Constrained Bi-objective Surrogate-Assisted Optimization of Problems with Heterogeneous Evaluation Times: Expensive Objectives and Inexpensive Constraints

In the past years, a significant amount of research has been done in optimizing computationally expensive and time-consuming objective functions using various surrogate modeling approaches. Constraints have often been neglected or assumed to be a by-product of the expensive objective computation and thereby being available after executing the expensive evaluation routines. However, many optimization problems in practice have separately evaluable computationally inexpensive geometrical or physical constraint functions, while the objectives may still be time-consuming. This scenario probably makes the simplest case of handling heterogeneous and multi-scale surrogate modeling in the presence of constraints. In this paper, we propose a method which makes use of the inexpensiveness of constraints to ensure all time-consuming objective evaluations are only executed for feasible solutions. Results on test and real-world problems indicate that the proposed approach finds a widely distributed set of near-Pareto-optimal solutions with a small budget of expensive evaluations.