Finding Knees in Bayesian Multi-objective Optimization

Arash Heidari, Jixiang Qing, Sebastian Rojas-Gonzalez, Jürgen Branke, Tom Dhaene, Ivo Couckuyt

Abstract: Multi-objective optimization requires many evaluations to identify a sufficiently dense approximation of the Pareto front. Especially for a higher number of objectives, extracting the Pareto front might not be easy nor cheap. On the other hand, the Decision-Maker is not always interested in the entire Pareto front, and might prefer a solution where there is a desirable trade-off between different objectives. An example of an attractive solution is the knee point of the Pareto front, although the current literature differs on the definition of a knee. In this work, we propose to detect knee solutions in a data-efficient manner (i.e., with a limited number of time-consuming evaluations), according to two definitions of knees. In particular, we propose several novel acquisition functions in the Bayesian Optimization framework for detecting these knees, which allows for scaling to many objectives. The suggested acquisition functions are evaluated on various benchmarks with promising results.