Wave models and dynamical analysis of evolutionary algorithms

Abstract

By drawing an analogy between the population of an evolutionary algorithm and a gas system (which we call a particle system), we first build wave models of evolutionary algorithms based on aerodynamics theory. Then, we solve the models linear and quasi-linear hyperbolic equations analytically, yielding wave solutions. These describe the propagation of the particle density wave, which is composed of leftward and rightward waves. We demonstrate the convergence of evolutionary algorithms by analyzing the mechanism underlying the leftward wave, and investigate population diversity by analyzing the rightward wave. To confirm these theoretical results, we conduct experiments that apply three typical evolutionary algorithms to common benchmark problems, showing that the experimental and theoretical results agree. These theoretical and experimental analyses also provide several new clues and ideas that may assist in the design and improvement of evolutionary algorithms.