Constrained optimization of engineering design problems: Analyses with Gauss map-based chaotic particle swarm optimization

Abstract

Constrained optimization rises as a challenging issue concerning the evaluation of restrictions, objective and constraints of a model. For this purpose, various optimization algorithms are specifically generated or improved to achieve the best design. Performance of algorithms is strictly concerned with the search capability of the phenomena used. Herein, a state-of-the-art approach can provide worse results on constrained optimization while its performance is remarkable on a different type of optimization problem. Many engineering design problems are categorized as constrained and nonlinear. Decision variables, constraint functions and objective function always change from one problem to another. This condition reveals the necessity of robust optimization algorithms. With this inspiration, after seeing its remarkable performance on different areas (global optimization, continuous function optimization, hybrid classifier design, etc.), this paper examines a state-of-the-art technique named Gauss map-based chaotic particle swarm optimization (GM-CPSO) on constrained optimization of engineering design problems. GM-CPSO is firstly adapted to operate for constrained optimization. Then, penalty function method is utilized to form the fitness output of optimization algorithm. Six challenging design problems are handled that are gear train design, I-shaped beam design, tension / compression spring design, three-bar truss design, tubular column design, and car side impact design. In experiments, GM-CPSO is compared with the state-of-the-art studies handling the design problems. As a result, GM-CPSO achieves the best results recorded in the literature or enhances the optimum result on the specified design problem.