Knee Detection in Bayesian Multiobjective Optimization Using Thompson Sampling

Real-world problems often consist of multiple conflicting objectives to be optimized simultaneously, featuring a set of Pareto-optimal solutions. Estimating the entire Pareto front can be computationally expensive, and is not always necessary, as decision makers (DMs) will likely be interested only in specific regions of the Pareto front. In the absence of knowledge about the DM preferences, the so-called knees in the Pareto front are considered to be particularly attractive. In this article, we propose using Thompson sampling in the Bayesian optimization framework to estimate the location of the knee regions in a data-efficient manner. Our experimental results show that the proposed methods accurately locate the knee regions after a very small number of evaluations, providing a computationally efficient approach to single- and multiknee detection in multiobjective optimization.