Global/Local Hybridization of the Multi-Objective Particle Swarm Optimization with Derivative-Free Multi-Objective Local Search

Simulation Based Design Optimization (SBDO) supports the designer in the design of complex engineering systems. The process consists in the application of several numerical simulations with the aim of explore and asses the design opportunities among all the feasible design solutions. The optimization algorithm manages the research of the best compromise between all the design objectives (such as the resistance and seakeeping of a ship or the drag and weight of an airplane). The objective functions may be noisy and/or often their derivatives are not directly provided by the simulation tools. Therefore, derivative-free optimization algorithms are used as a viable option for the SBDO process. Local or global optimization algorithms are preferred, whether the research region is or is not known a priori. The first class of algorithms explores accurately a limited domain region. The second class of algorithms explores efficiently the entire design space, providing approximate solutions. In order to combine the accuracy of local algorithms with the exploration capability of global methods in multi-objective problems, the multi-objective deterministic particle swarm optimization (MODPSO) is combined with a derivative-free multi-objective (DFMO) local optimization algorithm. Two implementations of MODPSO and their hybridizations with DFMO are presented. The resulting global/local hybrid implementations are tested using 16 analytical test problems. Their performances are assessed considering six metrics, providing the assessment of the proximity of the solutions to a reference Pareto front and the continuity of the approximated Pareto front.