An Enhanced Projection-Iterative-Methods-Based Optimizer for Complex Constrained Engineering Design Problems

This paper proposes an Enhanced Projection-Iterative-Methods-based Optimizer (EPIMO) to overcome the limitations of its predecessor, the Projection-Iterative-Methods-based Optimizer (PIMO), including deterministic parameter decay, insufficient diversity maintenance, and static exploration–exploitation balance. The enhancements incorporate three core strategies: (1) an adaptive decay strategy that introduces stochastic perturbations into the step-size evolution; (2) a mirror opposition-based learning strategy to actively inject structured population diversity; and (3) an adaptive adjustment mechanism for the Lévy flight parameter β to enable phase-sensitive optimization behavior. The effectiveness of EPIMO is validated through a multi-stage experimental framework. Systematic evaluations on the CEC 2017 and CEC 2022 benchmark suites, alongside four classical engineering optimization problems (Himmelblau function, step-cone pulley design, hydrostatic thrust bearing design, and three-bar truss design), demonstrate its comprehensive superiority. The Wilcoxon rank-sum test confirms statistically significant performance improvements over its predecessor (PIMO) and a range of state-of-the-art and classical algorithms. EPIMO exhibits exceptional performance in convergence accuracy, stability, robustness, and constraint-handling capability, establishing it as a highly reliable and efficient metaheuristic optimizer. This research contributes a systematic, adaptive enhancement framework for projection-based metaheuristics, which can be generalized to improve other swarm intelligence systems when facing complex, constrained, and high-dimensional engineering optimization tasks.