sParEGO – A Hybrid Optimization Algorithm for Expensive Uncertain Multi-objective Optimization Problems

Abstract

Evaluations of candidate solutions to real-world problems are often expensive to compute, are characterised by uncertainties arising from multiple sources, and involve simultaneous consideration of multiple conflicting objectives. Here, the task of an optimizer is to find a set of solutions that offer alternative robust trade-offs between objectives, where robustness comprises some user-defined measure of the ability of a solution to retain high performance in the presence of uncertainties. Typically, understanding the robustness of a solution requires multiple evaluations of performance under different uncertain conditions – but such an approach is infeasible for expensive problems with a limited evaluation budget. To overcome this issue, a new hybrid optimization algorithm for expensive uncertain multi-objective optimization problems is proposed. The algorithm – sParEGO – uses a novel uncertainty quantification approach to assess the robustness of a candidate design without having to rely on expensive sampling techniques. Hypotheses on the relative performance of the algorithm compared to an existing method for deterministic problems are tested using two benchmark problems, and provide preliminary indication that sParEGO is an effective technique for identifying robust trade-off surfaces.