A Non-Dominated Sorting Evolutionary Algorithm Updating When Required

TL;DR

This paper introduces NSGA-III-UR, a hybrid evolutionary algorithm that adaptively updates reference vectors only when necessary, improving performance on irregular Pareto fronts while maintaining simplicity on regular ones.

Contribution

The paper proposes NSGA-III-UR, which selectively updates reference vectors based on Pareto front regularity, combining the strengths of existing adaptive and non-adaptive methods.

Findings

NSGA-III-UR outperforms NSGA-III and A-NSGA-III on benchmark problems.

The adaptive update mechanism improves diversity and convergence.

Experimental results show robustness across diverse problem landscapes.

Abstract

The NSGA-III algorithm relies on uniformly distributed reference points to promote diversity in many-objective optimization problems. However, this strategy may underperform when facing irregular Pareto fronts, where certain vectors remain unassociated with any optimal solutions. While adaptive schemes such as A-NSGA-III address this issue by dynamically modifying reference points, they may introduce unnecessary complexity in regular scenarios. This paper proposes NSGA-III with Update when Required (NSGA-III-UR), a hybrid algorithm that selectively activates reference vector adaptation based on the estimated regularity of the Pareto front. Experimental results on benchmark suites (DTLZ1-7, IDTLZ1-2) and real-world problems demonstrate that NSGA-III-UR consistently outperforms NSGA-III and A-NSGA-III across diverse problem landscapes.