2018/09/27 by David Gaudrie, Gaudrie, David, Rodolphe Le Riche +8
Computer Science · Decision Sciences · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimal Experimental Design Methods #Optimization and Control (math.OC) #cs.LG #math.OC #stat.ML
paper · pdf · doi:10.48550/arxiv.1809.10482
Submission pre-print, extended version
openalex publication_date 2018/09/27 · arxiv created 2019/07/15 · arxiv updated 2019/07/16 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
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.