Enhanced Puzzle Optimization Algorithmfor Complex Engineering Design Problems

This paper introduced the Enhanced Puzzle Optimization Algorithm (EPOA), a hybrid metaheuristic that augmented the original Puzzle Optimization Algorithm (POA) with uniform crossover, random-resetting mutation, and explicit elitism. The contribution does not lie in inventing these operators individually, since they are classical search components, but in integrating them into POA’s two-phase search dynamics to address premature convergence, diversity loss, and best-solution preservation in a targeted manner. This paper formalized EPOA’s update rules, provided pseudocode and flow diagrams, and enforced bound handling for box-constrained problems. Comprehensive tests on the CEC2022 single-objective benchmark suite (F1–F12) showed that EPOA attained rank 1 on 11 of 12 functions and rank 3 on the remaining case, with large error reductions relative to baseline POA (e.g., on F1, the mean error dropped from 62.836 to 0.004; on F6, the mean error dropped from 2370.962 to 7.239). The method was further evaluated on six classical constrained engineering design problems (welded beam, tension/compression spring, speed reducer, pressure vessel, three-bar truss, and cantilever beam). Statistical indicators such as the mean and standard deviation were used to assess robustness. The results showed that EPOA delivered a strong exploration–exploitation balance and robust solution quality across rugged landscapes and real-world constraints.