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

optimization, metaheuristic, genetic, algorithm, GA, gravitational, search, GSA, cross, entropy, cross-entropy, eda, estimation-distribution-algorithm, genetic-algorithm, gravitational-search, optimizer, python
pip install optimal==0.2.0


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 __init__.py.

Optimizers can now be imported with:

from optimal import GenAlg, GSA, CrossEntropy