Skip to content
master
Switch branches/tags
Code

Latest commit

 

Git stats

Files

Permalink
Failed to load latest commit information.
Type
Name
Latest commit message
Commit time
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Leapfrog Optimizer Package

About

This package is based the Leapfrogging Optimization Algorithm published by Dr. R. Russell Rhinehart. The following publications explain the technique:

  • Rhinehart, R. R., M. Su, and U. Manimegalai-Sridhar, “Leapfrogging and Synoptic Leapfrogging: a new optimization approach”, Computers & Chemical Engineering, Vol. 40, 11 May 2012, pp. 67-81.

  • Manimegalai-Sridhar, U., A. Govindarajan, and R. R. Rhinehart, “Improved Initialization of Players in Leapfrogging Optimization”, Computers & Chemical Engineering, Vol. 60, 2014, 426-429.

  • Rhinehart, R. R., “Convergence Criterion in Optimilsation of Stochastic Processes”, Computers & Chemical Engineering, Vol. 68, 4 Sept 2014, pp 1-6.

Installation

You can install via pip or using the setup.py script in the source code. Instructions are shown below.

Minimum system Requirements for Installation

  • Python >= 3.6

Recommended System Requirements for Installation

  • Windows or Linux
  • x86 processor with a 64-bit architecture
  • Additional Python Packages:
    • scipy
    • numpy
    • pytest

Via pip

The lpfgopt package may be installed with pip using the following command:

$ pip install lpfgopt # You may need root privileges or the --user tag

If you wish to install locally with pip you may do the following:

  • Download and unzip the archive or clone it with git.
  • Open the main directory where setup.py is located and run the following command:
    $ pip install .

Via setup.py

  • Download the master branch and unzip the archive or clone it with git.
  • Open the main directory where "setup.py" is located and run the following command:
    $ python setup.py install     # You may need root priviliges or use the --user tag

Test the Installation

The software should be installed correctly. You may validate the installation by executing the following commands in a terminal:

$ python
>>> import lpfgopt
>>> lpfgopt.__version__
'X.X.X'
>>> lpfgopt.minimize(lambda x: x[0]**2 + 10, [[-10, 10]])['x']
[<approximately 0.0>]
>>>

If the above commands produce the output congratulations! You have successfully installed the package!

Usage

Use the lpfgopt.minimize function to solve optimization problems of the form:

$minimize$ $f(x)$ $s.t.:$

  • $g(x) \le 0$

  • $bound_{1,1} \le x[1] \le bound_{1,2}$

    $bound_{2,1} \le x[2] \le bound_{2,2}$

    $...$

    $bound_{n,1} \le x[n] \le bound_{n,2}$

where $n$ is the number of decision variables and $bound$ is an array-like with shape $(n, 2)$. $bound$ may be a list of lists or a numpy ndarray.

Example Usage

The following is a simple optimization where the minimum value of the following equation is found:

  • $f(x) = x^2+y^2$

  • Subject to:

    $g(x) = -x^2 - y + 10 \le 0$ or g(x) = -x^2 - y + 10 <= 0

    $$x, y \in [-5, 5]$$

# test_lpfgopt.py
from lpfgopt import minimize
import matplotlib.pyplot as plt

# set up the objective funciton, 
# constraint fuction and bounds
f = lambda x: sum([i**2 for i in x])
g = lambda x: -x[0]**2 + 10 - x[1] 
bounds = [[-5,5] for i in range(2)]

# run the optimization
sol = minimize(f, bounds, fconstraint=g)['x']
print(f"Solution is: {sol}")

# plot the results on a contour plot
gg = lambda x: -x**2 + 10 # for plotting purposes

plt.figure(figsize=(8,8))
x, y = np.linspace(-5,5,1000), np.linspace(-5,5,1000)
X, Y = np.meshgrid(x,y)
Z = f([X,Y])

plt.contourf(X,Y,Z)
plt.plot(x, gg(x), "r", label="constraint")
plt.plot(*sol, 'x', 
         markersize=14, 
         markeredgewidth=4, 
         color="lime", 
         label="optimum")
plt.ylim(-5,5)
plt.xlim(-5,5)
plt.legend()
plt.show()

This code will produce the following output:

Solution is: [-3.0958051486911997, 0.4159905027317925]

As well as a plot that should look similar to the following image: