fmga 0.2.1

Genetic algorithms for 2-dimensional function maximization.

fmga

fmga (function maximization through genetic algorithms) is a package that takes a genetic algorithm approach to maximization problem of non-convex objective functions in two dimensions.

The idea is to sample an evolving population of points converging to the function maximum over many iterations.

Installation

Install with pip:

pip install fmga

Import within the python script with:

import fmga

Execution

Given a function on two variables x and y, say:

def f(x, y):
    return x - math.sin(y) + 28

Pass this function as the objective_function argument to the population2D constructor (lambdas work too!):

population = fmga.population2D(objective_function=f, population_size=60)

The population can be set to breed and iterate by using the .converge() method.

population.converge(iterations=20)

To perform only one iteration of breeding and mutating, do:

population.iterate()

Access population mean fitness and mean L1 diversity stats through the .mean_fitness and .mean_diversity attributes:

print(population.mean_fitness, population.mean_diversity)

The .best_estimate() method returns the point closest to the function point of maxima in the population, as a Point2D object.

best_point = population.best_estimate()

Every Point2D object has attributes 'x' and 'y', signifying the coordinates of the maxima point.

print(best_point.x, " ", best_point.y)

To find the value of the function at this point, use:

print(best_point.fitness)

The objective function doesn't have to be differentiable, or even continuous in the specified domain!
The population of 2-dimensional points undergoes random mutations - and is selected through elitism along with breeding with selection weights inversely proportional to fitness and diversity ranks.

population2D Class Methods

The population2D constructor takes the following arguments:

population_size (default = 60) Number of points in the population.
objective_function The function to maximize!
elite_fraction (default = 0.1) Fraction of the population's points to be kept as elite during breeding. Must be between 0 and 1, inclusive.
x_min, x_max, y_min, y_max (default = 0, 100, 0, and 100 respectively) The domain where the points are spread.
mutation_probability (default = 0.05) How likely is is for a single point to mutate - this probability is the same for all points in the population. Must be between 0 and 1, inclusive.
mutation_range (default = 5) The range of the mutation when it does occur. Note that the point will never mutate out of the domain defined!
verbose (default = 2) How much output to be displayed when iterating population after population. Must take values 0, 1 or 2 with 2 representing the most output, and 0 representing none.