Expected Hypervolume Improvement with Constraints

Majid Abdolshah, Alistair Shilton, Santu Rana, Sunil Gupta, Svetha Venkatesh

Abstract: Bayesian optimisation has become a powerful framework for global optimisation of black-box functions that are expensive to evaluate and possibly noisy. In addition to expensive evaluation of objective functions, many real-world optimisation problems deal with similarly expensive black-box constraints. However, there are few studies regarding the role of constraints in multi-objective Bayesian optimisation. In this paper, we extend the Expected Hypervolume Improvement by introducing expectation of constraints satisfaction and merging them into a new acquisition function called Expected Hypervolume Improvement with Constraints (EHVIC). We analyse the performance of our algorithm by estimating the feasible region dominated by Pareto front using 4 benchmark functions. The proposed method is also evaluated on a realworld problem of Alloy Design. We demonstrate that EHVIC is an effective algorithm that provides a promising performance by comparing to a well-known related method.