Component-Sharing Preference in Expensive Multiobjective Optimization

Most of the current expensive multiobjective optimization (MOO) algorithms focus on identifying Pareto optimal solutions. However, in some applications such as multiobjective modular design, decision-makers often prefer a set of optimal solutions that share common components in the decision space, which may conflict with Pareto optimality. Existing expensive MOO algorithms are not specifically designed to address this preference. To bridge this gap, we propose modeling the component-sharing preference in MOO as a special bi-level multiobjective optimization problem. Specifically, the upper-level is a single-objective optimization problem that seeks the optimal shared variables, while the lower-level is a multiobjective optimization problem aimed at identifying trade-off solutions for given shared variable values. Moreover, the lower-level objective is expensive-to-evaluate and can only be evaluated for a limited number of times. To efficiently solve this problem, we introduce a data-efficient algorithm called Bayesian Bi-level Search (BBS). The effectiveness of BBS is validated through six new benchmark problems and a real-world application involving the planform shape design of Blended-Wing-Body underwater glider. The results show that our method effectively identifies solutions with shared components within limited computational budgets.