Approximate Expected Hypervolume Improvement for Parallel Expensive Multi-objective Optimization

Haihui Li, Zhenan He, Suling Duan

Keywords: Multi-objective optimization, Bayesian optimization, Expected Hypervolume Improvement, Batch selection.

Abstract: Many real-world optimization problems in science and engineering involve multiple conflicting objectives, with objective functions lacking explicit analytical form and computationally expensive to evaluate, which can be formulated as an expensive multi-objective optimization problem (EMOP). To address the challenge, multi-objective Bayesian optimization (MOBO) approaches approximating the Pareto front by using acquisition functions to select informative evaluation points, among which Expected Hypervolume Improvement (EHVI) is widely recognized for its ability to balance convergence and diversity. However, EHVI becomes computationally intractable for batch selection, requiring jointly evaluating improvements over multiple candidate solutions, and thus severely limits its scalability. To overcome this limitation, this paper introduces a decomposition-based approximate EHVI acquisition function that reformulates the original EHVI computation into a series of independent subproblems, each associated with a partial hypervolume improvement. This representation facilitates a novel batch selection strategy that jointly optimizes hypervolume improvement and sample diversity, promoting effective exploration of the Pareto front. In addition, a bi-level model management strategy is proposed to adaptively identify promising candidates and update surrogate models during the optimization process. Comprehensive experiments on synthetic and real-world benchmarks demonstrate that the proposed method achieves faster convergence and better diversity compared to several state-of-the-art MOBO algorithms.

Submission Number: 61