Smooth Tchebycheff Scalarization for Multi-Objective Optimization

TL;DR

This paper introduces a smooth Tchebycheff scalarization method for multi-objective optimization that is computationally efficient, theoretically sound, and capable of finding all Pareto solutions in differentiable problems.

Contribution

It proposes a novel smooth scalarization approach that reduces computational complexity and guarantees comprehensive Pareto solution coverage in gradient-based multi-objective optimization.

Findings

Effective in real-world applications

Lower computational complexity than existing methods

Capable of finding all Pareto solutions

Abstract

Multi-objective optimization problems can be found in many real-world applications, where the objectives often conflict each other and cannot be optimized by a single solution. In the past few decades, numerous methods have been proposed to find Pareto solutions that represent optimal trade-offs among the objectives for a given problem. However, these existing methods could have high computational complexity or may not have good theoretical properties for solving a general differentiable multi-objective optimization problem. In this work, by leveraging the smooth optimization technique, we propose a lightweight and efficient smooth Tchebycheff scalarization approach for gradient-based multi-objective optimization. It has good theoretical properties for finding all Pareto solutions with valid trade-off preferences, while enjoying significantly lower computational complexity compared to other methods. Experimental results on various real-world application problems fully demonstrate the effectiveness of our proposed method.