An improved PSO approach for solving non-convex optimization problems

The aim of this paper is to propose an improved particle swarm optimization (PSO) procedure for non-convex optimization problems. This approach embeds classical methods (Kuhn-Tucker (KT) conditions and the Hessian matrix) into the fitness function. This generates a semi-classical hybrid PSO algorithm (HPSO). The classical component improves the PSO algorithm in terms of its capabilities to search for optimal solutions in non-convex scenarios. In this work, the development and the testing of the refined HPSO algorithm was carried out. The HPSO algorithm was tested against four engineering design problems which were; `optimization of the design of a pressure vessel' (P1), `optimization of the design of a tension/compression spring' (P2) and two `design optimization problems in engineering' (P3 and P4). The computational performance of the HPSO algorithm was then compared against the best optimal solutions from previous work on the same engineering problems. Comparative studies and analysis were then carried out based on the optimized results. It was observed that the HPSO provided a better minimum with a higher quality constraint satisfaction as compared to the PSO approach in the previous work.