Surrogate-assisted constraint-handling technique for parametric multi-objective optimization

This work describes a new surrogate-assisted constraint-handling technique (CHT) for parametric multi-objective evolutionary algorithms, called Bayesian CHT. Parametric optimization finds optimal solutions as a function of one or more exogenous variables. The solution is a family of Pareto frontiers called the parameterized Pareto frontier (PPF). CHTs from non-parametric multi-objective evolutionary algorithms do not produce a good sampling of solutions on the PPF. The proposed CHT addresses this using Bayesian methods. A Gaussian process classifier serves as an uncertainty-quantified surrogate for problem constraints, enabling active learning and a novel repair mechanism that promotes sampling along the PPF. The new technique is evaluated on a suite of 36 test problems and two engineering cases of structural design. Quantitative results show that the proposed Bayesian CHT outperforms several state-of-the-art algorithms in most cases. From a qualitative perspective, the nondominated solutions are visualized to support the superiority of the new approach, which achieves a better spread of solutions on the PPF. The results of engineering studies also indicate that the new approach is computationally more efficient than the others.