    "        return [random.uniform(a, b) for a, b in zip([low] * size, [up] * size)]\n",
    "\n",
    "toolbox.register(\"attr_float\", uniform, BOUND_LOW, BOUND_UP, NDIM)\n",
    "toolbox.register(\"individual\", tools.initIterate, \n",
    "                 creator.Individual, toolbox.attr_float)\n",
    "toolbox.register(\"population\", tools.initRepeat, list, \n",
    "                 toolbox.individual)"
   ]
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   "source": [
    "Creating an example population distributed as a mesh."
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   "source": [
    "num_samples = 50\n",
    "limits = [np.arange(BOUND_LOW, BOUND_UP, (BOUND_UP - BOUND_LOW)/num_samples)] * NDIM\n",
    "sample_x = np.meshgrid(*limits)"
   ]
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   "source": [
    "flat = []\n",
    "for i in range(len(sample_x)):\n",
    "    x_i = sample_x[i]\n",
    "    flat.append(x_i.reshape(num_samples**NDIM))"
   ]
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   "source": [
    "example_pop = toolbox.population(n=num_samples**NDIM)"
   ]
  },
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   "source": [
    "for i, ind in enumerate(example_pop):\n",
    "    for j in range(len(flat)):\n",
    "        ind[j] = flat[j][i]"
   ]
  },
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   "source": [
    "fitnesses = toolbox.map(toolbox.evaluate, example_pop)\n",
    "for ind, fit in zip(example_pop, fitnesses):\n",
    "    ind.fitness.values = fit"
   ]
  },
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   "source": [
    "## Visualizing Dent "
   ]
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B9u3bNzKG6RIAAMA00dA5nv9Mf95nwP3Z3JyD5vAEAAAAGitbWT2v\nyJychw8fVrvd1qFDh7S6ujqt9AAAwII6tu4EGmoj/fkYMzPPdXEws12SHi7pekkfqyM5AAAAYJaK\nDFuXpNXVVYarAwCAqaFH5xBmdqyZnWlmp+dvd/fLJF0o6TRJv9qz2yskLUt6h7t/ezaZAgAAANPX\nrydnv0bOLM7MdPDgwVmmCAAAFtjCLUZkZk+U9MT017tIeqykyyT9fXrbFe7+ojT21PS+L7j7aT3H\nOV3SRyR9j6T3KhnO/mAlK7l/VtLD3P1bBfKZysTwAAAAVZtkYnjUq6qas0gjZ2+cmWlnZ2eixwUA\nAIuDxYjKub+kZ0j6BUmPUbJk/Wnpbc+Q9DN99rlNRZj26nygpLcpaeDcmx7n9ZIeUqSREwAAAGiq\nosPVB83dubKyIjPT0tKSNjY2+sYAAACUsXANne7+Cnc/xt1v17Mdk26n52KP9N7Wc6wvu/svuvvd\n3P0O7n6au+9192v6xQ9TpMArUwzOc2yUPCLERskjQmyUPCLERsmjabFR8ogQGyWPCLFR8ogQC0hJ\n46aZjWzkLBK3tbUlSdre3tba2tpU8gUAAItl4YauR5MNI5Kkdrs9dHL2/BCgRY6NkkeE2Ch5RIiN\nkkeE2Ch5NC02Sh4RYqPkESE2Sh4RYvPxDF0vxsxeo2QE0L0l3UnStqQvSTpf0hvd/RsljnV3Sa+U\n9N8knSzpa5L+RtIr3P3qAvtPdbqk/GupaE/PpaUlbW9va3l5mVXYAQDALRi6PgeWl5e1vr4+NKbV\nahEbKI8IsVHyiBAbJY8IsVHyaFpslDwixEbJI0JslDwixGIsL5C0JOkCJdMbvUPSdyS9TNJ/mNm9\nihzEzM6Q9HFJz5L0MUkHlcwj/3xJHzWzkyvPfAL79u0rFHf48GG1220aOQEAQHXcna3GTcn8n97t\ndn2Ubrfr7XZ74WOj5BEhNkoeEWKj5BEhNkoeTYuNkkeE2Ch5RIiNkkeEWHf3rG7xADVUEzZJtx9w\n+6sk7Uj644LHuSCN/9We2zvp7W8ucIzs2k1FdnxJ3ul0pvY4AABg/k1SczJ0vWasug4AAJqCoevV\nMLP7S/o3SRe4+0+NiD1D0iWSLnf3M3ruu6Okryv5MHCKu98w5DiV15z54eq7d+/W+eefrwMHDhQa\ntg4AADAIQ9cBAACA5nh8+vOiArHZmO4Le+9w9+sk/YOk4yU9pJLMxnT++edrZ2enbyOnmd2yHTx4\nsIbsAADAoqChEwAAAJgiM9tnZvvN7HVm9mFJL5f0R0rm2hzlPunPzw24/5L0Z6H5PquQNVrmHThw\noNC+w+bvXFlZkZlpaWlJGxsbE+UIAAAW07F1JwAAAADMuRdKOiX3+z9Iere7f7fAviekP68ZcH92\n+4lj5jaxoqusS8MbRLe2tiRJ29vbWltb0+bmZiX5AQCAxUGPTgAAAGCK3P2u7n6MksbOJ0tqS7rQ\nzJ4+61zyw8h7t/3795c+3vHHHz+ykbPT6cjMRjaItlotSdLy8rLW19dL5wIAAJpj//79A2uSSbAY\nUc1YjAgAADQFixFVw8zuqWQo+jXufsqI2Ncq6RH6Qnd/XZ/73yTpVyTtcfe3DDlOZTXncccdp5tu\nuknHHXecLrjgAq2uro7eqYCNjQ2tra1pfX29smMCAIDmYTEiAAAAoCHc/YuSPiPpzmY2tKFT0n+m\nP+8z4P5sbs5Bc3hW7sILL1S73R7YyDnu4kOrq6va3NykkRMAAIyNhs4giky6XmaC9nmOjZJHhNgo\neUSIjZJHhNgoeTQtNkoeEWKj5BEhNkoeEWJRubtJcknXjYjLLsxjrGcsl5ntkvRwSddL+ljlGQ5Q\npkFy2OJDAAAAlXN3tho3JQWuS/J2u+3DEBsrjwixUfKIEBsljwixUfJoWmyUPCLERskjQmyUPCLE\n5uM9QA0VfVPS0/KEPrcfI+kcSTuSPpC7/VhJZ0o6vc8+H0jjn9dz+8H09nML5JNdu6nLv646nU7p\n+wEAwGKbpOasvQhc9C27eMvLy97tdvtd31u0Wi1iA+URITZKHhFio+QRITZKHk2LjZJHhNgoeUSI\njZJHhFj3yYrORdskvUDStyVdKOk8Sa+W9FZJl6aNk5dLOjUXf2p2e59jnS7p6+n9f50eq5v+/hlJ\nJxXIZ2oNnb0Nl51Ox81sYCNmPt7MBh53165dLslbrVah1ycAAJgPNHQ2eMsuXpHirdvtervdXvjY\nKHlEiI2SR4TYKHlEiI2SR9Nio+QRITZKHhFio+QRIdZ9sqJz0TZJ95X0Rkn/JukKSd+VdJWkj0h6\nqaQ79sRnDZ2XDTje3dOG0q9K+k7aUHpQfXqNDth/Jg2dwxou+8UP69GZjyvS4xgAAMyHSWpOVl2v\nGauuAwCApmDV9eaaZs2Znzq00+lo7969Q+MPHjyoffv26cCBA0Njl5aWtL29reXlZR06dIhFigAA\nWBCT1Jw0dNaMhk4AANAUNHQ21zRqzp61kQo1cpaxsbGhtbU1ra+v08gJAMACoaGzwWjoBAAATUFD\nZ3NVWXP2NnBmt+3s7Ex8bAAAgElqzmMqzwYAAADAQjlw4EDf283slu3gwYMzzgoAACwaenTWjB6d\nAACgKejR2VzT7NE5bMh6PpZenwAAoAh6dAIAAACYiU6nIzNTp9ORuxeel7Nfr88yPT5XVlZkZlpa\nWtLGxsZYuQMA4irzPs//CRiEHp01o0cnAABoCnp0NlddNeeoFdbL9PjMx7bbbW1ublabLACgUisr\nK9ra2lKr1dLhw4dHLixX5n2e/xPmGz0650DV31jMc2yUPCLERskjQmyUPCLERsmjabFR8ogQGyWP\nCLFR8ogQC4zSr3fm3r17tbOzU6jX56B5PjOtVkuStLy8rPX19ckTBgCUUrZu2NrakiRtb29rbW1t\nZHyZ93n+T8BA7s5W4ybJs63dbvswxMbKI0JslDwixEbJI0JslDyaFhsljwixUfKIEBsljwix+XgP\nUEOxjVdzTlP+9WRmhfbpdDpuZt7pdEbGdrtdb7fb3u12J00VADCGsnVDq9VySb68vFzovbvM+zz/\nJ8y3SWrO2ouuRd+yi1fkD7/Mm8Q8x0bJI0JslDwixEbJI0JslDyaFhsljwixUfKIEBsljwix7pMV\nnWwxas5pyn8ALtJwCQBolmk2XAJ5NHQ2eMsuXp3fbjQtNkoeEWKj5BEhNkoeEWKj5NG02Ch5RIiN\nkkeE2Ch5RIh1n6zoZItRc1Yt37i5e/fuob0zaQgFgDh27drlkrzVak2lJgImMUnNyWJENWMxIgAA\n0BQsRtRc06o5x11MaFRsEWUXuQAAHMViPoiMxYgAAAAAzEy26FDeqMWEisT2W9BokLKLXAAAjmIx\nH8wrGjoBAAAATKTT6YxcWb3T6cjMCsVK0r59+4bez4d0ACi/Enrm8OHDarfbOnToED3iMVcYul4z\nhq4DAICmYOh6c1Vdc+Z7c+7Zs0fnnntu5ccd1SC6sbGhtbU1ra+v8yEdwMJiCDrmEUPXAQAAAMzM\nnj17bvnZr5GzzBD0vDK9PldXV7W5uUkjJ4CF1oTe7WX+Txj3/w8gQ4/OmtGjEwAANAU9Optr1jVn\n1QsPAcC8G3eBtTp6t5fpfd8bX9XCdSxIN9/o0QkAAAAgpH4LD02rx864c9UBQN3GXWCt7t7to+ZT\n7lXFwnUSC9JhMBo6gyhSjJUp3OY5NkoeEWKj5BEhNkoeEWKj5NG02Ch5RIiNkkeE2Ch5RIgFRsk3\nXu7evbvwEPRhH5LLNojywRdAU9U5BH2SL5+KNFyWmZakaGwThuyjJu7OVuMmybOt3W77MMTGyiNC\nbJQ8IsRGySNCbJQ8mhYbJY8IsVHyiBAbJY8Isfl4D1BDsY1Xc05T/vVkZoVjO51OJcd0d2+1Wi7J\nl5eXvdvtln4OAFCXbrfr7Xa7lveusu+1nU7HzWzo+/e01Xm+MH2T1Jy1F12LvmUXr0gxVqZwm+fY\nKHlEiI2SR4TYKHlEiI2SR9Nio+QRITZKHhFio+QRIdZ9sqKTLUbNOU1FGy/di39ILnNMdz74AqjX\nrl27XJK3Wq3a3ofKvm+Ouw8wTTR0NnjLLl6RN8Eyhds8x0bJI0JslDwixEbJI0JslDyaFhsljwix\nUfKIEBsljwix7pMVnWwxas6q5T8c7969u/IePhF6DQFAUWVHSkw7hyK9M915r0U8k9ScrLpeM1Zd\nBwAATcGq6801jZozvzJu9jurqwNYZEtLS9re3tby8rIOHTpUywJBZVdEByJi1XUAAAAAtRq0IMW0\nVlgvikW3AMzK4cOH1W63K2nkHPe9s8zCP8A8okdnzejRCQAAmoIenc017R6du3fv1nvf+96RcYN6\nfU6zB1L+2O12W5ubm5UdG8D8WVlZ0dbWllqtlg4fPlxLr0yp2HsnMK/o0QkAAABgpvK9hgY1cvYa\n1Oszb9++fUPvL9vLqdVqSZKWl5e1vr5eKE8Ai2tra0uStL29rbW1tZqzSRR575y1Mu/Fdffsx2Kh\noRMAAABAaXv37tXOzs7I3pdlh1GW+UA/qlFUqnYoKYD5V/WXI00agj5urkXei4vE0iCKKjB0vWYM\nXQcAAE3B0PXmmmXNOc4w9IMHD2rfvn06cODAyHgW2gAwTRsbG1pbW9P6+nolX440aQh6mVzLvBcX\njS36+FGmF8D0MHQdAAAAQDhFe/kU7R0qsdAGgNEmWYRsdXVVm5ubU2k8m/UQ9El6SI7Ktcx78Tjv\n28MeP+L0AoiDHp01o0cnAABoCnp0Nlf0Hp2zRm8gYL5FWoSsTI/1qpXtTVpnrmUef2lpSdvb21pe\nXmZakjlFj845UOSbpjLfSs1zbJQ8IsRGySNCbJQ8IsRGyaNpsVHyiBAbJY8IsVHyiBALDJPvNbR7\n9+6hPXcizMFGbyBgvkWZZ1Mq12N9WjlIxXqTVpXruIo+PnMvYyh3Z6txk+TZ1m63fRhiY+URITZK\nHhFio+QRITZKHk2LjZJHhNgoeUSIjZJHhNh8vAeoodjGqzmnJf9aMrOJY/MxnU6n1OMXiW+1Wi7J\nl5eXvdvtjowH0Czdbtfb7XZlf99l3uOmZZwcOp2Om1mh90UgkklqztqLrkXfsotXpMgqU5DNc2yU\nPCLERskjQmyUPCLERsmjabFR8ogQGyWPCLFR8ogQ6z5Z0ckWo+as0q5du271wbtoQ2OR2LIf6MvG\nV90IAmC+lf0yZV5zAGaFhs4Gb9nFK1JklSnI5jk2Sh4RYqPkESE2Sh4RYqPk0bTYKHlEiI2SR4TY\nKHlEiHWfrOhki1FzVmmcRk73Yj2Mpt2jE0B82ZcprVar9i8lquwZOe77Fb0zsUgmqTlZjKhmLEYE\nAACagsWImmsaNWe2GESmyoWHyi6IUdUCGixSBMRR9YJCURZKK7tAELCIJqk5aeisGQ2dAACgKWjo\nbK5p1JwbGxt6/OMfrxtuuGFgA2OUhoWiIq3UDCy6qlfWjtLAGP19sUx+0Z8LmotV1wEAAADM1Orq\nqq677rrCK/Tu27dvBlkdNc4KxVWv1AxgfNNcWbvICuSjjLsKeqfTkZnNtGFw3FzLvG8Pi510xXig\nDBo6AQAAAExdv4aFMh9+J/mgXPTD+jQbVoBFtLKyIjPT0tKSNjY2Su27urqqzc3Nyv4Wp9nAWKZB\ncO/evYW/IJqGMrmWaRAuGjvrL72weGjoBAAAAFCJ3sbIMg0LVfUc6qfoB/CqG1aARbe1tSVJ2t7e\n1tra2sTHm+QLj2k2MFbRQ7SoSXtHjsq1zPv2OI3Hwx6fnp+oAnN01ow5OgEAQFMwR2dzzarmLDsH\n3jTngqtqgSKJRYqAcc3rPJtSte8xZYxzDurKtezjR7q+qBdzdAIAAAAIpUgPp2n2HKqy91bVvdKA\nRTGv82xK1b3HTJJD0XNQ93D5cR6/33ObZCoELBB3Z6txk+SSvNVqebfb9WF27dpFbKA8IsRGySNC\nbJQ8IsRGyaNpsVHyiBAbJY8IsVHyiBDr7p7VLR6ghmIbr+acluz42dbpdKb2WHVotVouyZeXlwv9\nrQCYjk6n42ZW2XtM/n3LzCo55rRzqPocRDLqueXPVbvdnnF2mKVJas7ai65F38r8oRIbK48IsVHy\niBAbJY8IsVHyaFpslDwixEbJI0JslDwixObjPUANxTZezVm1/Gso2wZ9UM/H1PUBfdwcut2ut9tt\nGjmxcMp+IdY0TX5fWkR86bQ4Jqk5ay+6Fn3LLl6RP9Qyf9TzHBsljwixUfKIEBsljwixUfJoWmyU\nPCLERskjQmyUPCLEuk9WdLLFqDmr1q+hs0hPnKp6TpVtIKg6h3lvBALKfiFW9ph1N+xV2Tty3Oc1\nzz00q8aXTouDhs4Gb9nFK/KHWuaPep5jo+QRITZKHhFio+QRITZKHk2LjZJHhNgoeUSIjZJHhFj3\nyYpOthg1Z9WKNnL2xhZpDJ1Gw2XVDSzTaAQCIplGD7qqv3CI0nA6jS9zgEU1Sc3Jqus1Y9V1AADQ\nFKy63lzTqjnLrORbJHaaq7aXzbeIqleUBqLZ2NjQ2tqa1tfXK3t9l/27LXO8Olfqrvp5Va1MftGf\nC+Yfq64DAAAAmLlhK+n2riRcdtXdqldtH5XvOKa5ojRQlUlWql5dXdXm5malr++yf7dl1LkS+zSf\n1yDj5rpv375KYidZMR6YFnp01owenQAAoCno0dlcddSc4/SyqrrHZVHT6L20srKira0ttVotHT58\nmIZQ1Cb/+m6329rc3Kz0mHX3+Kv6fSNKD9EiyuQ6jR6dTTpXaBZ6dAIAAAAIq2gvq6p7XI6jTE+n\nYba2tiRJ29vbWltbq+SYwDharZYkaXl5Wevr65Ufv4q/mUl6Bk7zfaOKHqJlTHIeRuVapsfpOL1T\nBz0+vT4xazR0AgAAAKhE/gPt7t27h35QntaH30mPW1XDxrQbl4Cipj3FQtWNgVV92TCuOoag91Pk\nPJTJtUyDcNHYsueq7muLxcDQ9ZoxdB0AADQFQ9eba1Y157jDKIfFlh0iG2XI/DQWccFiizQdwjSH\ni1e9QFFdDZbj5BAh76oVeU7z+LwxmUlqTho6a0ZDJwAAaAoaOptr2jVn/kNqpq454Kr8wDytD9+R\nGqzQHFXPtRmpcWke59mM8qVL3Yo8pwjXC7FMVHO6O1uNmySX5K1Wy7vdrg+za9cuYgPlESE2Sh4R\nYqPkESE2Sh5Ni42SR4TYKHlEiI2SR4RYd/esbvEANRTbeDXnNGSvo/zW6XRG7tfpdNzMRsZO67hF\n5B/bzCY+Xr/jttvtyo6L+dZqtVySLy8vF3rPHmVar+8Iyr5vzGsOTcG5Qq9Jas7ai65F38oUOcTG\nyoUexKMAACAASURBVCNCbJQ8IsRGySNCbJQ8mhYbJY8IsVHyiBAbJY8Isfl4D1BDsY1Xc05D/nUk\nVf8htcqGy7Km9byqbrBCs5T9kinT7Xa93W5X9pqp+vU9zfeBsqb1hUeZ49X53tU0o87VuH8zaK5J\nas7ai65F37KLV6TIKVMQzXNslDwixEbJI0JslDwixEbJo2mxUfKIEBsljwixUfKIEOs+WdHJFqPm\nnIbsdSTJ9+zZ0zem7gaQaA0Voxqs+FA/38p+yTQtVb++88+rih6idb9v9Mtj3nq+NkWUvxnMDg2d\nDd6yi1ekgCnzDd48x0bJI0JslDwixEbJI0JslDyaFhsljwixUfKIEBsljwix7pMVnWwxas5pKPI6\nqruhoO7HL4sP9fNtXnv0TrOHaJ1/t1EaXAcpk1/05zLIvP7NYDAaOhu8TbPoBAAAqBINnc3d6q45\ni3y4nuaH9Wl8uJ9mgwEf6pshwhD0SA1X0+whumhD0Md9PxzVIFw0NtLryr36aRsQ3yQ1J6uu14xV\n1wEAQFOw6npz1V1zVr3qbtkVeqexkvE0Vwne2NjQ2tqa1tfX+67IzqrtMVS9CvqkOVTxOmQl9hjG\nfT8cdc2KxjbpXGE+TVJzHlN5NgAAAAAWnpndsknSzs5O4caKAwcOFH6cIrF79+4t9fhllcm3iNXV\nVW1ubg5swNza2pIkbW9va21trdLHXlQrKysyMy0tLWljY6PQPq1WS5K0vLys9fX1aaZXSNWvw337\n9k18jPz7wMGDB0vtO82/26rP1SiTnIdRuXY6HZlZoYbpMrGjHn+S5wRM1TjdQNnmZxgRAABAUZpg\nGBHb4tWcKjGc0r3c8NCqhpJqguGZw3KY5LhFjBrazmJG5eWvWdF5UasaTjut1+Gscxl1vKrm2Rw3\nxzpXQZ/m++E0FHn8aVxbIDNJzcnQ9ZrVPYwIAACgKIauN9esas78cMe8uofADjKt4ZnTHvY5amh7\nhCHVdRpnaP/S0pK2t7e1vLysQ4cOzXQ6gEjDhKc5XLyq94G6z9c4zynSlABVKfKc5vF5YzYYug4A\nAACgVv0aOQcNkYw45HFaQ1mncdxRQ9uLDKkeZ6h2U4wztP/w4cNqt9szb+TsVcXrJdJw8XGGSpcx\n6yHovYoO75/2eahD2edUxVQIQCHjdANla/YwIgAAgHFogmFEbPNfcyo3jFEjhpSqwJDHoscaN959\nesND6x52WmRIdf58DRuqXXQYfJnh8mWH1peNb9qq9dMcfl7FkOJx/ramqe6pK6Kdj8g4VxjXJDVn\n7UXXom/Zxau6IJjn2Ch5RIiNkkeE2Ch5RIiNkkfTYqPkESE2Sh4RYqPkESHWfbKiky1GzTlN+Q+0\nu3fvLhw76MNv2caaqht3piXKB/+ijYFFG0SLxpWNHSe+qrkzy4pybavOYxp/WxHO1bjPq+4vMppk\n1LmK8DpATDR0jlfs3V3SWyV9VdK2pMslvU7SiSWOcUTSzoDtawWPMZWCYJ5jo+QRITZKHhFio+QR\nITZKHk2LjZJHhNgoeUSIjZJHhNh8vAeo5dhK177ZtZuaqhcTyr8+p9WjcxbHGnbsOhtkizYGFm0Q\nLdOLsmyPy6b00IxybaMvUNR7zLrO1TT/zlFMhNcBYpqk5qy96Kpjk3SGpG8oaZB8j6TflfTB9PfP\nSDq54HGOSLpK0sv7bHsLHmMqBcE8x0bJI0JslDwixEbJI0JslDyaFhsljwixUfKIEBsljwix7pMV\nnWy1179Tb+gcZpwGhbKNNVU27kzzw3fTGleKNoiW6UVZtsdlXT00y2pKY3tZ0+jBGOH5Re+ZWeYc\nRTif42hq3pg+GjrLF3oXpI2av9pzeye9/c0Fj3NE0mUT5uKSKi8I5jk2Sh4RYqPkESE2Sh4RYqPk\n0bTYKHlEiI2SR4TYKHlEiHWfrOhkq3eL1NDZhF470/zwzVDO+Ma9Bk1pbI9gWucq+t/MuI2Xo14D\nRWOjnavojc2ozyQ1pyX7Lw4zO0PSJZIud/czeu67o6SvKzmhp7j7DSOOdUTSjrufPkE+SeW5YNcB\nAAA0T7aqtrvfdnlthFZ3zZlfkX3Wqw6P89gHDx7Uvn37dODAgZmvkJzP18y0s7Mz08dHjGtQ9d9M\nnX+D01bn9Sp7XsvkWubYRWMjvLaLWllZ0dbWllqtlg4fPqzV1dW6U8IMTVJzHlN5NvFlfx0X9t7h\n7tdJ+gdJx0t6SMHjtczs6Wb2MjN7vpmdZWaLeF4BAACAW5jZLdvu3btlZgM/gOdjDx48WOiYw+IG\n2bdvX6G4vXv3amdnZ6Jcq3DgwIFaH38eTHq++l2DWeh0OkP/ZiZR9O9glIivxbqul1T+vI7Ktcxr\nYJzXy6DHj3Jdt7a2JEnb29taW1urLQ800DjdQJu8SXqtkuHpvzHg/jel9/9ygWNdrv4LEV0q6VEF\n86l1GBEAAEBRmmAYEVvtNfDMa05Nedhl0eG8qnio5jg5lFFmaPs8Dmmu2jjnq6rhtFW/9qLlUvVr\ncdwc67xeZfepe6h22YXg6nyPacoiZJiOSWrO2ouuWW+SzksbI39xwP3npPe/uMCxXi7pLEltSS1J\n95X0Zkk3S7pe0v0KHIOGTgAA0Ag0dDZ3m2XNmf+QXLQBoGjsOA0RTViBuurHrzvHaZlFQ1SVojQY\nuTdjQaG6z1edjeKRRHmPacoiZJgOGjrLFXmVNXQOeYys1+h7CsT2LQbz29lnnz3s+gMAAFTm7LPP\nHlmbeICajq10fTqThs5du3aVbuR0L95YEGEBk7oXE6qyR1bdDaJlH79pDVHTbAiM0LC2iF8iLIIm\n9frE/KKhs1yRV9nQ9SGPcUZ6jCsKxNKjEwAANAINnc3dZlVzjtPIWZdpfVCP0ABQ9BpMo0F03Ngi\n56qu19a0GsUnyaOq11akv9e6v8iYx96Z0xLpdYP5RENnuSLvl9JGyD8YcP8F6f2rEzzGCekxbigQ\nS0MnAABoBBo6m7vNqubM5lST5Hv27OkbE+UD8rTyiPD8ijbYVN0gOkls5PkNIzRe9+YRtfE0wuu/\nNw96HFav7p7tmH80dJYr8k7X0QWDrOe+XZKuk7QlaWmCx/jJ9DE+WSDWJXmr1Ro590Q2FGjRY6Pk\nESE2Sh4RYqPkESE2Sh5Ni42SR4TYKHlEiI2SR4RY98mKTrZ6t1k1dBaZU61IA0TZD8njfKieVqPZ\nsONG+/BfdYNo2dim9KCLct2YZ3O8PKK/vuZRlNcBmouGzvKF3gfShsjn9dx+ML393Nxtx0o6U9Lp\nPbFnSjq+z7FPlXRJepyXFMjllgvYbrcLXehFj42SR4TYKHlEiI2SR4TYKHk0LTZKHhFio+QRITZK\nHhFi8/EeoJ5jK13/ZteudvnXXVUri5eNr0tT8uxVpoEteuNlkddfr7qHVE9T9Hk2xz3evLwOo71e\nimpq3ohjkpqz9qKrjk1Jr86vK2mM/GtJr5bUTX//jKSTcrGnprdf3nOM/Up6fh6SdK6k10j6S0nf\nTuPPl3RsgVxcki8vL4/sSZENBVr02Ch5RIiNkkeE2Ch5RIiNkkfTYqPkESE2Sh4RYqPkESHWfbKi\ncxE3SSdLek5ab35e0g2Srpb0YUm/qJ7RRSOOdSStMfttXyuwf60NnfkPvbt37y610MW0enTO4liz\nPDaKyV+DpqzsXeaYdb+umjAv6TRM8p5VdH7cyAuL9Yre0Iz4Jqk5ay8A69ok3V3SWyV9VdJ3JF2u\npEfnCT1xp6YF5GU9tz9K0ruUNIx+S9KNkr6hZI7Pp5fIwyUV+nBRZCjQIsRGySNCbJQ8IsRGySNC\nbJQ8mhYbJY8IsVHyiBAbJY8Ise6TFZ2LuEn6n2kd+WVJ75B0jqQ/TmvHHUl/UeJYRyRdJenlfba9\nBfYP09BZpLGi7IfkafW4q7phpexqxjQSDDfOuar7/E7j8at+zdZ9jiLkMq2Gy7LHHycucoOwe6zX\nF+KiobPBW91FJwAAQFE0dJau81YlPa7P7adI+kLa2Pnkgsc60vvFe8lcwjR0Rv9gW3euTWqwqNs4\n56qqRvFxXyfMs1lOUxagKnsNij6vKufRrfu9rV8edb++EBcNnQ3e6i46AQAAiqKhs9Ia8KVpQ+fv\nF4xvXENn/sPssOHq0/zwPc6x615MaNRjRGmsqNo4z6vOcxGpsWZe59msyixeW3UP1S7bW5yFohAd\nDZ0N3mjoBAAATUFDZ6U14IvShs5OwfgjSqZcerqkl0l6vqSzJB1TcP+Z1pz5D7KjPlSPEzdOY0XV\nQ3qn1VAwqsFimuerSmUff5xzW2fj0rw1BubN2zybTXttTUuR19gsXofzeG5RPRo6G7zR0AkAAJqC\nhs7K6r9jJf1H2tD5mIL7XK7+CxFdKulRBfavtaGzrjno5rExqurzVeY5jRs7jaG/dYveGBjpfNad\nS92PH0UTen3u2rXLJXmr1So8fzjmEw2dDd5o6AQAAE1BQ2dl9d+BtJHy/BL7vFxJD862pJak+0p6\ns6SbJV0v6X4j9q+toXP37t1DY6ucg27cYxcVoSdS1eerTMPGuLGRh/5GaQSbZqP8PA2tj/A+MM/q\n/nvIP3673Z754yMOGjobvNHQCQAAmoKGzkpqv19PGzk/JenECo732vR47xkRd5telr3b2WefPfji\nlzSNhoW6G0vqPO44ptGAXCa2KY1LURoEo8+zOa1jTpJD3Q2486jM1BnTeA20Wi2X5MvLy/ToXABn\nn332yNrEx6iNzJPCBzUxs6Ty5DoAAIDgzEyS5O5WcyqNZGbPk/QGJY2cP+HumxUc8wxJl0i60t3b\nQ+LC1JzZ60iSOp2O9u7dW2sOZqadnZ3Qx52mgwcPat++fTpw4MDIa1EmtimqfD1GeG1npnGtIry+\nI53jRTTt18DGxobW1ta0vr6u1dXVSo+NZpmo5hyndZSt0m/1C89BUWa+inmOjZJHhNgoeUSIjZJH\nhNgoeTQtNkoeEWKj5BEhNkoeEWLdj/bk8AA1VNM2SS9Q0vPyE5LuXOFxT0iPe8OIuDCjiLJcVFGP\nrPzx6l6te9Rxp/W4+H/svXuQbFte1/ldzTlDVh5OAa05EATq7QanW8IBBoahxRC60BYiCIqHyJEJ\naKAbA48yQJdl0DPK3AMO8qos0YEGZaZ56kzJQ/FcDtzLdBYD8lIZG2nlod2NL4QSETjX9kB315o/\nKvN03rxZmWvtvVfu78r8fCJWnHszv7n2d++dlfXLb61H82tbaqTwNo427PL963C/UsnxWkrrQo2e\noU7a1Jy9F3273uY/KNatQYHWy4eD1sWHg9bFh4PWxUdtWhcfDloXHw5aFx8O2nl9NKihamqSvkRX\nYeRPS3phx31/3LTvN63Rze5d78y/77qYHjmv7XtH5a52TId8HK5tzvu2j/7asquhcI7XrrXb/B4A\nWEWbmrP3wm/X2+zmpaxBkbNexTZrXXw4aF18OGhdfDhoXXzUpnXx4aB18eGgdfHhoI2xXdG5q03S\nl06DyH+oNWty6mo39pdKevHC4y+VdGuJ/gldTVu/lPTaNX33GnTOf1k/PDzsdOffmsKlrkPebaXJ\nNXC4bu47sS/2uU2bL5U8do6+a22J90ApXN5bsB0QdFbcZjcv5cvFZDKJo9Fo57UuPhy0Lj4ctC4+\nHLQuPmrTuvhw0Lr4cNC6+HDQxtiu6NzFJumzpyHk2yWdSrq3pH32nP6Jqf6tC/3ck/RQ0lOSXifp\nqyV9t6T/MtXfl3RjjReboDPly3rOF+YawqUZKV5rCjZSaRMs9TFK1yWwKeGj6/dXU499jgzMvQY5\nXrvWpl5fh/fsNn52QX8QdFbc+i46AQAAAFIh6Myu856cBpHvnP67rE3m9LOg8y0L/Xy0pL8t6eck\n/SdJvyPpVyU9LekzE71svOacrQG72LoOC7qm78Ag5fg1eLxO33XQXQKXwKbEz0HX17bva9XkfPp+\nf+WQ+h7o+z4senC/ruAPQWfFjaATAAAAaoGgs97WR82ZGnKW+nJc40iz1OOnhho516CptkRw2fc9\n6PI96Rb+lBwBXUso3ff7qwR9fc7Os43XFfqDoLPiRtAJAAAAtUDQWW/ro+acrQGbMzqxq9Aup98c\n+g51cn3kXIOmWufg0iHs3ub3YYz9LxngdC36xH0jNO4T5ELQWXEj6AQAAIBaIOist/VRc04mk3jr\n1q0ia9D1Nf2577BgRpPprF1qaxm55XC/angfuoRQjM4sR9/32OFnEeqCoLPiRtAJAAAAtUDQWW9z\nrjlLhHY5/ebgMD00h1KbqNSCw/1gnc1mPrbpfehAzojPEteeewu5EHRW3JyLTgAAAIB5CDrrbW41\nZ5MvvV0FRm2+cLtPD91W3Kag9x3UuK+z6XC/usbp/peg9GeX870FT9rUnOHq9dAXIYSrypP7AAAA\nAOaEECRJMcbQsxXIxK3mnL2XZv99eXm5Fcee73s8Huvo6KizvneZPt8vpTw4vVdOT091fHysk5OT\nTnw43K8Ucu5Bzjk53dtU+vK8v7+vhw8fajAY6MGDBzo4ONjIccGfNjXnCzp3AwAAAAAAsEAI4XGb\n5+TkZKX29PQ0ud912kWWHbsN4/FYIYSVQUEbv9tA2/Pv+p41oWsPx8fHrftoc12Pjo50eXlZJNza\n5P1qcw1y7kHOOa3q1+mzIOWzqwQPHz6UJD169Eh37tzZ2HFhy2kyDJTW/TSiwWAQJ5NJXMXt27fR\nGvlw0Lr4cNC6+HDQuvioTeviw0Hr4sNB6+LDQRtju2lENI+as09mHmatqyngOdoY+59CmeJ3XuM+\n1TPXa+79irGOZQs26WVdf33v7t7Xz1juNcg5v5xzSu23ls+Ckh4Gg0GUFIfDYVIdArtDm5qz96Jr\n19v8h8ZoNFp2fx+D1suHg9bFh4PWxYeD1sVHbVoXHw5aFx8OWhcfDtp5fTSooWjNas6+mH+vSd3u\nAJ6jzfXa16Yc85pVgU0Jr7l9pnpt2n+X5HotiXtwutjnpq9Xk/PJfU2pQLbLDdYc3rMlPUwmkzga\njQg54Xm0qTl7L7p2vc1uXspfMHL+2rHNWhcfDloXHw5aFx8OWhcftWldfDhoXXw4aF18OGhjbFd0\n0jxqzr5YDDrX0edu4aWDhRS/qYFNiUC0dHDZ54jarsPAPkPbRWrY3b3psTc98ndTdPlZUBIHD7B7\nEHRW3GY3L+XLRc5fO7ZZ6+LDQeviw0Hr4sNB6+KjNq2LDwetiw8HrYsPB22M7YpOmkfN2Rc1fVF2\n8NrliLBFXc5SAM7BZZP7VEMo7vD+m9HnkgFO16FP1t2DTVyn2gJk2A4IOitufRedAAAAAKkQdNbb\n+q45+/iy3rTPVV7dwpeuA9GcPvum9MjbXA+u4anDe3YXRmf2Rd8/Bw7vL9hO2tSc4er10BchhKvK\nk/sAAAAA5sx2y44xhjVSMMO95pzfiT2EoMvLy5WalJ2BU/os4dOR09NTHR8f6+TkZKM7Kpck9/1Q\nghLXtevzcnjPOtyrbaXva+vw/oLtpE3N+YLO3QAAAAAAADTk5ORkreb4+LjzPnMp0Wcpjo6OdHl5\naRkwhRAet9PT0+TXjcdjhRA6CwObeChxXbs8r0W6eM82uVYlz2nXWXdtm763m1DTZyJsOU2GgdK2\nZxoRAAAAQCpqMY2IRs25iOamPB4eHna+KUeJqa+1bB5SE+p56m0JD07vgRrWJS1Bzj1I1Trd11RK\n3y+WGIBStKk5mbreM+7TiAAAAABmMHW9Xhxrztwpj11OEy453bPENPxaaHJeDtfCfbq4wzXq20vJ\npStStU103K/+rwHUCVPXAQAAAADAnv39/cfTKOdJmfJYavp17jT4HEpMw98kbaa9pp5XV9Oa23h1\nny4+T9/vF4dp6CWXrkjVpuq4X/1fA9hBmgwDpW33NCIAAACAZajFNCIaNWeM8TnTKLViCui655tq\n27wmla6mt5e4BrnnPa9PmfZa8rrmHLvvKdUlp4t30Wef96np8XNfk3MPUrWpuq5/vktR0oPD+UHd\ntKk5ey+6dr3Nbt5gMIiTyWTZ/X3M7du30Rr5cNC6+HDQuvhw0Lr4qE3r4sNB6+LDQeviw0EbY7ui\nk+ZRc/bNYDDIDgHWhVZNAq5VgcUmvqDnhqFdXYPSwWWf6/VtWxg4z7ats9n1z6wbXf98l6Kkh5ru\nF3hC0Flxm/9wGY1Gy+7vY9B6+XDQuvhw0Lr4cNC6+KhN6+LDQeviw0Hr4sNBO6+PBjUUrVnN2TeT\nySTeunWr0w19crQpzPfX58jAEtcg91r1FVY0uac1hIFdv1cdfDTpy+U69EnKNSh9nbgP4EybmrP3\nomvX2+zmDYfDtSMpZn8B33Wtiw8HrYsPB62LDweti4/atC4+HLQuPhy0Lj4ctDG2KzppHjWnM/Nf\nulN2YZ/hPk24KX1Ove0bh7C5xPug6/Nq6rHL90GTc6rlfVgSh1GffdyH3JkksLsQdFbcZjcv5Yd8\nMpnE0Wi081oXHw5aFx8OWhcfDloXH7VpXXw4aF18OGhdfDhoY2xXdNI8ak5nagmBXILQGmh6rRyu\ncYkQqOvz2tZAGK7o89qWOvZ8vykzSWB3aVNzhqvXQ1+EEK4qT+4DAAAAmDPbKTvGGNZIwYwaas75\nndiv2yE4RbNMG0LQ5eVl5z677HcbaXqtTk9PdXx8rJOTk9Y7Ree8Z0rT5XlJ3Z9bk/66Pid4F31e\n21Kfc3t7e3r06JGGw6GeeuopHRwcdNIvbB9tas4XdO4GAAAAAAAggRDC43Z4eKgQQnLAcnx8nHyc\nk5OTNjaz+50/r9PT0yLH7oM255VzD46OjnR5edl5uJPznrmONteg6/Maj8dZPzM5pF6rUvdqFTn3\noOafxVXXdpPn1eXn54MHDzQajQg5oSxNhoHSdmsaEQAAAECM7aYR0ag5F9HcFEYlTr1VxnTKUuvP\ndbW2Xs65uJB7vxzWYuz6Oudeg037q9FL7nFz7kGq1uk+pND1+3ARh59d2G3a1Jy9F1273hyLTgAA\nAIBlEHTW2xxrzsWgc5MbD5UONVL6LxHAtAmMSui7pOmx3TerKhFYuVyrVEr+wSNVW1sgWksoDdAU\ngs6Km2PRCQAAALAMgs56m2PNOf+F+fDwcK2m1IYYfY2G6jqAydU20fc5yqv0PUvFPThd7HPT16rJ\n+ZT8g0eqtsTPY0lWnVfJMNLl/GH7IeisuDkWnQAAAADLIOistznWnF1NAV/UuY9MnNF1AJOrbaLv\nky69Op13Dbu7Nz12ahDmME26y5/Hvt9fJcPIvs8NdgeCzoqbY9EJAAAAsAyCznpbrTVnqVFW60IN\npy/zJUavNdV3QdNr26XXEkFQre+ZVWxidGZtdPkHmlKUvAcOoTTsBgSdFbfZzRsMBnEymSy7v4+5\nffs2WiMfDloXHw5aFx8OWhcftWldfDhoXXw4aF18OGhjbFd00jxqTncWv6CXGPWY64Ppmd3icG1L\nBEFdn5dDYNjknAjC1t+70veWewDbAEFnxW3+Q240Gi27v49B6+XDQeviw0Hr4sNB6+KjNq2LDwet\niw8HrYsPB+28PhrUULRmNac78+/JnLCoj3UTUzTbTpNr0OV1a9pXDdPFm/4sdAnv8WbkjBjflj+k\n8F6BrmlTc/ZedO16m9284XC4diTFYDBAa+TDQeviw0Hr4sNB6+KjNq2LDwetiw8HrYsPB22M7YpO\nmkfN6cz8F+Uuvyw36bOG6akONLkG7lPQm+K+SVGpnwPIp89QsNSxnX4WYTsg6Ky4zW5eypeLyWQS\nR6PRzmtdfDhoXXw4aF18OGhdfNSmdfHhoHXx4aB18eGgjbFd0UnzqDldmS2jMN+uI/eLeqkv4Ck+\nahrl1MRr3+fnEAaWomRw6hxE5dwDp/uVQ59rBPf5eQiQA0Fnxc296AQAAACYQdBZb3OvOXNGc+Z+\nUS/1BbyPXePbhLw5odGmR2c2vUc1hIEuAVBfPkr+YaLrny8XSobSfX4eAuRA0Flxcy86AQAAAGYQ\ndNbb3GvO2TIKkuLdu3dXanO/qK/6Al46AOk6vG0T8uaERn1Op+1ztGGJa9D1ubmEwqmU/MNElz9f\nTmFoSS8EklALBJ0VN/eiEwAAAGAGQWe9zb3mXLWMwuKX/prWeOx61/iSIzr7DEC6DnacwsCS59ZH\nKFzyPRhj3j3o8uer7+s6Tx8/i05BL0CM7WrO3ouuXW/uRScAAADADILOelvNNWeT0Y61rDE5IzXY\nyA1AaglM3Kegt3mfuG9S1Ob4KdfWYQRh7jITzmvulvJQIuidrb08GAyS1wIHmNGm5gxXr4e+CCFc\nVZ7cBwAAADAnhCBJijGGnq1AJjXXnLP3nSSNx2MdHR2t1YUQdHl5ubbv09NTHR8f6+TkZGm/qceG\nd9HkPpT00MV9K3FOTT2ue8+W9rCtPxMp19Xtvd2lhxL3db7P0Wiki4uL1n3C7tCm5nxB524AAAAA\nAABaEkJo/OX75OQkSXd0dKTLy8ukfo+Pj5P63CZm9yCEoNPT0+zXp96Hro8/Ho8VQigSxLU9p2Xk\nvLdy3rMlPJS8tn2Se11LvA9y6dJDifs6GAwkScPhUGdnZ530CZBEk2GgNKYRAQAAwO6hFtOIaNSc\nOWhuGqV6nCKrSqazliL3HsTY7X1ocvwSuK/d2bSvbX7vlqCrKfClPbiwau1lgHW0qTl7L7p2vc1u\nXsq6FTlrXGyz1sWHg9bFh4PWxYeD1sVHbVoXHw5aFx8OWhcfDtoY2xWdNI+asxYWg862O6Y3DR9y\ng41N7+hc+hr0HYR1ffy+z2ceh0C4ptCsFvoK5x0+YwC6hKCz4jb/wTEajZbd38eg9fLhoHXx4aB1\n8eGgdfFRm9bFh4PWxYeD1sWHg3ZeHw1qKFqzmrMW5t+bh4eHazXrAoUcbRuvXezonNJf2343PToz\n55xKHH+Zj67eB03PrUscPKTQ9L3tfE6L9OW71Gdcyc9OgFW0qTl7L7p2vc1u3nA4XDuSYjAY5NXF\nJQAAIABJREFUoDXy4aB18eGgdfHhoHXxUZvWxYeD1sWHg9bFh4M2xnZFJ82j5qyFrqeIlgwfSnot\nFYpuOjhyCUtKXIOuz62Jx75GZuZ6LRHMuwWiq+5FSa+l+na7vrA7EHRW3GY3L+XLRc4aF9usdfHh\noHXx4aB18eGgdfFRm9bFh4PWxYeD1sWHgzbGdkUnzaPmrJ35L92Hh4fJ4c66IKj0l/mcICrHS06/\nfU5T7vr6Nu3Pfa3Nxf42HQqXDC5z+0/VpnhwCetK3ttSP98sbwB9QdBZcduWohMAAAC2H4LOetu2\n1JylggKXEYcx+gcLDiMOHUZRzih5bu4jb3O9lgjmUzy4/Hy7BK4ANUDQWXHblqITAAAAth+Cznpb\n7TXnfECQO8qrq1GUhBRXOIRGNYyi7HvUaZPjlwwuS9HV0hGb+Pnu43qVOC8+C2ETtKk5w9XroS9C\nCFeVJ/cBAAAAzAkhSJJijKFnK5BJ7TXn7L03Yzwe6+joKEkfQtDl5eXK/k9PT3V8fKyTk5Nr+83t\nswbmz2ndNW3zmq77Srlfm/CR2mcf75cmx+/6urpQw893iffgYr9dnVff1wp2gzY1J0Fnz9RedAIA\nAMDuQNBZL7XXnPNfrG/duqVnn302WV8iuLquz1JhRSq5x+87DHMJTEoEfLW9F3advq9XqZ+Fvj4L\nAdrSpuZ8QeduAAAAAAAAOuTGjRuSpJs3b+r+/fvPez6E8Lidnp5qPB4rhLD0S/iiNpVVfS7j+Pj4\n2udyPDT1u+r4yzg5OUnSHR0d6fLysvNwI/X4q2h6rUqcU+77ZRVNzqvL4+8C665X0/dWE7r4WZhR\n4n3AewvcYURnz9T+13UAAADYHRjRWS+115zn5+e6c+eOzs7OdHBw8Lznc0ZDlRxFmDrSqZTf3JFW\nXY1kdJyCXmKabl/BjsvI112m9D3Y1mUDAJrCiE4AAAAAANhaDg4OdHFxsTTkXCRnNFSXI6ekZiOd\nuvSbe/wSIxlzRpKWGh0qdX9vpfxRsstoOzKwxHldR6mRx6naTY6izKHEPbjuZ6HUNXC9tgCd0GQH\nI1r3O2AOBoM4mUziKm7fvo3WyIeD1sWHg9bFh4PWxUdtWhcfDloXHw5aFx8O2hjb7YBJ86g5t43Z\nec1aFztF5/bXhJzdlze9U3OT8+/6mjXtr8S1KnluqTu897UTe47XEto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      "text/plain": [
       "<matplotlib.figure.Figure at 0x108430630>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 338,
       "width": 669
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(11,5))\n",
    "plt.subplot(1,2,1)\n",
    "for ind in example_pop: plt.plot(ind[0], ind[1], 'k.', ms=3)\n",
    "plt.xlabel('$x_1$');plt.ylabel('$x_2$');plt.title('Decision space');\n",
    "plt.subplot(1,2,2)\n",
    "for ind in example_pop: plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'k.', ms=3)\n",
    "plt.xlabel('$f_1(\\mathbf{x})$');plt.ylabel('$f_2(\\mathbf{x})$');\n",
    "plt.xlim((0.5,3.6));plt.ylim((0.5,3.6)); plt.title('Objective space');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We also need `a_given_individual`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "a_given_individual = toolbox.population(n=1)[0]\n",
    "a_given_individual[0] = 0.5\n",
    "a_given_individual[1] = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "a_given_individual.fitness.values = toolbox.evaluate(a_given_individual)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Implementing the Pareto dominance relation between two individuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def pareto_dominance(ind1, ind2):\n",
    "    'Returns `True` if `ind1` dominates `ind2`.'\n",
    "    extrictly_better = False\n",
    "    for item1 in ind1.fitness.values:\n",
    "        for item2 in ind2.fitness.values:\n",
    "            if item1 > item2:\n",
    "                return False\n",
    "            if not extrictly_better and item1 < item2:\n",
    "                extrictly_better = True\n",
    "    return extrictly_better"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "*Note:* Bear in mind that DEAP implements a Pareto dominance relation that probably is more efficient than this implementation. The previous function would be something like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def efficient_pareto_dominance(ind1, ind2):\n",
    "    return tools.emo.isDominated(ind1.fitness.values, ind2.fitness.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Lets compute the set of individuals that are `dominated` by `a_given_individual`, the ones that dominate it (its `dominators`) and the remaining ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "subslide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "dominated = [ind for ind in example_pop \n",
    "             if pareto_dominance(a_given_individual, ind)]\n",
    "dominators = [ind for ind in example_pop \n",
    "              if pareto_dominance(ind, a_given_individual)]\n",
    "others = [ind for ind in example_pop \n",
    "          if not ind in dominated and not ind in dominators]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def plot_dent():\n",
    "    'Plots the points in decision and objective spaces.'\n",
