Cooperative Metaheuristics with Dynamic Dimension Reduction for High-Dimensional Optimization Problems

Owing to their global search capabilities and gradient-free operation, metaheuristic algorithms are widely applied to a wide range of optimization problems. However, their computational demands become prohibitive when tackling high-dimensional optimization challenges. To effectively address these challenges, this study introduces cooperative metaheuristics integrating dynamic dimension reduction (DR). Building upon particle swarm optimization (PSO) and differential evolution (DE), the proposed cooperative methods C-PSO and C-DE are developed. In the proposed methods, the modified principal components analysis (PCA) is utilized to reduce the dimension of design variables, thereby decreasing computational costs. The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations, resulting in the important dimensions being dynamically identified. Compared with the static one, the dynamic DR strategy can achieve precise identification of important dimensions, thereby enabling accelerated convergence toward optimal solutions. Furthermore, the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated. Metaheuristic algorithms (PSO, DE) and cooperative metaheuristics (C-PSO, C-DE) are examined by 15 benchmark functions and two engineering design problems (speed reducer and composite pressure vessel). Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency. Compared to standard metaheuristic algorithms, cooperative metaheuristics achieve a reduction in computational cost of at least 40%. The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.