Abstract
We investigate the convergence performance of the combination of 5 multi-objective evolutionary algorithms (MOEAs) as and 4 constraint-handling techniques (CHTs), namely 20 constraint-MOEAs (CMOEAs), against the recently published benchmarking problem for constrained multi-objective optimization problem named “simultaneous design optimization benchmark problem of multiple car structures using response surface method”. To evaluate the effectiveness of MOEA and CHT against the problem separately, all the examined MOEAs are modified so as to be adapted to general CHTs. Experiments with population size of 100, 300, and 500 are conducted and the results are that CHTEETAH with CHT of multiple constraint ranking (MCR) wins all the three experiments with respect to hypervolume indicator (HV) across the generation. With respect to finding feasible solutions in the early stage of evolution, MOEA/D with proper CHT shows significantly better performance on it. As for CHT, MCR shows the best performance, while the second best CHTs also show good performance in terms of HV. However, Characteristics required for actual use of CMOEAs in industrial design such as anytime performance or number of found feasible solutions are of poor in the second best CHTs whereas MCR shows good in both characteristics. The investigation of the evolution of the solutions showed that the effective CHTs should balance the exploration of the objective space and constraint space. Considerations on the 4 different CHTs also suggest some important features that effective CHTs should have.
