🤖 AI Summary
This work addresses the persistent challenge in unconstrained single-objective numerical optimization of simultaneously achieving effective global exploration, efficient late-stage exploitation, and high evaluation efficiency. Building upon the RDEx framework, the authors propose a smooth, exploitation-biased branch rate update mechanism complemented by a budget-aware coordinate-pattern local search strategy. Through phased ablation studies and comprehensive U-score evaluation, they identify a conservative yet highly effective configuration for late-stage local search. The resulting algorithm substantially enhances both convergence speed and solution quality, improving the U-score from 33,602.0 to 37,448.0 (+11.45%). Furthermore, it outperforms state-of-the-art algorithms by a significant margin, achieving a U-score of 178,966.5—34.43% higher—thereby demonstrating its superior performance.
📝 Abstract
Unconstrained single-objective numerical optimization requires a careful balance among global exploration, late-stage exploitation, and function-evaluation efficiency. This paper presents DE-2LS, a late-stage, local-search-enhanced differential evolution framework built on RDEx for unconstrained single-objective optimization with variable bounds. The proposed method preserves the original RDEx evolutionary search engine and introduces two conservative refinements: a smoothed exploitation-biased branch-rate update in the late search stage and a guarded coordinate-pattern local-search that serves as a budget-aware refinement mechanism. Since the considered setting is unconstrained apart from variable bounds, all selection and local-search acceptance decisions are based solely on objective values. To determine the final algorithm configuration, we conduct a staged ablation study by testing multiple settings of the EB-rate smoothing mechanism, the initial EB-rate, the standard-branch Gaussian sampling scale, the selection-pressure parameters, and the local-search coefficients. The final configuration is selected using a U-score-based evaluation that jointly reflects solution quality and convergence speed. Experimental results show that DE-2LS consistently improves the original RDEx in direct head-to-head comparison. In particular, DE-2LS increases the U-score from $33602.0$ to $37448.0$, corresponding to an improvement of $11.45\%$. Moreover, compared with several competitive and IEEE CEC-winning algorithms, DE-2LS achieves the best overall U-score of $178966.5$, outperforming the others by $34.43\%$. These results show that a carefully designed late-stage local-search strategy can improve both convergence speed and the final objective quality of the algorithm. The source code of DE-2LS is available at https://github.com/ChauhanDikshit?tab=repositories.