Diversity-Preserving Exploitation of Crossover

TL;DR

This paper introduces a new genetic algorithm paradigm, DiPEC, that balances crossover exploitation with diversity preservation, leading to improved optimization efficiency and broader applicability.

Contribution

The paper proposes the DiPEC paradigm and the DEGA algorithm, which maintain diversity during crossover, achieving superior theoretical and empirical performance.

Findings

DEGA finds the optimum of LeadingOnes with O(n^{5/3} log^{2/3} n) evaluations.

Standard genetic algorithms require Θ(n^2) evaluations for LeadingOnes.

DEGA performs well on various benchmark problems beyond LeadingOnes.

Abstract

Crossover is a powerful mechanism for generating new solutions from a given population of solutions. Crossover comes with a discrepancy in itself: on the one hand, crossover usually works best if there is enough diversity in the population; on the other hand, exploiting the benefits of crossover reduces diversity. This antagonism often makes crossover reduce its own effectiveness. We introduce a new paradigm for utilizing crossover that reduces this antagonism, which we call diversity-preserving exploitation of crossover (DiPEC). The resulting Diversity Exploitation Genetic Algorithm (DEGA) is able to still exploit the benefits of crossover, but preserves a much higher diversity than conventional approaches. We demonstrate the benefits by proving that the (2+1)-DEGA finds the optimum of LeadingOnes with $O(n^{5/3}\log^{2/3} n)$ fitness evaluations. This is remarkable since standard genetic algorithms need $\Theta(n^2)$ evaluations, and among genetic algorithms only some artificial and specifically tailored algorithms were known to break this runtime barrier. We confirm the theoretical results by simulations. Finally, we show that the approach is not overfitted to Leadingones by testing it empirically on other benchmarks and showing that it is also competitive in other settings. We believe that our findings justify further systematic investigations of the DiPEC paradigm.