    "    plt.figure(figsize=(10,5))\n",
    "    plt.subplot(1,2,1)\n",
    "    for ind in dominators: plt.plot(ind[0], ind[1], 'r.')\n",
    "    for ind in dominated: plt.plot(ind[0], ind[1], 'g.')\n",
    "    for ind in others: plt.plot(ind[0], ind[1], 'k.', ms=3)\n",
    "    plt.plot(a_given_individual[0], a_given_individual[1], 'bo', ms=6);\n",
    "    plt.xlabel('$x_1$');plt.ylabel('$x_2$');\n",
    "    plt.title('Decision space');\n",
    "    plt.subplot(1,2,2)\n",
    "    for ind in dominators: plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'r.', alpha=0.7)\n",
    "    for ind in dominated: plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'g.', alpha=0.7)\n",
    "    for ind in others: plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'k.', alpha=0.7, ms=3)\n",
    "    plt.plot(a_given_individual.fitness.values[0], a_given_individual.fitness.values[1], 'bo', ms=6);\n",
    "    plt.xlabel('$f_1(\\mathbf{x})$');plt.ylabel('$f_2(\\mathbf{x})$');\n",
    "    plt.xlim((0.5,3.6));plt.ylim((0.5,3.6));\n",
    "    plt.title('Objective space');\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Having `a_given_individual` (blue dot) we can now plot those that are dominated by it (in green), those that dominate it (in red) and those that are uncomparable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
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8f3D2LQvHCOTJ13N+/jxWHDes5V5xXM7K4UqNj49rYGBA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dTM5BkAHxaRm1Ir0DJcG6uxbds2/O7v/i5EBNevX0c+n0dXV1fTXOPl+bcAlLJkdTKTdfOVTfKY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10eb35cc0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 351,
       "width": 711
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_dent()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Obtaining the nondominated front."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "non_dom = tools.sortNondominated(example_pop, k=len(example_pop), \n",
    "                                 first_front_only=True)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WjqVLl12xjWkewoEDl3DgwF6EQiFs3ryZkz+IiIgo7ykRsbsN2iilBAAm+5lisRjuvHM1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\ny0v7WZXWOpjh0q9ij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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b681080>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 311,
       "width": 319
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5))\n",
    "for ind in example_pop:\n",
    "    plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'k.', ms=3, alpha=0.5)\n",
    "for ind in non_dom:\n",
    "    plt.plot(ind.fitness.values[0], ind.fitness.values[1], 'bo', alpha=0.74, ms=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "slideshow": {
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    }
   },
   "source": [
    "## So, is this the end?\n",
    "\n",
    "* Ok, now we know how to solve MOPs by sampling the search space.\n",
    "* MOPs, in the general case are NP-hard problems.\n",
    "* Brute force is never the solution in just a-little-more-complex cases.\n",
    "\n",
    "An example, solving the TSP problem using brute force:\n",
    "<table>\n",
    "<tr><th>$n$ cities</th><th>time</th>\n",
    "<tr><td>10</td><td>3 secs</td></tr>\n",
    "<tr><td>12</td><td>3 secs &times; 11 &times; 12 = 6.6 mins</td></tr>\n",
    "<tr><td>14</td><td>6.6 mins &times; 13 &times; 14 = 20 hours</td></tr>\n",
    "<tr><td>24</td><td>3 secs &times; 24! / 10! = <a href=\"https://www.google.com/search?q=3+seconds+*+24!+%2F+10!+in+years\">16 billion years</a></td></tr></table>\n",
    "\n",
    "_Note_: See my PhD EC course notebooks https://github.com/lmarti/evolutionary-computation-course on solving the TSP problem using EAs."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end",
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    "slide_helper": "subslide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Preference-based alternatives\n",
    "\n",
    "* A **Decision Maker** can define a set of weights $w_1,\\ldots,w_M$ for each function $f_1(),\\ldots,f_M()$.\n",
    "* We can convert a MOP into a SOP:\n",
    "\n",
    "$$\n",
    "\\begin{array}{rl}\n",
    "\\mathrm{minimize}             & F(\\mathbf{x})= w_1f_1(\\mathbf{x})+\\cdots + w_if_i(\\mathbf{x}) +\\cdots +w_Mf_M(\\mathbf{x})\\,,\\\\ \n",
    "\\mathrm{subject}\\ \\mathrm{to} & c_1(\\mathbf{x}),\\ldots,c_C(\\mathbf{x})\\le 0\\,,\\\\\n",
    "\t\t\t\t\t\t\t  & d_1(\\mathbf{x}),\\ldots,d_D(\\mathbf{x})= 0\\,,\\\\\n",
    "& \\text{with}\\ \\mathbf{x}\\in\\mathcal{D}\\,,\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "* A single-objective optimizer $\\implies$ only one solution not the complete PF.\n",
    "* Mathematical programming.\n",
    "* Requires (a lot) of _a priori_ knowledge but is relatively simple."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The *Decision Maker*\n",
    "\n",
    "<div align='center'><img src='static/920267262856611.jpeg' width='56%'></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
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     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Lexicographical ordering of the objectives\n",
    "\n",
    "<table><tr><td width='25%'>\n",
    "<div align='center'><img align='center'src=\"http://upload.wikimedia.org/wikipedia/commons/f/fb/Animal_Farm_-_1st_edition.jpg\" width=\"100%\"></div>\n",
    "</td><td width='75%'>\n",
    "<h3> All objectives are important...</h3>\n",
    "<h2>...but some objectives are more important than others.</h2>\n",
    "</td></tr></table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
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     "slide_helper": "subslide_end",
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     "slide_type": "slide"
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   },
   "source": [
    "## Better idea: Use the Pareto dominance relation to guide the search\n",
    "\n",
    "* We can use the Pareto dominance relation to determine how good an individual is.\n",
    "\n",
    "Ideas:\n",
    "\n",
    "* For a solution $\\mathbf{x}$, how many individuals dominate $\\mathbf{x}$?\n",
    "* ... and how many $\\mathbf{x}$ dominates?\n",
    "\n",
    "**This looks like the perfect task for an evolutionary algorithm.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
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    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Evolutionary Algorithms\n",
    "\n",
    "<div align='center'><img src='static/moea.png' width='65%'></div>\n",
    "\n",
    "Mating selection + Variation (Offsping generation) + Enviromental selection $\\implies$ global + local  parallel search features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "## Elements to take into account using evolutionary algorithms\n",
    "\n",
    "* **Individual representation** (binary, Gray, floating-point, etc.);\n",
    "* **evaluation** and **fitness assignment**;\n",
    "* **mating selection**, that establishes a partial order of individuals in the population using their fitness function value as reference and determines the degree at which individuals in the population will take part in the generation of new (offspring) individuals.\n",
    "* **variation**, that applies a range of evolution-inspired operators, like *crossover*, *mutation*, etc., to synthesize offspring individuals from the current (parent) population. \n",
    "    * This process is supposed to prime the fittest individuals so they play a bigger role in the generation of the offspring."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* **environmental selection**, that merges the parent and offspring individuals to produce the population that will be used in the next iteration. This process often involves the deletion of some individuals using a given criterion in order to keep the amount of individuals bellow a certain threshold.\n",
    "* **stopping criterion**, that determines when the algorithm should be stopped, either because the optimum was reach or because the optimization process is not progressing."
