On the Impact of Crossover in Many-Objective Optimization: A Runtime Analysis of NSGA-III

2026-05-11

AI Summary

This study addresses the limited theoretical understanding of the role and advantages of crossover operators in multi-objective evolutionary algorithms, particularly within NSGA-III. Focusing on the classical m-objective OneJumpZeroJump benchmark function, the authors employ rigorous runtime complexity analysis to demonstrate for the first time on a standard testbed that incorporating crossover significantly accelerates the convergence of NSGA-III. Specifically, they prove that NSGA-III with crossover asymptotically outperforms its crossover-free counterpart across a broad range of parameter settings. Additionally, the paper establishes a lower bound on the runtime of the crossover-free NSGA-III in the four-objective case, thereby providing formal theoretical evidence supporting the efficacy of crossover in multi-objective optimization.

Abstract

In recent years, a theoretical understanding has rapidly advanced regarding how popular multi-objective evolutionary algorithms (MOEAs) can optimize many-objective problems. However, the benefits of using crossover in many-objective optimization are theoretically not understood, except for specifically designed benchmark functions tuned to particular crossover operators, and still lag significantly behind its practical use. In this paper, we build upon this line of research and present a theoretical runtime analysis of the widely used NSGA-III algorithm on the classical $m$-objective $m$-OneJumpZeroJump function ($m$-OJZJ for short). Our results demonstrate that NSGA-III with crossover optimizes $m$-OJZJ asymptotically faster than NSGA-III without crossover for any number $m$ of objectives for huge parameter regimes. We complement our analysis by providing a lower runtime bound on $4$-OJZJ when crossover is turned off.

Problem

• crossover
• many-objective optimization
• NSGA-III
• runtime analysis
• theoretical understanding

Innovation

• crossover
• many-objective optimization
• NSGA-III
• runtime analysis
• theoretical analysis