decc: Cooperative Co-evolutionary Differential Evolution

Cooperative Co-evolutionary Differential Evolution algorithms in Python with NumPy.

This repository provides simple implementations for some CC-based DE algorithms. All the implementations are from scratch using NumPy, they might slightly differ from the original papers.

Quick Start

The decc library works with two entities:

• Problem represents a minimization problem (objective function, dimensionality and bounds).
  • The objective function must receives a matrix as input (each row represents a solution) and produce a matrix as output (each row is the objective value for the respective solution).
• Optimizer represents a DE algorithm for solving a minimization problem.
  • Maximization of a real function g is equivalent to minimize -g.

In order to use an optimizer, you must first define a problem. Currently, there are two optimizer available: (i) DECC (also known as CCDE), with the variants DECC-O and DECC-H; and (ii) DECC-G. A basic example is found below:

import numpy as np

from decc import Problem
from decc.optimizers.decc import DECCOptimizer
from decc.optimizers.decc_g import DECCGOptimizer

def objective(x: np.ndarray) -> np.ndarray:
    # The Sphere function is a common
    #   benchmark for optimizers
    return np.sum(x ** 2, axis=-1)


# First, we must define the problem
problem = Problem(objective,
                  dims=100,
                  lower_bound=-100.0,
                  upper_bound=100.0)

# Then, we can instantiate the optimizers
F = 0.5
CR = 0.8
seed = 42
max_fn = int(1e5)
pop_size = 50
decc_h = DECCOptimizer(problem,
                       seed,
                       pop_size,
                       grouping='halve',
                       F=F,
                       CR=CR,
                       max_fn=max_fn)
decc_o = DECCOptimizer(problem,
                       seed,
                       pop_size,
                       grouping='dims',
                       F=F,
                       CR=CR,
                       max_fn=max_fn)
decc_g = DECCGOptimizer(problem,
                        seed,
                        pop_size,
                        n_subproblems=max(1, problem.dims // 4),
                        sansde_evaluations=max_fn // 3,
                        de_evaluations=max_fn // 5,
                        F=F,
                        CR=CR,
                        max_fn=max_fn)

# Lastly, we can optimize the objective and
#   retrieve the results.
for optimizer in [decc_o, decc_h, decc_g]:
    result = optimizer.optimize()
    print(f'{optimizer}: {result["best_fitness"]}')

# DECC-O: 1.638248431845568e-05
# DECC-H: 0.0006988301174715161
# DECC-G: 1.5340782547163752e-10

Roadmap

• Add support for DECC-DG;
• Add support for DECC-gDG;
• Improve documentation;
• Add unit tests;
• Add validation benchmark functions from the original papers;