Example code of a group of bio-inspired algorithms using jupyter notebooks and python
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README.md

[Under construction]

Evolutionary Algorithms Library (EAL)

The following library wraps the evolutionary process of the evolutionary algorithms to make them easier to use. It has a modular structure that makes easy to implement new operators for the selection, crossover, mutation, replacement operations or optimization functions.

The EAL library includes:

  • Single-run Logger
  • Multi-run Logger
  • File logging and plotting
  • Optimization Functions
  • Built-in simple mutations
  • Built-in simple crossovers
  • Built-in simple selection methods
  • Built-in simple replacement methods
  • Genetic Algorithms process
  • Evolutionary strategies process (simple version (1 sigma))
  • Evolutionary strategies (array of sigmas)
  • A Grid-based Genetic Algorithm for Multimodal Real Function Optimization by Jose Chaquet and Enrique Carmona

Optimization functions

The optimization functions are adapted pieces of code, obtained from the web

In particular, the library has implemented the following functions:

  • Ackley
  • Forrester
  • Beale
  • Rothyp
  • Booth
  • Easom
  • Griweank
  • Matyas
  • Powell
  • Zakharov
  • Sphere
  • Schwefel
  • Rastrigin

An example of some of the functions plotted can be found here

EAL class

The EAL class is a wrapper of the evolutionary process. It accepts a great number of parameters that set up the evolutionary algorithm. It puts together all the implemented features and operators and supports different evolutionary paradigms like: Genetic Algorithms (ga), Evolution Strategies (es) or Grid-Based Genetic Algorithms (gga)

Initialization Parameters

  • n_dimensions: number of dimensions used to solve the problem. [10]
  • n_population: size of the population (its number of chromosomes). [100]
  • n_iterations: number of iterations to do. [1000]
  • n_children: number of childrens to generate. [100]
  • xover_prob: croosover probability. [0.8]
  • mutat_prob: mutation probability. [0.1]
  • minimization: True if we want to minimize the objetive function. [False]
  • seed: set the seed for reproducibility. [12345]
  • initialization: How to initialize the population. ['uniform']
    • 'permutation': Each chromosome is a permutation of n_dimensions.
    • 'uniform': Initialize each chromosome randomly sampling it from a uniform distribution.
  • problem: sets the objetive function. [Acley] )]*
  • selection: sets the selection function (check Selection section). ['wheel']
    • 'Tournament':
    • 'Wheel'
  • crossover: sets the crossover operator (check Crossovers section). ['blend']
    • 'one-point'
    • 'one-point-permutation'
    • 'two-point'
    • 'blend'
  • mutation: sets the mutation operator(check Mutation section). ['non-uniform']
    • 'pos-swap'
    • 'uniform'
    • 'non-uniform':
    • 'gaussian'
  • replacement: (check Replacement section). ['elitist']
    • 'Elitist':
    • 'Worst-parents':
  • tournament_competitors: number of competitors in the tournament selection. [3]
  • tournament_winners: number of winners in the tournament selection. [1]
  • replacement_elitism: rate of eletism for the eletist replacement. [0.5]

Initializations

[TODO]: rewrite and explain each method

  • uniform uses a uniform distribution to sample the elements.
  • permutation creates a permutation of N elements.

Selections

[TODO]: rewrite and explain each method

  • wheel: sample from the parents population with a probability of each member proportional to the value of their fitness
  • tournament:

Mutations

[TODO]: rewrite and explain each method

  • position swap:
  • uniform:
  • non-uniform:
  • gaussian: (Note: this is the mutation used for Evolutionary Strategies (es))

Crossovers

[TODO]: rewrite and explain each method

  • one-point:
  • one-point (permutation):
  • two-point:
  • blend:

Replacements

[TODO]: rewrite and explain each method

  • worst-fitness: removes the chromosomes inside the parensts population with the worst fitness.
  • elitist:

Code example

Use of Genetic Algorithms

from evolutionary import EAL, optim_functions as functions

# Example of a Genetic Algorithm to solve the ackley function
eal_ga = EAL(
    seed=82634,
    minimization=False,
    problem=functions.Ackley,
    n_dimensions=10,
    n_population=100,
    n_iterations=1000,
    n_children=100,
    xover_prob=0.8,
    mutat_prob=0.1,
    selection='wheel',
    crossover='blend',
    mutation='non_uniform',
    replacement='elitist'
)
eal_ga.fit(type="ga")

Graph returned after the 1000 iterations using a Genetic Algorithm with Wheel selection, Blend Crossover, Non-Uniform mutation and Elitist replacement. It tries to find the global minima in the Ackley Function with a croosover probability of 0.8 and mutation probability of 0.1. The number of chromosomes in the population is 100 and the number of generated children is also 100.

GA image

Use of Evolutionary Strategies

from evolutionary import EAL, optim_functions as functions

# Example of a Evolutionary Strategy to solve the ackley function
eal_es = EAL(
    seed=82634,
    minimization=False,
    problem=functions.Ackley,
    n_dimensions=10,
    n_population=50,
    n_iterations=1000,
    n_children=50,
    xover_prob=0.8,
    mutat_prob=0.2,
    selection='tournament',
    crossover=None,
    mutation='gaussian',
    replacement='elitist'
)

eal_es.fit(type="es")

Graph returned after the 1000 iterations using an Evolutionary Strategy with Tournament selection, it doesn't apply any croosover operator, Gaussian mutation with a global sigma value and Elitist replacement. It tries to find the global minima in the Ackley Function with a mutation probability of 0.1. The number of chromosomes in the population is 50 and the number of generated children is also 50.

ES image