New S-CARD-CMSA framework boosts multimodal optimization with density-filtered reporting

Multimodal optimization aims to find multiple optimal solutions in a single run—a challenge for many real-world engineering and design problems. Dikshit Chauhan's S-CARD-CMSA, submitted to the IEEE CEC 2026 Competition on Benchmarking Niching Methods, offers a novel framework that enhances existing evolutionary strategies without altering their core search dynamics. Built on the covariance matrix self-adaptation evolution strategy with repelling subpopulations (RS-CMSA-ESII), the framework preserves its sampling, covariance adaptation, taboo-region updates, and restart mechanisms.

Two conservative extensions drive the improvement. First, a passive secondary candidate archive records the best candidates at restart 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 maintains the same mean RPR as a medium score-aware rule while reducing redundant reports, boosting mean precision, F1-score, and the official-score-oriented average. The method's source code is available online, and all evaluations were conducted without using true global-minimum locations during optimization, ensuring fairness.