An intelligent hybrid grey wolf-particle swarm optimizer for optimization in complex engineering design problem

Engineering design optimization problems present significant challenges due to the complexity of objective functions, which often involve both continuous and discrete design variables, along with multiple constraints. GWO and PSO are well-known heuristic algorithms with efficient search ability and reasonable execution time. They are often used to solve complex optimization problems, but there are still problems such as premature convergence and limited global search efficiency. To overcome these limitations and enhance solution quality, this study proposes a novel Hybrid Grey Wolf-Particle Swarm Optimization (HGWPSO) algorithm. HGWPSO integrates the exploration ability of GWO with the rapid convergence and exploitation efficiency of PSO. The algorithm's performance is first validated using CEC₂022 benchmark functions and then applied to eight complex engineering design problems, including pressure vessel design, compression spring design, three-bar truss design, gear train design, cantilever beam design, welded beam design, transmission line parameter estimation, and reactive power planning problem. The improvement in the average best optimal value varies across different cases, demonstrating the effectiveness of the proposed method. In Case 1, the improvement is 71. 61%, while in Cases 2 and 4 obtained a 99% improvement. Case 3 shows an enhancement of 53. 46%, and Case 5 reaches 71. 92%, whereas Case 6 also obtained 99%. In Case 7, the improvement depends on the bundle configuration, with two-bundle conductors showing a 76. 91% increase, three-bundle conductors achieving 43. 94%, and four-bundle conductors reaching 46. 57%. Finally, in Case 8, the improvement is 1. 02%. The obtained results demonstrate that HGWPSO achieves better performance than other methods in terms of convergence rate, cost function minimization, and constraint handling. This study highlights the effectiveness of HGWPSO as a powerful tool for solving complex engineering design problems.