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A python metaheuristic optimization library. Currently supports Genetic Algorithms, Gravitational Search, and Cross Entropy.

Project Description

Optimal (beta)

A python metaheuristic optimization library. Built for easy extension and usage.

Warning: Optimal is in beta. API may change. I will do my best to note any breaking changes in this readme, but no guarantee is given.

Supported metaheuristics:

  • Genetic algorithms (GA)
  • Gravitational search algorithm (GSA)
  • Cross entropy (CE)


pip install optimal


import math

from optimal import GenAlg
from optimal import Problem
from optimal import helpers

# The genetic algorithm uses binary solutions.
# A decode function is useful for converting the binary solution to real numbers
def decode_ackley(binary):
    # Helpful functions from helpers are used to convert binary to float
    # x1 and x2 range from -5.0 to 5.0
    x1 = helpers.binary_to_float(binary[0:16], -5.0, 5.0)
    x2 = helpers.binary_to_float(binary[16:32], -5.0, 5.0)
    return x1, x2

# ackley is our fitness function
# This is how a user defines the goal of their problem
def ackley_fitness(solution):
    x1, x2 = solution

    # Ackley's function
    # A common mathematical optimization problem
    output = -20 * math.exp(-0.2 * math.sqrt(0.5 * (x1**2 + x2**2))) - math.exp(
        0.5 * (math.cos(2 * math.pi * x1) + math.cos(2 * math.pi * x2))) + 20 + math.e

    # You can prematurely stop the metaheuristic by returning True
    # as the second return value
    # Here, we consider the problem solved if the output is <= 0.01
    finished = output <= 0.01

    # Because this function is trying to minimize the output,
    # a smaller output has a greater fitness
    fitness = 1 / output

    # First return argument must be a real number
    # The higher the number, the better the solution
    # Second return argument is a boolean, and optional
    return fitness, finished

# Define a problem instance to optimize
# We can optionally include a decode function
# The optimizer will pass the decoded solution into your fitness function
# Additional fitness function and decode function parameters can also be added
ackley = Problem(ackley_fitness, decode_function=decode_ackley)

# Create a genetic algorithm with a chromosome size of 32,
# and use it to solve our problem
my_genalg = GenAlg(32)
best_solution = my_genalg.optimize(ackley)

print best_solution

Important notes:

  • Fitness function must take solution as its first argument
  • Fitness function must return a real number as its first return value

For further usage details, see comprehensive doc strings.

Major Changes


Moved a number of options from Optimizer to Optimizer.optimize


Renamed common.random_solution_binary to common.random_binary_solution, and common.random_solution_real to common.random_real_solution


problem now an argument of Optimizer.optimize, instead of Optimizer.__init__.


max_iterations now an argument of Optimizer.optimize, instead of Optimizer.__init__.


Optimizer now takes a problem instance, instead of a fitness function and kwargs.


Library reorganized with greater reliance on

Optimizers can now be imported with:

from optimal import GenAlg, GSA, CrossEntropy


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