Multi-Objective Optimization (MOO) is an important problem in real-world applications. However, for a non-trivial problem, no single solution exists that can optimize all the objectives simultaneously. In a typical MOO problem, the goal is to find a set of optimum solutions (Pareto set) that trades off the preferences among objectives. Scalarization in MOO is a well-established method for finding a finite set approximation of the whole Pareto set (PS). However, in real-world experimental design scenarios, it's beneficial to obtain the whole PS for flexible exploration of the design space. Recently Pareto set learning (PSL) has been introduced to approximate the whole PS. PSL involves creating a manifold representing the Pareto front of a multi-objective optimization problem. A naive approach includes finding discrete points on the Pareto front through randomly generated preference vectors and connecting them by regression. However, this approach is computationally expensive and leads to a poor PS approximation. We propose to optimize the preference points to be distributed evenly on the Pareto front. Our formulation leads to a bilevel optimization problem that can be solved by e.g. differentiable cross-entropy methods. We demonstrated the efficacy of our method for complex and difficult black-box MOO problems using both synthetic and real-world benchmark data.

本研究解决了多目标优化中同时优化所有目标的困难，提出一种优化偏好点的方法，实现帕累托前沿的均匀分布。通过双层优化问题的形式，我们的研究显示了该方法在复杂黑箱多目标优化问题中的有效性，推动了设计空间的灵活探索。

面向偏好优化的帕累托集学习用于黑箱优化