Diversity-Preserving Exploitation of Crossover

2025-07-02

AI Summary

Crossover operators in genetic algorithms face a fundamental trade-off: their effectiveness depends critically on population diversity, yet their repeated application accelerates diversity loss, thereby undermining their own utility. Method: This paper proposes DiPEC—a novel paradigm explicitly designed to jointly preserve diversity and enable effective crossover exploitation—and instantiates it in the (2+1)-DEGA algorithm, which integrates differential evolution–inspired mutation with adaptive crossover control. Contribution/Results: We provide a rigorous theoretical analysis proving that (2+1)-DEGA achieves an expected optimization time of $O(n^{5/3}log^{2/3} n)$ on the LeadingOnes function, breaking the classical $Omega(n^2)$ lower bound for standard genetic algorithms. Empirical evaluation demonstrates that (2+1)-DEGA significantly outperforms canonical GAs and exhibits strong generalization across diverse benchmark problems—including unimodal, multimodal, and deceptive landscapes. This work establishes a new theoretically grounded and practically effective design paradigm for evolutionary algorithms.

Technology Category

• Search and Optimization: Evolutionary Computation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Web Mining and Content Analysis: Models for Web evolution

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 $Θ(n^2)$ 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.

Problem

• Balancing crossover benefits and diversity loss
• Improving genetic algorithm efficiency with DiPEC
• Achieving faster convergence in optimization problems

Innovation

• Diversity-preserving crossover exploitation (DiPEC)
• Diversity Exploitation Genetic Algorithm (DEGA)
• Optimal LeadingOnes with O(n^5/3) evaluations