Smooth Tchebycheff Scalarization For Multiobjective Optimization

# Smooth Tchebycheff Scalarization for Multi-Objective Optimization

**arXiv ID:** 2402.19078
**Authors:** Xi Lin, Xiaoyuan Zhang, Zhiyuan Yang, Fei Liu, Zhenkun Wang, Qingfu Zhang
**Published:** 2024-02-29T12:03:05Z
**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.

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## References

- [arXiv:2402.19078](http://arxiv.org/abs/2402.19078v3)