PSDRIME: A Self-Adaptive Multi-Strategy RIME for Engineering Optimization

Emulating freezing fog deposition, the RIME algorithm integrates soft-rime search with hard-rime puncture mechanisms to enhance optimization but still suffers from local optima entrapment and limited global search. To surmount these hurdles, we design three novel mechanisms and integrate them into RIME algorithm to propose a new variant named PSDRIME. Specifically, we first propose a Proportional-Integral-Derivative Guided Adaptive Exploration mechanism, which utilizes the rate of change in the global optimum as feedback to regulate population updates, balancing exploration and exploitation. Moreover, to mitigate stagnation in local regions, we design a Stagnation-Triggered Perturbation mechanism that applies directed perturbations to stagnant individuals, facilitating escape from local optima. Additionally, we develop a Lightweight Duplicate-detection Perturbation mechanism that introduces minor perturbations to individuals that are highly similar to the current global optimum, thereby preserving population diversity to forestall premature convergence. The proposed algorithm is evaluated on the IEEE CEC2017 benchmark suite and compared with eight original algorithms, three RIME variants, five improved variants, and seven CEC competition champion algorithms. Results demonstrate that PSDRIME achieves superior convergence accuracy and stability compared with competing methods, alleviating premature convergence and enhancing global exploration and local optima avoidance capability. In addition, PSDRIME is applied to four constrained engineering design problems, where it consistently achieves the best objective values, including a minimum weight of 0.0127 for the tension–compression spring problem and a minimum cost of 1.7000 for the welded beam problem. These results confirm the robustness and generalization capability of PSDRIME in benchmark and real-world constrained optimization scenarios.