DE-2LS: Differential Evolution with Lightweight Late Local Search for Constrained Numerical Optimization

2026-06-26

AI Summary

This work addresses constrained single-objective numerical optimization under a fixed function evaluation budget, where balancing feasibility, convergence, and computational efficiency is critical. Building upon the RDEx framework, the authors propose a controlled, lightweight coordinate-pattern local search mechanism applied only in the late stages of evolution. This strategy performs a budget-limited, fine-grained search around the current best solution and incorporates a feasibility-aware solution comparison rule. By deferring local refinement until later phases, the method avoids premature or excessive exploitation, thereby preserving global exploration capacity while significantly enhancing local search efficacy without compromising efficiency. Empirical evaluations demonstrate that the proposed algorithm achieves the highest U-score (80,968) and the best overall ranking (48) among competing methods, representing a 5.58% improvement in U-score over the baseline RDEx.

Abstract

Constrained single-objective numerical optimization requires a careful balance among feasibility, objective convergence, and computational efficiency under a fixed function-evaluation budget. This paper proposes DE-2LS, a late-stage, locally search-enhanced variant of differential evolution built on the RDEx framework. The proposed method preserves the original RDEx components, including mutation and crossover operators, success-history adaptation, archive mechanism, population-size reduction, and $ε$-based constraint handling. A lightweight coordinate-pattern local search is added as a guarded polishing component around the current best solution. It is activated only in the late stage of the run, uses a small evaluation budget, and accepts candidates through a feasibility-aware comparison rule. Ablation results show that the finalized DE-2LS configuration achieves the best U-score among all tested variants, confirming that controlled late-stage refinement is more effective than aggressive or premature local search. In the direct comparison with RDEx, DE-2LS achieves a 5.58\% gain in U-score. In the four-algorithm comparison, DE-2LS obtains the highest overall U-score of 80968 and the best total rank of 48 among RDEx, CL-SRDE, and UDE-III. These results indicate that DE-2LS improves the exploitation capability of the RDEx-based search framework while preserving its speed advantage under the combined speed-accuracy scoring criterion. The source code of DE-2LS is available at https://github.com/ChauhanDikshit?tab=repositories.

Problem

• constrained numerical optimization
• differential evolution
• local search
• computational efficiency
• feasibility

Innovation

• Differential Evolution
• Late-stage Local Search
• Constrained Optimization
• Lightweight Local Search
• Feasibility-aware Comparison