Dikshit Chauhan

Dikshant, Dikshit Chauhan, Chen Hao et al.

We extend RDEx-CSOP with 3 changes that target stagnation & late-stage variance, plus minor parameter tuning. The second scale factor in the standard branch is sampled independently from a truncated Cauchy. A small feasible-only JADE-style archive (|A|_max = 50) is added & sampled with probability |A|/(|A|+|P|). Per-individual stagnation counter triggers, after 180 no-improvement generations, three local overrides on standard branch: pull toward the global best, lift the archive sampling floor to 0.65, & saturate CR to 0.95 when population success rate is below 0.10. The exploitation biased branch & every other RDEx component are left untouched. On CEC CSOP suite (D=30, 25 runs), RDEx-CASK is competitive with RDEx, UDE-III, & CL-SRDE in feasibility-aware quality & improves time-to-target on most problems.

Dikshit Chauhan

Multimodal optimization aims to locate multiple globally optimal or near-optimal solutions in a single run. This paper presents \emph{S-CARD-CMSA}, a score-aware candidate-archive and density-filtered reporting framework built on the covariance matrix self-adaptation evolution strategy with repelling subpopulations (RS-CMSA-ESII). The method is developed for the IEEE CEC 2026 Competition on Benchmarking Niching Methods for Multimodal Optimization. Rather than modifying the core search dynamics of RS-CMSA-ESII, S-CARD-CMSA preserves its sampling, covariance adaptation, taboo-region update, restart, and termination mechanisms. Two conservative extensions are introduced. First, a passive secondary candidate archive records the restart-level best candidates without influencing the search trajectory. Second, a score-aware density-filtered reporting rule constructs the final solution set by balancing robust peak ratio and precision-driven F1-score. Development experiments show that the density-filtered rule preserves the peak coverage obtained by a medium score-aware rule while reducing redundant reports. On a broader validation subset, it maintains the same mean RPR while improving mean precision, F1-score, and the official-score-oriented average. The method does not use true global-minimum locations during optimization; such information is used only for offline development analysis and post-run scoring. The source code of S-CARD-CMSA is available at https://github.com/ChauhanDikshit.

Dikshit Chauhan, Anupam Trivedi

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.

Dikshit Chauhan

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.

Dikshit Chauhan, Shivani, P. N. Suganthan

Nature has long inspired the development of swarm intelligence (SI), a key branch of artificial intelligence that models collective behaviors observed in biological systems for solving complex optimization problems. Particle swarm optimization (PSO) is widely adopted among SI algorithms due to its simplicity and efficiency. Despite numerous learning strategies proposed to enhance PSO's performance in terms of convergence speed, robustness, and adaptability, no comprehensive and systematic analysis of these strategies exists. We review and classify various learning strategies to address this gap, assessing their impact on optimization performance. Additionally, a comparative experimental evaluation is conducted to examine how these strategies influence PSO's search dynamics. Finally, we discuss open challenges and future directions, emphasizing the need for self-adaptive, intelligent PSO variants capable of addressing increasingly complex real-world problems.

Dikshit Chauhan, Bapi Dutta, Indu Bala et al.

Integrating Large Language Models (LLMs) and Evolutionary Computation (EC) represents a promising avenue for advancing artificial intelligence by combining powerful natural language understanding with optimization and search capabilities. This manuscript explores the synergistic potential of LLMs and EC, reviewing their intersections, complementary strengths, and emerging applications. We identify key opportunities where EC can enhance LLM training, fine-tuning, prompt engineering, and architecture search, while LLMs can, in turn, aid in automating the design, analysis, and interpretation of ECs. The manuscript explores the synergistic integration of EC and LLMs, highlighting their bidirectional contributions to advancing artificial intelligence. It first examines how EC techniques enhance LLMs by optimizing key components such as prompt engineering, hyperparameter tuning, and architecture search, demonstrating how evolutionary methods automate and refine these processes. Secondly, the survey investigates how LLMs improve EC by automating metaheuristic design, tuning evolutionary algorithms, and generating adaptive heuristics, thereby increasing efficiency and scalability. Emerging co-evolutionary frameworks are discussed, showcasing applications across diverse fields while acknowledging challenges like computational costs, interpretability, and algorithmic convergence. The survey concludes by identifying open research questions and advocating for hybrid approaches that combine the strengths of EC and LLMs.

Dikshit Chauhan, Shivani, Donghwi Jung et al.

Multi-modal optimization involves identifying multiple global and local optima of a function, offering valuable insights into diverse optimal solutions within the search space. Evolutionary algorithms (EAs) excel at finding multiple solutions in a single run, providing a distinct advantage over classical optimization techniques that often require multiple restarts without guarantee of obtaining diverse solutions. Among these EAs, differential evolution (DE) stands out as a powerful and versatile optimizer for continuous parameter spaces. DE has shown significant success in multi-modal optimization by utilizing its population-based search to promote the formation of multiple stable subpopulations, each targeting different optima. Recent advancements in DE for multi-modal optimization have focused on niching methods, parameter adaptation, hybridization with other algorithms including machine learning, and applications across various domains. Given these developments, it is an opportune moment to present a critical review of the latest literature and identify key future research directions. This paper offers a comprehensive overview of recent DE advancements in multimodal optimization, including methods for handling multiple optima, hybridization with EAs, and machine learning, and highlights a range of real-world applications. Additionally, the paper outlines a set of compelling open problems and future research issues from multiple perspectives