RDEx-CASK: Cauchy Mutation, Archive, and Stagnation Kick for RDEx-CSOP

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.

This paper proposes RCMAES, a novel variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for CEC benchmark optimization. RCMAES integrates a dimension-dependent nonlinear population-size reduction strategy with an adaptive restart mechanism within a pure CMA-ES framework. RCMAES is evaluated on three benchmark suites (CEC2017, CEC2020, and CEC2022) and compared with state-of-the-art DE algorithms as well as its closely related counterpart, BIPOP-aCMAES. Experimental results show that RCMAES achieves competitive and robust performance across all benchmarks.

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.