   ]
  },
  {
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   "metadata": {
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    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "## Pseudocode of an evolutionary algorithm\n",
    "\n",
    "```\n",
    "def evolutionary_algorithm(): \n",
    "  populations = [] # a list with all the populations\n",
    "    \n",
    "  populations[0] =  initialize_population(pop_size)\n",
    "  t = 0\n",
    "    \n",
    "  while not stop_criterion(populations[t]):\n",
    "    fitnesses = evaluate(populations[t])\n",
    "    offspring = matting_and_variation(populations[t],\n",
    "                                      fitnesses)\n",
    "    populations[t+1] = environmental_selection(           \n",
    "                                      populations[t],\n",
    "                                      offspring)\n",
    "    t = t+1\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The crossover operator\n",
    "\n",
    "One point crossover\n",
    "<img src='https://upload.wikimedia.org/wikipedia/commons/5/56/OnePointCrossover.svg' width='47%'>\n",
    "\n",
    "Two-point crossover\n",
    "<img src='https://upload.wikimedia.org/wikipedia/commons/c/cd/TwoPointCrossover.svg' width='47%'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# The Non-dominated Sorting Genetic Algorithm (NSGA-II)\n",
    "\n",
    "* NSGA-II algorithm is one of the pillars of the EMO field.\n",
    "    * Deb, K., Pratap, A., Agarwal, S., Meyarivan, T., *A fast and elitist multiobjective genetic algorithm: NSGA-II*, IEEE Transactions on Evolutionary Computation, vol.6, no.2, pp.182,197, Apr 2002 doi: [10.1109/4235.996017](http://dx.doi.org/10.1109/4235.996017)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Key element of NSGA-II\n",
    "\n",
    "* Fitness assignment relies on the Pareto dominance relation:\n",
    "    1. Rank individuals according the dominance relations established between them. \n",
    "    2. Individuals with the same domination rank are then compared using a local crowding distance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
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    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
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   },
   "source": [
    "## NSGA-II fitness assigment in detail\n",
    "\n",
    "* The first step consists in classifying the individuals in a series of categories $\\mathcal{F}_1,\\ldots,\\mathcal{F}_L$. \n",
    "* Each of these categories store individuals that are only dominated by the elements of the previous categories,\n",
    "$$\n",
    "\\begin{array}{rl}\n",
    "\t\\forall \\mathbf{x}\\in\\mathcal{F}_i: &\\exists \\mathbf{y}\\in\\mathcal{F}_{i-1} \\text{ such that } \\mathbf{y}\\preccurlyeq\\mathbf{x},\\text{ and }\\\\ \n",
    "\t                            &\\not\\exists\\mathbf{z}\\in \\mathcal{P}_t\\setminus\\left( \\mathcal{F}_1\\cup\\ldots\\cup\\mathcal{F}_{i-1}\n",
    "\t                            \\right)\\text{ that }\\mathrm{z}\\preccurlyeq\\mathrm{x}\\,;\n",
    "\\end{array}\n",
    "$$\n",
    "with $\\mathcal{F}_1$ equal to $\\mathcal{P}_t^\\ast$, the set of non-dominated individuals of $\\mathcal{P}_t$.\n",
    "\n",
    "* After all individuals are ranked a local crowding distance is assigned to them. \n",
    "* The use of this distance primes individuals more isolated with respect to others. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
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     "slide_helper": "subslide_end",
     "slide_type": "subslide"
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    "slide_helper": "slide_end",
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     "slide_type": "slide"
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   },
   "source": [
    "## Crowding distance\n",
    "* For each category set $\\mathcal{F}_l$, having $f_l=|\\mathcal{F}_l|$,\n",
    "    * for each individual $\\mathrm{x}_i\\in\\mathcal{F}_l$, set $d_{i}=0$.\n",
    "    * for each objective function $m=1,\\ldots,M$,\n",
    "        * $\\mathbf{I}=\\mathrm{sort}\\left(\\mathcal{F}_l,m\\right)$ (generate index vector).\n",
    "        * $d_{I_1}^{(l)}=d_{I_{f_l}}^{(l)}=\\infty$. (**key**)\n",
    "        * for $i=2,\\ldots,f_l-1$,\n",
    "            * Update distances as,\n",
    "\n",
    "$$\n",
    "d_i = d_i + \\frac{f_m\\left(\\mathrm{x}_{I_{i+1}}\\right)-f_m\\left(\\mathrm{x}_{I_{i+1}}\\right)} {f_m\\left(\\mathrm{x}_{I_{1}}\\right)-f_m\\left(\\mathrm{x}_{I_{f_l}}\\right)}$$\n",
    "\n",
    "Here the $\\mathrm{sort}\\left(\\mathcal{F},m\\right)$ function produces an ordered index vector $\\mathbf{I}$ with respect to objective function $m$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<div align='center'><img src='static/population.png' width='74%'/></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Sorting the population by rank and distance.\n",
    "\n",
    "* Having the individual ranks and their local distances they are sorted using the crowded comparison operator, stated as: \n",
    "    * An individual $\\mathrm{x}_i$ _is better than_ $\\mathrm{x}_j$ if:\n",
    "        * $\\mathrm{x}_i$ has a better rank: $\\mathrm{x}_i\\in\\mathcal{F}_k$, $\\mathrm{x}_j\\in\\mathcal{F}_l$ and $k<l$, or;\n",
    "        * if $k=l$ and $d_i>d_j$.\n",
    "        \n",
    "**Now we have key element of the the non-dominated sorting GA.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
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     "slide_type": "slide"
    }
   },
   "source": [
    "## Implementing NSGA-II\n",
    "\n",
    "We will deal with [DTLZ3](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/dtlz3/), which is a more difficult test problem.\n",
    "\n",
    "* DTLZ problems can be configured to have as many objectives as desired, but as we want to visualize results we will stick to two objectives.\n",
    "* The Pareto-optimal front of DTLZ3 lies in the first [orthant](http://en.wikipedia.org/wiki/Orthant) of a unit (radius 1) hypersphere located at the coordinate origin ($\\mathbf{0}$).\n",
    "* It has many local optima that run parallel to the global optima and render the optimization process more complicated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<div align='center'><img src='http://www.cs.cinvestav.mx/~emoobook/apendix-e/galeria4/dtlz3a.jpg' width=\"65%\" align='center'/></div>\n",
    "\n",
    "from Coello Coello, Lamont and Van Veldhuizen (2007) Evolutionary Algorithms for Solving Multi-Objective Problems, Second Edition. Springer [Appendix E](http://www.cs.cinvestav.mx/~emoobook/apendix-e/apendix-e.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "New `toolbox` instance with the necessary components."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "toolbox = base.Toolbox()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
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     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "BOUND_LOW, BOUND_UP = 0.0, 1.0\n",
    "toolbox.register(\"evaluate\", lambda ind: benchmarks.dtlz3(ind, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Describing attributes, individuals and population and defining the selection, mating and mutation operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
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   },
   "outputs": [],
   "source": [
    "toolbox.register(\"attr_float\", uniform, BOUND_LOW, BOUND_UP, NDIM)\n",
    "toolbox.register(\"individual\", tools.initIterate, creator.Individual, toolbox.attr_float)\n",
    "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)\n",
    "toolbox.register(\"mate\", tools.cxSimulatedBinaryBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0)\n",
    "toolbox.register(\"mutate\", tools.mutPolynomialBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0, indpb=1.0/NDIM)\n",
    "toolbox.register(\"select\", tools.selNSGA2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's also use the `toolbox` to store other configuration parameters of the algorithm. This will show itself usefull when performing massive experiments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
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     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "toolbox.pop_size = 50\n",
    "toolbox.max_gen = 500\n",
    "toolbox.mut_prob = 0.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A compact NSGA-II implementation\n",
    "\n",
    "Storing all the required information in the `toolbox` and using DEAP's `algorithms.eaMuPlusLambda` function allows us to create a very compact -albeit not a 100% exact copy of the original- implementation of NSGA-II."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def nsga_ii(toolbox, stats=None, verbose=False):\n",
    "    pop = toolbox.population(n=toolbox.pop_size)\n",
    "    pop = toolbox.select(pop, len(pop))\n",
    "    return algorithms.eaMuPlusLambda(pop, toolbox, mu=toolbox.pop_size, \n",
    "                                     lambda_=toolbox.pop_size, \n",
    "                                     cxpb=1-toolbox.mut_prob,\n",
    "                                     mutpb=toolbox.mut_prob, \n",
    "                                     stats=stats, \n",
    "                                     ngen=toolbox.max_gen, \n",
    "                                     verbose=verbose)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Running the algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "We are now ready to run our NSGA-II."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 37.6 s, sys: 296 ms, total: 37.9 s\n",
      "Wall time: 38.9 s\n"
     ]
    }
   ],
   "source": [
    "%time res, logbook = nsga_ii(toolbox)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "We can now get the Pareto fronts in the results (`res`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "fronts = tools.emo.sortLogNondominated(res, len(res))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Resulting Pareto fronts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "internals": {
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    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+qQSXtjxVZnts370K41f13WuYIyPSuWDyJGCTu292913A9cBZ5frl7o8ALWY2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\neQZj50VJUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108e3ff28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_colors = ('b','r', 'g', 'm', 'y', 'k', 'c')\n",
    "fig, ax = plt.subplots(1, figsize=(4,4))\n",
    "for i,inds in enumerate(fronts):\n",
    "    par = [toolbox.evaluate(ind) for ind in inds]\n",
    "    df = pd.DataFrame(par)\n",
    "    df.plot(ax=ax, kind='scatter', label='Front ' + str(i+1), \n",
    "                 x=df.columns[0], y=df.columns[1], \n",
    "                 color=plot_colors[i % len(plot_colors)])\n",
    "plt.xlabel('$f_1(\\mathbf{x})$');plt.ylabel('$f_2(\\mathbf{x})$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "* It is better to make an animated plot of the evolution as it takes place."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Animating the evolutionary process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "We create a `stats` to store the individuals not only their objective function values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "stats = tools.Statistics()\n",
    "stats.register(\"pop\", copy.deepcopy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "toolbox.max_gen = 4000 # we need more generations!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Re-run the algorithm to get the data necessary for plotting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "subslide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 46.5 s, sys: 199 ms, total: 46.7 s\n",
      "Wall time: 46.9 s\n"
     ]
    }
   ],
   "source": [
    "%time res, logbook = nsga_ii(toolbox, stats=stats)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from JSAnimation import IPython_display\n",
    "import matplotlib.colors as colors\n",
    "from matplotlib import animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def animate(frame_index, logbook):\n",
    "    'Updates all plots to match frame _i_ of the animation.'\n",
    "    ax.clear()    \n",
    "    fronts = tools.emo.sortLogNondominated(logbook.select('pop')[frame_index], \n",
    "                                           len(logbook.select('pop')[frame_index]))\n",
    "    for i,inds in enumerate(fronts):\n",
    "        par = [toolbox.evaluate(ind) for ind in inds]\n",
    "        df = pd.DataFrame(par)\n",
    "        df.plot(ax=ax, kind='scatter', label='Front ' + str(i+1), \n",
    "                 x=df.columns[0], y =df.columns[1], alpha=0.47,\n",
    "                 color=plot_colors[i % len(plot_colors)])\n",
    "        \n",
    "    ax.set_title('$t=$' + str(frame_index))\n",
    "    ax.set_xlabel('$f_1(\\mathbf{x})$');ax.set_ylabel('$f_2(\\mathbf{x})$')\n",
    "    return None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(4,4))\n",
    "ax = fig.gca()\n",
    "anim = animation.FuncAnimation(fig, lambda i: animate(i, logbook), \n",
    "                               frames=len(logbook), interval=60, \n",
    "                               blit=True)\n",
    "anim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The previous animation makes the notebook too big for online viewing. To circumvent this, it is better to save the animation as video and (manually) upload it to YouTube."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "anim.save('nsgaii-dtlz3.mp4', fps=15, bitrate=-1, dpi=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/Cm7r4cJq59s\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x10b681cc0>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('Cm7r4cJq59s')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Here it is clearly visible how the algorithm \"jumps\" from one local-optimum to a better one as evolution takes place."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# MOP benchmark problem toolkits\n",
    "\n",
    "Each problem instance is meant to test the algorithms with regard with a given feature: local optima, convexity, discontinuity, bias, or a combination of them.\n",
    "\n",
    "* [*ZDT1-6*](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/): Two-objective problems with a fixed number of decision variables.\n",
    "     * E. Zitzler, K. Deb, and L. Thiele. Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2):173-195, 2000. ([pdf](http://www.tik.ee.ethz.ch/sop/publicationListFiles/zdt2000a.pdf))\n",
    "* [*DTLZ1-7*](http://www.tik.ee.ethz.ch/sop/download/supplementary/testproblems/): $m$-objective problems with $n$ variables.\n",
    "     * K. Deb, L. Thiele, M. Laumanns and E. Zitzler. Scalable Multi-Objective Optimization Test Problems. CEC 2002, p. 825 - 830, IEEE Press, 2002. ([pdf](http://www.tik.ee.ethz.ch/sop/publicationListFiles/dtlz2002a.pdf))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "frag_helper": "fragment_end",
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     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* [*CEC'09*](http://dces.essex.ac.uk/staff/zhang/moeacompetition09.htm): Two- and three- objective problems that very complex Pareto sets.\n",
    "    * Zhang, Q., Zhou, A., Zhao, S., & Suganthan, P. N. (2009). Multiobjective optimization test instances for the CEC 2009 special session and competition. In 2009 IEEE Congress on Evolutionary Computation (pp. 1–30). ([pdf](http://dces.essex.ac.uk/staff/zhang/MOEAcompetition/cec09testproblem0904.pdf.pdf))\n",
    "* [*WFG1-9*](http://www.wfg.csse.uwa.edu.au/publications.html#toolkit): $m$-objective problems with $n$ variables, very complex.\n",
    "    * Huband, S., Hingston, P., Barone, L., & While, L. (2006). A review of multiobjective test problems and a scalable test problem toolkit. IEEE Transactions on Evolutionary Computation, 10(5), 477–506. doi:10.1109/TEVC.2005.861417"
   ]
  },
  {
   "cell_type": "markdown",
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     "slide_type": "subslide"
    }
   },
   "source": [
    "DTLZ5 and DTLZ6 have an $m-1$-dimensional Pareto-optimal front.\n",
    "* This means that in 3D the Pareto optimal front is a 2D curve.\n",
    "<div align='center'><img src='http://www.cs.cinvestav.mx/~emoobook/apendix-e/galeria4/dtlz5a.jpg' width=\"38%\" align='center'/></div>\n",
    "* In two dimensions the front is **a point**."
