Smooth Tchebycheff Scalarization for Multi-Objective Optimization
This work addresses multi-objective optimization problems with conflicting objectives, common in real-world applications, by providing a more efficient and theoretically sound method, though it appears incremental as it builds on existing scalarization techniques.
The authors tackled the problem of high computational complexity and poor theoretical properties in existing multi-objective optimization methods by proposing a smooth Tchebycheff scalarization approach, which achieves significantly lower computational complexity while maintaining good theoretical properties for finding all Pareto solutions.
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.