A Step Forward in Studying the Compact Genetic Algorithm

TL;DR

This paper provides a theoretical analysis of the compact Genetic Algorithm (cGA), modeling its convergence behavior with a Markov process and ODEs, demonstrating that it converges to local optima.

Contribution

It introduces a novel theoretical framework for analyzing the convergence of the cGA using Markov processes and differential equations.

Findings

The cGA converges to local optima of the target function.

The ODE model accurately approximates the cGA's behavior.

Convergence to local optima is theoretically proven.

Abstract

The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent population instead of using traditional recombination and mutation operators. The cGA only needs a small amount of memory; therefore, it may be quite useful in memory-constrained applications. This paper introduces a theoretical framework for studying the cGA from the convergence point of view in which, we model the cGA by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then, we prove that the corresponding ODE converges to local optima and stays there. Consequently, we conclude that the cGA will converge to the local optima of the function to be optimized.