   ]
  },
  {
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   "execution_count": 39,
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   "outputs": [],
   "source": [
    "def dtlz5(ind, n_objs):\n",
    "    from functools import reduce\n",
    "    g = lambda x: sum([(a - 0.5)**2 for a in x])\n",
    "    gval = g(ind[n_objs-1:])\n",
    "    \n",
    "    theta = lambda x: math.pi / (4.0 * (1 + gval)) * (1 + 2 * gval * x)\n",
    "    fit = [(1 + gval) * math.cos(math.pi / 2.0 * ind[0]) *\n",
    "           reduce(lambda x,y: x*y, [math.cos(theta(a)) for a in ind[1:]])]\n",
    "    for m in reversed(range(1, n_objs)):\n",
    "        if m == 1:\n",
    "            fit.append((1 + gval) * math.sin(math.pi / 2.0 * ind[0]))\n",
    "        else:\n",
    "            fit.append((1 + gval) * math.cos(math.pi / 2.0 * ind[0]) *\n",
    "                       reduce(lambda x,y: x*y, [math.cos(theta(a)) for a in ind[1:m-1]], 1) *\n",
    "                       math.sin(theta(ind[m-1])))\n",
    "    return fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
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   "source": [
    "def dtlz6(ind, n_objs):\n",
    "    from functools import reduce\n",
    "    gval = sum([a**0.1 for a in ind[n_objs-1:]])\n",
    "    theta = lambda x: math.pi / (4.0 * (1 + gval)) * (1 + 2 * gval * x)\n",
    "    fit = [(1 + gval) * math.cos(math.pi / 2.0 * ind[0]) * \n",
    "           reduce(lambda x,y: x*y, [math.cos(theta(a)) for a in ind[1:]])]\n",
    "    for m in reversed(range(1, n_objs)):\n",
    "        if m == 1:\n",
    "            fit.append((1 + gval) * math.sin(math.pi / 2.0 * ind[0]))\n",
    "        else:\n",
    "            fit.append((1 + gval) * math.cos(math.pi / 2.0 * ind[0]) *\n",
    "                       reduce(lambda x,y: x*y, [math.cos(theta(a)) for a in ind[1:m-1]], 1) *\n",
    "                       math.sin(theta(ind[m-1])))\n",
    "    return fit            "
   ]
  },
  {
   "cell_type": "markdown",
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     "slide_type": "subslide"
    }
   },
   "source": [
    "DTLZ7 has many disconnected Pareto-optimal fronts.\n",
    "\n",
    "<div align='center'><img src='http://www.cs.cinvestav.mx/~emoobook/apendix-e/galeria4/dtlz7b.jpg' width=\"38%\" align='center'/></div>"
   ]
  },
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     "slide_type": "subslide"
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   "outputs": [],
   "source": [
    "def dtlz7(ind, n_objs):\n",
    "    gval = 1 + 9.0 / len(ind[n_objs-1:]) * sum([a for a in ind[n_objs-1:]])\n",
    "    fit = [ind for ind in ind[:n_objs-1]]\n",
    "    fit.append((1 + gval) * (n_objs - sum([a / (1.0 + gval) * (1 + math.sin(3 * math.pi * a)) for a in ind[:n_objs-1]])))\n",
    "    return fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "frag_helper": "fragment_end",
     "frag_number": 12,
     "slide_type": "subslide"
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    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "How does our NSGA-II behaves when faced with different benchmark problems?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
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     "frag_helper": "fragment_end",
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    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "problem_instances = {'ZDT1': benchmarks.zdt1, 'ZDT2': benchmarks.zdt2,\n",
    "                     'ZDT3': benchmarks.zdt3, 'ZDT4': benchmarks.zdt4,\n",
    "                     'DTLZ1': lambda ind: benchmarks.dtlz1(ind,2),\n",
    "                     'DTLZ2': lambda ind: benchmarks.dtlz2(ind,2),\n",
    "                     'DTLZ3': lambda ind: benchmarks.dtlz3(ind,2),\n",
    "                     'DTLZ4': lambda ind: benchmarks.dtlz4(ind,2, 100),\n",
    "                     'DTLZ5': lambda ind: dtlz5(ind,2),\n",
    "                     'DTLZ6': lambda ind: dtlz6(ind,2),\n",
    "                     'DTLZ7': lambda ind: dtlz7(ind,2)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "toolbox.max_gen = 1000\n",
    "\n",
    "stats = tools.Statistics(lambda ind: ind.fitness.values)\n",
    "stats.register(\"obj_vals\", np.copy)\n",
    "\n",
    "def run_problem(toolbox, problem):\n",
    "    toolbox.register('evaluate', problem)\n",
    "    return nsga_ii(toolbox, stats=stats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "frag_helper": "fragment_end",
     "frag_number": 12
    },
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     "slide_type": "-"
    }
   },
   "source": [
    "Running NSGA-II solving all problems. Now it takes longer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
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    "slide_helper": "slide_end",
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     "slide_type": "fragment"
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 58s, sys: 348 ms, total: 1min 58s\n",
      "Wall time: 1min 59s\n"
     ]
    }
   ],
   "source": [
    "%time results = {problem: run_problem(toolbox, problem_instances[problem]) \\\n",
    "                 for problem in problem_instances}"
   ]
  },
  {
   "cell_type": "markdown",
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     "frag_number": 103,
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     "slide_type": "subslide"
    }
   },
   "source": [
    "Creating this animation takes more programming effort."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
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   "outputs": [],
   "source": [
    "class MultiProblemAnimation:\n",
    "    def init(self, fig, results):\n",
    "        self.results = results\n",
    "        self.axs = [fig.add_subplot(3,4,i+1) for i in range(len(results))]\n",
    "        self.plots =[]\n",
    "        for i, problem in enumerate(sorted(results)):\n",
    "            (res, logbook) = self.results[problem]\n",
    "            pop = pd.DataFrame(data=logbook.select('obj_vals')[0])\n",
    "            plot = self.axs[i].plot(pop[0], pop[1], 'b.', alpha=0.47)[0]\n",
    "            self.plots.append(plot)\n",
    "        fig.tight_layout()\n",
    "            \n",
    "    def animate(self, t):\n",
    "        'Updates all plots to match frame _i_ of the animation.'\n",
    "        for i, problem in enumerate(sorted(results)):\n",
    "            #self.axs[i].clear()\n",
    "            (res, logbook) = self.results[problem]\n",
    "            pop = pd.DataFrame(data=logbook.select('obj_vals')[t])\n",
    "            self.plots[i].set_data(pop[0], pop[1])\n",
    "            self.axs[i].set_title(problem + '; $t=' + str(t)+'$') \n",
    "            self.axs[i].set_xlim((0, max(1,pop.max()[0])))\n",
    "            self.axs[i].set_ylim((0, max(1,pop.max()[1])))\n",
    "        return self.axs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": [
    "mpa = MultiProblemAnimation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false,
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     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "fig = plt.figure(figsize=(14,6))\n",
    "anim = animation.FuncAnimation(fig, mpa.animate, init_func=mpa.init(fig,results), \n",
    "                               frames=toolbox.max_gen, interval=60, blit=True)\n",
    "anim"
   ]
  },
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     "slide_type": "slide"
    }
   },
   "source": [
    "Saving the animation as video and uploading it to YouTube."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
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   },
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   "source": [
    "anim.save('nsgaii-benchmarks.mp4', fps=15, bitrate=-1, dpi=500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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    {
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       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/8t-aWcpDH0U\"\n",
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       "            allowfullscreen\n",
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    "YouTubeVideo('8t-aWcpDH0U')"
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  {
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   },
   "source": [
    "* It is interesting how the algorithm deals with each problem: clearly some problems are harder than others.\n",
    "* In some cases it \"hits\" the Pareto front and then slowly explores it."
   ]
  },
  {
   "cell_type": "markdown",
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    },
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   },
   "source": [
    "# Experiment design and reporting results\n",
    "\n",
    "* Watching an animation of an EMO algorithm solve a problem is certainly fun. \n",
    "* It also allows us to understand many particularities of the problem being solved.\n",
    "* But, as [Carlos Coello](http://delta.cs.cinvestav.mx/~ccoello/) would say, we are *not* in an art appreciation class.\n",
    "* We should follow the key concepts provided by the [scientific method](http://en.wikipedia.org/wiki/Scientific_method).\n",
    "* I urge you to study the [experimental design](http://en.wikipedia.org/wiki/Design_of_experiments) topic in depth, as it is an essential knowledge.\n",
    "\n",
    "<p>\n",
    "<div class=\"alert alert-info\" role=\"alert\">\n",
    "**Evolutionary algorithms are stochastic algorithms; therefore their results must be assessed by repeating experiments until you reach an statistically valid conclusion.** \n",
    "</div>\n",
    "</p>"
   ]
  },
  {
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   "source": [
    "## We need to evaluate performance\n",
    "\n",
    "1. *Closeness* to the Pareto-optimal front.\n",
    "2. *Diversity* of solutions.\n",
    "3. *Coverage* of the Pareto-optimal fronts.\n",
    "\n",
    "<p>\n",
    "<div class=\"alert alert-success\" role=\"alert\">\n",
    "<span class=\"label label-success\">Research hint!</span> The design analysis and application of performance indicators is one of the main research topic in the EMO field.</div>\n",
    "</p>"
   ]
  },
  {
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   "source": [
    "## The hypervolume indicator\n",
    "\n",
    "<table align='center' width=\"92%\">\n",
    "<tr>\n",
    "<td width='50%'>\n",
    "<img src='https://ls11-www.cs.uni-dortmund.de/_media/rudolph/hypervolume/hv.png' width='92%'>\n",
    "</td>\n",
    "<td width='50%'>\n",
    "<img src='https://ls11-www.cs.uni-dortmund.de/_media/rudolph/hypervolume/hvemm3d.png' width='92%'>\n",
    "</td>\n",
    "</tr>\n",
    "</table>\n",
    "_Note_: Taken from Günter Rudolph's [site on the hypervolume indicator](https://ls11-www.cs.uni-dortmund.de/rudolph/hypervolume/start)."
   ]
  },
  {
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   "source": [
    "## Formalization of the hypervolume\n",
    "\n",
    "For a set of solutions $\\mathcal{A}$,\n",
    "$$\n",
    "I_\\mathrm{hyp}\\left(\\mathcal{A}\\right) = \\mathrm{volume}\\left(\n",
    "\t\t\t\t\t\\bigcup_{\\forall \\mathbf{a}\\in\\mathcal{A}}{\\mathrm{hypercube}(\\mathbf{a},\\mathbf{r})}\\right)\\,.\n",
    "$$\n",
    "\n",
    "* We need a *reference point*, $\\mathbf{r}$.\n",
    "* Hypervolume is Pareto compliant (Fleischer, 2003): for sets $\\mathcal{A}$ and $\\mathcal{B}$, $\\mathcal{A}\\preccurlyeq\\mathcal{B} \\implies I_\\mathrm{hyp}(A)>I_\\mathrm{hyp}(B)$.\n",
    "* Calculating hypervolume is **#P-hard**, i.e. superpolynomial runtime unless **P** = **NP** (Bringmann and Friedrich, 2008)."
   ]
  },
  {
   "cell_type": "markdown",
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   },
   "source": [
    "## An illustrative simple/sample experiment\n",
    "\n",
    "Let's make a relatively simple experiment:\n",
    "\n",
    "* **Hypothesis**: The mutation probability of NSGA-II matters when solving the DTLZ3 problem.\n",
    "* **Procedure**: We must perform an experiment testing different mutation probabilities while keeping the other parameters constant."
   ]
  },
  {
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   },
   "source": [
    "### Notation\n",
    "\n",
    "As usual we need to establish some notation:\n",
    "\n",
    "* *Multi-objective problem* (or just *problem*): A multi-objective optimization problem, as defined above.\n",
    "* *MOEA*: An evolutionary computation method used to solve multi-objective problems.\n",
    "* *Experiment*: a combination of problem and MOEA and a set of values of their parameters.\n",
    "* *Experiment run*: The result of running an experiment.\n",
    "* We will use `toolbox` instances to define experiments. "
   ]
  },
  {
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   },
   "source": [
    "We start by creating a `toolbox` that will contain the configuration that will be shared across all experiments."
