Budgeted Multi-Objective Optimization with a Focus on the Central Part of the Pareto Front -- Extended Version
This work addresses a domain-specific problem for practitioners in fields like engineering or design who need efficient optimization with limited experiments, though it is incremental as it builds on existing Bayesian methods.
The paper tackles the challenge of multi-objective optimization under severe budget constraints by focusing on the central part of the Pareto front, proposing a Bayesian method (C-EHI) that improves solution optimality and coverage in this zone, with numerical experiments showing it outperforms state-of-the-art algorithms.
Optimizing nonlinear systems involving expensive computer experiments with regard to conflicting objectives is a common challenge. When the number of experiments is severely restricted and/or when the number of objectives increases, uncovering the whole set of Pareto optimal solutions is out of reach, even for surrogate-based approaches: the proposed solutions are sub-optimal or do not cover the front well. As non-compromising optimal solutions have usually little point in applications, this work restricts the search to solutions that are close to the Pareto front center. The article starts by characterizing this center, which is defined for any type of front. Next, a Bayesian multi-objective optimization method for directing the search towards it is proposed. Targeting a subset of the Pareto front allows an improved optimality of the solutions and a better coverage of this zone, which is our main concern. A criterion for detecting convergence to the center is described. If the criterion is triggered, a widened central part of the Pareto front is targeted such that sufficiently accurate convergence to it is forecasted within the remaining budget. Numerical experiments show how the resulting algorithm, C-EHI, better locates the central part of the Pareto front when compared to state-of-the-art Bayesian algorithms.