A Novel Evolutionary Bayesian Optimization Algorithm Based on Decomposition for Expensive Constrained Multiobjective Optimization Problems
提出CMOEBO/D算法，将昂贵约束多目标优化问题分解为近似约束子问题，通过新填充准则CPoB和双层候选选择策略，平衡收敛性、可行性和多样性，适用于计算成本高的优化场景。
This article proposes a novel constrained multiobjective evolutionary Bayesian optimization algorithm based on decomposition (named CMOEBO/D) for expensive constrained multiobjective optimization problems (CMOPs). In CMOEBO/D, an expensive CMOP is decomposed into some approximate constrained subproblems by Gaussian process models, reference vectors, and the augmented Tchebycheff function. Then, we devise a new infill criterion (named CPoB) to evaluate the performance of solutions. Specifically, in CPoB, on each approximate constrained subproblem, any two solutions are compared based on the product of two probabilities. For each solution, the first probability (denoted as PoB) is its likelihood of outperforming the other in terms of the predicted augmented Tchebycheff function value, and the second probability (denoted as PoF) is its likelihood of satisfying all constraints. It is obvious that PoB and PoF measure the convergence and feasibility of a solution, respectively. Based on CPoB, the approximate constrained subproblems are solved via collaborative evolutionary optimization to obtain their near-optimal solutions. Furthermore, by combining the information of the database, we design a bilevel candidate selection strategy to select some of these near-optimal solutions for expensive fitness evaluations, which can make good diversity, convergence, and feasibility contributions simultaneously to the database. Extensive experiments verify the competitiveness of CMOEBO/D.