   ]
  },
  {
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   "source": [
    "toolbox = base.Toolbox()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 103,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "BOUND_LOW, BOUND_UP = 0.0, 1.0\n",
    "NDIM = 30\n",
    "\n",
    "# the explanation of this... a few lines bellow\n",
    "def eval_helper(ind):\n",
    "    return benchmarks.dtlz3(ind, 2)\n",
    "\n",
    "toolbox.register(\"evaluate\", eval_helper)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 103,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def uniform(low, up, size=None):\n",
    "    try:\n",
    "        return [random.uniform(a, b) for a, b in zip(low, up)]\n",
    "    except TypeError:\n",
    "        return [random.uniform(a, b) for a, b in zip([low] * size, [up] * size)]\n",
    "\n",
    "toolbox.register(\"attr_float\", uniform, BOUND_LOW, BOUND_UP, NDIM)\n",
    "toolbox.register(\"individual\", tools.initIterate, creator.Individual, toolbox.attr_float)\n",
    "toolbox.register(\"population\", tools.initRepeat, list, toolbox.individual)\n",
    "\n",
    "toolbox.register(\"mate\", tools.cxSimulatedBinaryBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0)\n",
    "toolbox.register(\"mutate\", tools.mutPolynomialBounded, low=BOUND_LOW, up=BOUND_UP, eta=20.0, indpb=1.0/NDIM)\n",
    "\n",
    "toolbox.register(\"select\", tools.selNSGA2)\n",
    "\n",
    "toolbox.pop_size = 200\n",
    "toolbox.max_gen = 500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 103,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We add a `experiment_name` to `toolbox` that we will fill up later on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 103
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "toolbox.experiment_name = \"$P_\\mathrm{mut}=\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 103
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "We can now replicate this toolbox instance and then modify the mutation probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 103
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "mut_probs = (0.05, 0.15, 0.3)\n",
    "number_of_experiments = len(mut_probs)\n",
    "toolboxes=list([copy.copy(toolbox) for _ in range(number_of_experiments)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 103,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "Now `toolboxes` is a list of copies of the same toolbox. One for each experiment configuration (population size)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 103,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "...but we still have to set the population sizes in the elements of `toolboxes`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 103
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "for i, toolbox in enumerate(toolboxes):\n",
    "    toolbox.mut_prob = mut_probs[i]\n",
    "    toolbox.experiment_name = toolbox.experiment_name + str(mut_probs[i]) +'$'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$P_\\mathrm{mut}=0.05$ 0.05\n",
      "$P_\\mathrm{mut}=0.15$ 0.15\n",
      "$P_\\mathrm{mut}=0.3$ 0.3\n"
     ]
    }
   ],
   "source": [
    "for toolbox in toolboxes:\n",
    "    print(toolbox.experiment_name, toolbox.mut_prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Experiment design\n",
    "\n",
    "As we are dealing with stochastic methods their results should be reported relying on an statistical analysis.\n",
    "\n",
    "* A given  experiment (a `toolbox` instance in our case) should be repeated a *sufficient* amount of times. \n",
    "* In theory, the more runs the better, but how much in enough? In practice, we could say that about *30* runs is enough.\n",
    "* The non-dominated fronts produced by each experiment run should be compared to each other. \n",
    "* We have seen in class that a number of *performance indicators*, like the *hypervolume*, *additive* and *multiplicative epsilon indicators*, among others, have been proposed for that task.\n",
    "* We can use statistical visualizations like [box plots](http://en.wikipedia.org/wiki/Box_plot) or [violin plots](http://en.wikipedia.org/wiki/Violin_plot) to make a visual assessment of the indicator values produced in each run.\n",
    "* We must apply a set of [statistical hypothesis tests](http://en.wikipedia.org/wiki/Statistical_hypothesis_testing) in order to reach an statistically valid judgment of the results of an algorithms. \n",
    "\n",
    "\n",
    "_Note_: I personally like the number [42](http://en.wikipedia.org/wiki/42_%28number%29) as it is the [answer to The Ultimate Question of Life, the Universe, and Everything](http://en.wikipedia.org/wiki/Phrases_from_The_Hitchhiker%27s_Guide_to_the_Galaxy#Answer_to_the_Ultimate_Question_of_Life.2C_the_Universe.2C_and_Everything_.2842.29)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "number_of_runs = 42"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Running experiments in parallel \n",
    "As we are now solving more demanding problems it would be nice to make our algorithms to run in parallel and profit from modern multi-core CPUs.\n",
    "\n",
    "* In DEAP it is very simple to parallelize an algorithm (if it has been properly programmed) by providing a parallel `map()` function throu the `toolbox`.\n",
    "* Local parallelization can be achieved using Python's [`multiprocessing`](https://docs.python.org/2/library/multiprocessing.html) or [`concurrent.futures`](https://docs.python.org/3/library/concurrent.futures.html) modules.\n",
    "* Cluster parallelization can be achived using IPython Parallel or [SCOOP](http://en.wikipedia.org/wiki/Python_SCOOP_%28software%29), that seems to be recommended by the DEAP guys as it was part of it.\n",
    "\n",
    "*Note*: You can have a very good summary about this issue in http://blog.liang2.tw/2014-handy-dist-computing/."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Progress feedback\n",
    "\n",
    "* Another issue with these long experiments has to do being patient.\n",
    "* A little bit of feedback on the experiment execution would be cool.\n",
    "* We can use the integer progress bar from [IPython widgets](http://nbviewer.ipython.org/github/jvns/ipython/blob/master/examples/Interactive%20Widgets/Index.ipynb) and report every time an experiment run is finished."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.html import widgets\n",
    "from IPython.display import display"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "progress_bar = widgets.IntProgressWidget(description=\"Starting...\", \n",
    "                                         max=len(toolboxes)*number_of_runs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### A side-effect of using process-based parallelization\n",
    "\n",
    "Process-based parallelization based on `multiprocessing` requires that the parameters passed to `map()` be [pickleable](https://docs.python.org/3.4/library/pickle.html).\n",
    "\n",
    "* The direct consequence is that `lambda` functions can not be directly used. \n",
    "* This is will certainly ruin the party to all `lambda` fans out there! *-me included*.\n",
    "* Hence we need to write some wrapper functions instead.\n",
    "* But, that wrapper function can take care of filtering out dominated individuals in the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def run_algo_wrapper(toolboox):\n",
    "    result,a = nsga_ii(toolbox)\n",
    "    pareto_sets = tools.emo.sortLogNondominated(result, len(result))\n",
    "    return pareto_sets[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# All set! Run the experiments..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "%%time\n",
    "from multiprocessing import Pool\n",
    "display(progress_bar)\n",
    "\n",
    "results = {}\n",
    "pool = Pool()\n",
    "for toolbox in toolboxes:\n",
    "    results[toolbox.experiment_name] = pool.map(run_algo_wrapper, [toolbox] * number_of_runs)\n",
    "    progress_bar.value +=number_of_runs\n",
    "    progress_bar.description = \"Finished %03d of %03d:\" % (progress_bar.value, progress_bar.max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "As you can see, even this relatively small experiment took lots of time!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "As running the experiments takes so long, lets save the results so we can use them whenever we want."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 129
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "pickle.dump(results, open('nsga_ii_dtlz3-results.pickle', 'wb'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "In case you need it, this file is included in the github repository.\n",
    "\n",
    "To load the results we would just have to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "loaded_results = pickle.load(open('nsga_ii_dtlz3-results.pickle', 'rb'))\n",
    "results = loaded_results # <-- (un)comment when needed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "`results` is a dictionary, but a pandas `DataFrame` is a more handy container for the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "res = pd.DataFrame(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td> [[1.0, 0.5000269727348605, 0.4999616400061205,...</td>\n",
       "      <td> [[0.9999999999999867, 0.4001150913352416, 0.40...</td>\n",
       "      <td> [[0.9999999999999996, 0.5000103341990221, 0.59...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td> [[0.9999999999999996, 0.5000347245740564, 0.50...</td>\n",
       "      <td> [[0.9999999999999994, 0.3000864089066496, 0.50...</td>\n",
       "      <td> [[0.9999999999999021, 0.4004161957652541, 0.49...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td> [[0.999999999813255, 0.5999721288215643, 0.499...</td>\n",
       "      <td> [[0.9999999999999981, 0.4995172500410508, 0.49...</td>\n",
       "      <td> [[0.9999999999999997, 0.4001590675284601, 0.50...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td> [[0.9999999998399098, 0.4998310912965175, 0.49...</td>\n",
       "      <td> [[0.9999999999415495, 0.5000078089803229, 0.39...</td>\n",
       "      <td> [[0.9999999999999546, 0.5000090989133338, 0.39...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td> [[0.9999999999999997, 0.5011132736209546, 0.50...</td>\n",
       "      <td> [[0.9999999999997499, 0.50003632075969, 0.5001...</td>\n",
       "      <td> [[1.0, 0.49942156718161346, 0.4998754336732803...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                               $P_\\mathrm{mut}=0.05$  \\\n",
       "0  [[1.0, 0.5000269727348605, 0.4999616400061205,...   \n",
       "1  [[0.9999999999999996, 0.5000347245740564, 0.50...   \n",
       "2  [[0.999999999813255, 0.5999721288215643, 0.499...   \n",
       "3  [[0.9999999998399098, 0.4998310912965175, 0.49...   \n",
       "4  [[0.9999999999999997, 0.5011132736209546, 0.50...   \n",
       "\n",
       "                               $P_\\mathrm{mut}=0.15$  \\\n",
       "0  [[0.9999999999999867, 0.4001150913352416, 0.40...   \n",
       "1  [[0.9999999999999994, 0.3000864089066496, 0.50...   \n",
       "2  [[0.9999999999999981, 0.4995172500410508, 0.49...   \n",
       "3  [[0.9999999999415495, 0.5000078089803229, 0.39...   \n",
       "4  [[0.9999999999997499, 0.50003632075969, 0.5001...   \n",
       "\n",
       "                                $P_\\mathrm{mut}=0.3$  \n",
       "0  [[0.9999999999999996, 0.5000103341990221, 0.59...  \n",
       "1  [[0.9999999999999021, 0.4004161957652541, 0.49...  \n",
       "2  [[0.9999999999999997, 0.4001590675284601, 0.50...  \n",
       "3  [[0.9999999999999546, 0.5000090989133338, 0.39...  \n",
       "4  [[1.0, 0.49942156718161346, 0.4998754336732803...  "
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## A first glace at the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CK2bOnCn88pdvU1VVTkrKo+3qQbfFpyD65lpHNacvxJtOoxIYwJQpJjIzYygu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L4E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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e4c1c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = res.applymap(lambda pop: [toolbox.evaluate(ind) for ind in pop])\n",
    "plt.figure(figsize=(11,3))\n",
    "for i, col in enumerate(a.columns):\n",
    "    plt.subplot(1, len(a.columns), i+1)\n",
    "    for pop in a[col]:\n",
    "        x = pd.DataFrame(data=pop)\n",
    "        plt.scatter(x[0], x[1], marker='.', alpha=0.5)\n",
    "    plt.title(col)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "The local Pareto-optimal fronts are clearly visible!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Calculating performance indicators\n",
    "\n",
    "* As already mentioned, we need to evaluate the quality of the solutions produced in every execution of the algorithm. \n",
    "* We will use the hypervolumne indicator for that.\n",
    "* We already filtered each population a leave only the non-dominated individuals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Calculating the *reference point*: a point that is **“worst”** than any other individual in every objective."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 145
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def calculate_reference(results, epsilon=0.1):\n",
    "    alldata = np.concatenate(np.concatenate(results.values))\n",
    "    obj_vals = [toolbox.evaluate(ind) for ind in alldata]\n",
    "    return np.max(obj_vals, axis=0) + epsilon"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 156
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "reference = calculate_reference(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 156,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 24.2078374 ,  23.34556811])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 156,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We can now compute the hypervolume of the Pareto-optimal fronts yielded by each algorithm run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 156
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "import deap.benchmarks.tools as bt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 156
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "hypervols = res.applymap(lambda pop: bt.hypervolume(pop, reference))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 161,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td> 484.044706</td>\n",
       "      <td> 475.835606</td>\n",
       "      <td> 467.011099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td> 470.434293</td>\n",
       "      <td> 448.911864</td>\n",
       "      <td> 505.030486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td> 497.999042</td>\n",
       "      <td> 543.511069</td>\n",
       "      <td> 466.046722</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td> 498.620375</td>\n",
       "      <td> 457.577314</td>\n",
       "      <td> 511.391365</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td> 496.731738</td>\n",
       "      <td> 537.063814</td>\n",
       "      <td> 422.195642</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   $P_\\mathrm{mut}=0.05$  $P_\\mathrm{mut}=0.15$  $P_\\mathrm{mut}=0.3$\n",
       "0             484.044706             475.835606            467.011099\n",
       "1             470.434293             448.911864            505.030486\n",
       "2             497.999042             543.511069            466.046722\n",
       "3             498.620375             457.577314            511.391365\n",
       "4             496.731738             537.063814            422.195642"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hypervols.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 161,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## How can we interpret the indicators?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Option A: Tabular form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>  42.000000</td>\n",
       "      <td>  42.000000</td>\n",
       "      <td>  42.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td> 467.170450</td>\n",
       "      <td> 449.429266</td>\n",
       "      <td> 462.117480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>  85.074852</td>\n",
       "      <td>  67.852181</td>\n",
       "      <td>  68.171960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td> 215.955445</td>\n",
       "      <td> 266.283832</td>\n",
       "      <td> 141.399743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td> 451.705130</td>\n",
       "      <td> 412.557156</td>\n",
       "      <td> 441.953739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td> 498.309709</td>\n",
       "      <td> 454.553244</td>\n",
       "      <td> 467.093601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td> 520.230539</td>\n",
       "      <td> 500.134986</td>\n",
       "      <td> 501.287171</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td> 557.024453</td>\n",
       "      <td> 544.707224</td>\n",
       "      <td> 551.328320</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       $P_\\mathrm{mut}=0.05$  $P_\\mathrm{mut}=0.15$  $P_\\mathrm{mut}=0.3$\n",
       "count              42.000000              42.000000             42.000000\n",
       "mean              467.170450             449.429266            462.117480\n",
       "std                85.074852              67.852181             68.171960\n",
       "min               215.955445             266.283832            141.399743\n",
       "25%               451.705130             412.557156            441.953739\n",
       "50%               498.309709             454.553244            467.093601\n",
       "75%               520.230539             500.134986            501.287171\n",
       "max               557.024453             544.707224            551.328320"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hypervols.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Option B: Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "import seaborn\n",
    "seaborn.set(style=\"whitegrid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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Zq0fi4+MpLCwgMKI9AAER7SkrK2PhwkU2jkxYS8XFLDs728aRCGsrKjIV9HNkyhUhhBDi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\nE/hmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113934c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(15,3))\n",
    "plt.subplot(1,2,1, title='Violin plots of NSGA-II with $P_{\\mathrm{mut}}$')\n",
    "seaborn.violinplot(hypervols, alpha=0.74)\n",
    "plt.ylabel('Hypervolume'); plt.xlabel('Mutation probabilities')\n",
    "plt.subplot(1,2,2, title='Box plots of NSGA-II with $P_{\\mathrm{mut}}$')\n",
    "seaborn.boxplot(hypervols, alpha=0.74)\n",
    "plt.ylabel('Hypervolume'); plt.xlabel('Mutation probabilities');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Option C: Statistical hypothesis test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "* Choosing the correct statistical test is essential to properly report the results.\n",
    "* [Nonparametric statistics](http://en.wikipedia.org/wiki/Nonparametric_statistics) can lend a helping hand.\n",
    "* [Parametric statistics](http://en.wikipedia.org/wiki/Parametric_statistics) could be a better choice in some cases. \n",
    "* Parametric statistics require that *all* data follow a known distribution (frequently a normal one).\n",
    "* Some tests -like the [normality test](http://en.wikipedia.org/wiki/Normality_test)- can be apply to verify that data meet the parametric stats requirements.\n",
    "* In my experience that is very unlikely that all your EMO result meet those characteristics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "We start by writing a function that helps us tabulate the results of the application of an statistical hypothesis test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "import itertools\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def compute_stat_matrix(data, stat_func, alpha=0.05):\n",
    "    '''A function that applies `stat_func` to all combinations of columns in `data`.\n",
    "    Returns a squared matrix with the p-values'''\n",
    "    p_values = pd.DataFrame(columns=data.columns, index=data.columns)\n",
    "    for a,b in itertools.combinations(data.columns,2):\n",
    "        s,p = stat_func(data[a], data[b]) \n",
    "        p_values[a].ix[b] = p\n",
    "        p_values[b].ix[a] = p\n",
    "    return p_values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 163,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The [Kruskal-Wallis H-test](http://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.kruskal.html) tests the null hypothesis that the population median of all of the groups are equal.\n",
    "\n",
    "* It is a non-parametric version of [ANOVA](http://en.wikipedia.org/wiki/Analysis_of_variance). \n",
    "* The test works on 2 or more independent samples, which may have different sizes. \n",
    "* Note that rejecting the null hypothesis does not indicate which of the groups differs. \n",
    "* Post-hoc comparisons between groups are required to determine which groups are different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 174
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.1170925062938863, 0.12763939044708175)"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.kruskal(*[hypervols[col] for col in hypervols.columns])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 174,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "We now can assert that the results are not the same but which ones are different or similar to the others the others?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 174,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In case that the null hypothesis of the Kruskal-Wallis is rejected the Conover–Inman procedure (Conover, 1999, pp. 288-290) can be applied in a pairwise manner in order to determine if the results of one algorithm were significantly better than those of the other.\n",
    "\n",
    "* Conover, W. J. (1999). *Practical Nonparametric Statistics*. John Wiley & Sons, New York, 3rd edition.\n",
    "\n",
    "_Note_: If you want to get an extended summary of this method check out my [PhD thesis](http://lmarti.com/pubs). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 174,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def conover_inman_procedure(data, alpha=0.05):\n",
    "    num_runs = len(data)\n",
    "    num_algos = len(data.columns)\n",
    "    N = num_runs*num_algos\n",
    "\n",
    "    _,p_value = stats.kruskal(*[data[col] for col in data.columns])\n",
    "    \n",
    "    ranked =  stats.rankdata(np.concatenate([data[col] for col in data.columns]))\n",
    "    \n",
    "    ranksums = []\n",
    "    for i in range(num_algos):\n",
    "        ranksums.append(np.sum(ranked[num_runs*i:num_runs*(i+1)]))\n",
    "\n",
    "    S_sq = (np.sum(ranked**2) - N*((N+1)**2)/4)/(N-1)\n",
    "\n",
    "    right_side = stats.t.cdf(1-(alpha/2), N-num_algos) * \\\n",
    "                 math.sqrt((S_sq*((N-1-p_value)/(N-1)))*2/num_runs)\n",
    "    \n",
    "    res = pd.DataFrame(columns=data.columns, index=data.columns)\n",
    "\n",
    "    for i,j in itertools.combinations(np.arange(num_algos),2):\n",
    "        res[res.columns[i]].ix[j] = abs(ranksums[i] - ranksums[j]/num_runs) > right_side\n",
    "        res[res.columns[j]].ix[i] = abs(ranksums[i] - ranksums[j]/num_runs) > right_side\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 174,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
       "      <td>  NaN</td>\n",
       "      <td> True</td>\n",
       "      <td> True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
       "      <td> True</td>\n",
       "      <td>  NaN</td>\n",
       "      <td> True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
       "      <td> True</td>\n",
       "      <td> True</td>\n",
       "      <td>  NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      $P_\\mathrm{mut}=0.05$ $P_\\mathrm{mut}=0.15$  \\\n",
       "$P_\\mathrm{mut}=0.05$                   NaN                  True   \n",
       "$P_\\mathrm{mut}=0.15$                  True                   NaN   \n",
       "$P_\\mathrm{mut}=0.3$                   True                  True   \n",
       "\n",
       "                      $P_\\mathrm{mut}=0.3$  \n",
       "$P_\\mathrm{mut}=0.05$                 True  \n",
       "$P_\\mathrm{mut}=0.15$                 True  \n",
       "$P_\\mathrm{mut}=0.3$                   NaN  "
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "conover_inman_procedure(hypervols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 174,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "We now know in what cases the difference is sufficient as to say that one result is better than the other."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 174,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Another alternative is the [Friedman test](http://en.wikipedia.org/wiki/Friedman_test).\n",
    "\n",
    "* Its null hypothesis that repeated measurements of the same individuals have the same distribution. \n",
    "* It is often used to test for consistency among measurements obtained in different ways. \n",
    "    * For example, if two measurement techniques are used on the same set of individuals, the Friedman test can be used to determine if the two measurement techniques are consistent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 174,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(41.4318936877076, 0.45177834097859693)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hyp_transp = hypervols.transpose()\n",
    "measurements = [list(hyp_transp[col]) for col in hyp_transp.columns]\n",
    "stats.friedmanchisquare(*measurements)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 174,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "[Mann–Whitney U test](http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test) (also called the Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test (WRS), or Wilcoxon–Mann–Whitney test) is a nonparametric test of the null hypothesis that two populations are the same against an alternative hypothesis, especially that a particular population tends to have larger values than the other.\n",
    "\n",
    "It has greater efficiency than the $t$-test on non-normal distributions, such as a mixture of normal distributions, and it is nearly as efficient as the $t$-test on normal distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
       "      <td>        NaN</td>\n",
       "      <td> 0.03572306</td>\n",
       "      <td> 0.08074789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
       "      <td> 0.03572306</td>\n",
       "      <td>        NaN</td>\n",
       "      <td>  0.1549628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
       "      <td> 0.08074789</td>\n",
       "      <td>  0.1549628</td>\n",
       "      <td>        NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      $P_\\mathrm{mut}=0.05$ $P_\\mathrm{mut}=0.15$  \\\n",
       "$P_\\mathrm{mut}=0.05$                   NaN            0.03572306   \n",
       "$P_\\mathrm{mut}=0.15$            0.03572306                   NaN   \n",
       "$P_\\mathrm{mut}=0.3$             0.08074789             0.1549628   \n",
       "\n",
       "                      $P_\\mathrm{mut}=0.3$  \n",
       "$P_\\mathrm{mut}=0.05$           0.08074789  \n",
       "$P_\\mathrm{mut}=0.15$            0.1549628  \n",
       "$P_\\mathrm{mut}=0.3$                   NaN  "
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_p_values=compute_stat_matrix(hypervols, stats.mannwhitneyu)\n",
    "raw_p_values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The [familywise error rate](http://en.wikipedia.org/wiki/Familywise_error_rate) (FWER) is the probability of making one or more false discoveries, or [type I errors](http://en.wikipedia.org/wiki/Type_I_and_type_II_errors), among all the hypotheses when performing multiple hypotheses tests.\n",
    "\n",
    "_Example_: When performing a test, there is a $\\alpha$ chance of making a type I error. If we make $m$ tests, then the probability of making one type I error is $m\\alpha$. Therefore, if an $\\alpha=0.05$ is used and 5 pairwise comparisons are made, we will have a $5\\times0.05 = 0.25$ chance of making a type I error.\n",
    "\n",
    "* FWER procedures (such as the [Bonferroni correction](http://en.wikipedia.org/wiki/Bonferroni_correction)) exert a more stringent control over false discovery compared to False discovery rate controlling procedures. \n",
    "* FWER controlling seek to reduce the probability of even one false discovery, as opposed to the expected proportion of false discoveries. \n",
    "* Thus, FDR procedures have greater power at the cost of increased rates of type I errors, i.e., rejecting the null hypothesis of no effect when it should be accepted."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "One of these corrections is the [Šidák correction](http://en.wikipedia.org/wiki/%C5%A0id%C3%A1k_correction) as it is less conservative than the [Bonferroni correction](http://en.wikipedia.org/wiki/Bonferroni_correction):\n",
    "$$\\alpha_{SID} = 1-(1-\\alpha)^\\frac{1}{m},$$\n",
    "where $m$ is the number of tests.\n",
    "\n",
    "* In our case $m$ is the number of combinations of algorithm configurations taken two at a time.\n",
    "* There are other corrections that can be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.016952427508441503"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.misc import comb\n",
    "alpha=0.05\n",
    "alpha_sid = 1 - (1-alpha)**(1/comb(len(hypervols.columns), 2))\n",
    "alpha_sid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Let's apply the corrected alpha to `raw_p_values`. If we have a cell with a `True` value that means that those two results are the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false,
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
       "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$P_\\mathrm{mut}=0.05$</th>\n",
       "      <td> False</td>\n",
       "      <td> False</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$P_\\mathrm{mut}=0.15$</th>\n",
       "      <td> False</td>\n",
       "      <td> False</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$P_\\mathrm{mut}=0.3$</th>\n",
       "      <td> False</td>\n",
       "      <td> False</td>\n",
       "      <td> False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      $P_\\mathrm{mut}=0.05$ $P_\\mathrm{mut}=0.15$  \\\n",
       "$P_\\mathrm{mut}=0.05$                 False                 False   \n",
       "$P_\\mathrm{mut}=0.15$                 False                 False   \n",
       "$P_\\mathrm{mut}=0.3$                  False                 False   \n",
       "\n",
       "                      $P_\\mathrm{mut}=0.3$  \n",
       "$P_\\mathrm{mut}=0.05$                False  \n",
       "$P_\\mathrm{mut}=0.15$                False  \n",
       "$P_\\mathrm{mut}=0.3$                 False  "
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "raw_p_values.applymap(lambda value: value <= alpha_sid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Further -and highly recommended- reading\n",
    "\n",
    "* Cohen, P. R. (1995). _Empirical Methods for Artificial Intelligence_ (Vol. 139). Cambridge: MIT press. [link](http://mitpress.mit.edu/books/empirical-methods-artificial-intelligence)\n",
    "* Bartz-Beielstein, Thomas (2006). _Experimental Research in Evolutionary Computation: The New Experimentalism_. Springer [link](http://link.springer.com/book/10.1007%2F3-540-32027-X)\n",
    "* García, S., & Herrera, F. (2008). _An Extension on “Statistical Comparisons of Classifiers over Multiple Data Sets” for all Pairwise Comparisons_. Journal of Machine Learning Research, 9, 2677–2694. [pdf](http://www.jmlr.org/papers/v9/garcia08a.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_helper": "subslide_end",
     "slide_type": "subslide"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Current research directions\n",
    "\n",
    "* Many-objective problems.\n",
    "* What about using performance indicators for fitness assignment?\n",
    "    * SMS-EMOA, HypE, IBEA, etc.\n",
    "* Make the variation smarter by including machine learning:\n",
    "    * MO-CMA-ES, MIDEA, MONEDA, MARTEDA, etc.\n",
    "* Why not evolve sets instead of individuals?\n",
    "    * Set-based multi-objective optimization.\n",
    "* Decomposition: \n",
    "    * MOEA/D.\n",
    "* Preferences and interactivity\n",
    "    * r-NSGA-II, NSGA-III.\n",
    "* Fitness landscapes.\n",
    "\n",
    "Check out http://simco.gforge.inria.fr/doku.php?id=openproblems "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_type": "subslide"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Final remarks\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "internals": {
     "frag_helper": "fragment_end",
     "frag_number": 183,
     "slide_helper": "subslide_end"
    },
    "slide_helper": "slide_end",
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "In this class/notebook we have seen some key elements:\n",
    "\n",
    "1. The Pareto dominance relation in action.\n",
    "2. The NSGA-II algorithm.\n",
    "3. Some of the existing MOP benchmarks. \n",
    "4. How to perform experiments and draw statistically valid conclusions from them.\n",
    "\n",
    "Bear in mind that:\n",
    "\n",
    "* When working in EMO topics problems like those of the CEC'09 or WFG toolkits are usually involved.\n",
    "* The issue of devising a proper experiment design and interpreting the results is a fundamental one.\n",
    "* The experimental setup presented here can be used with little modifications to single-objective optimization and even to other machine learning or stochastic algorithms.\n",
    "* **No-free-lunch theorem**."
   ]
  }
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