Smooth Tchebycheff Scalarization for Multi-Objective Optimization
<|reference_start|>Smooth Tchebycheff Scalarization for Multi-Objective Optimization: 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.<|reference_end|>
@article{lin2024smooth,
    title={Smooth Tchebycheff Scalarization for Multi-Objective Optimization},
    author={Xi Lin, Xiaoyuan Zhang, Zhiyuan Yang, Fei Liu, Zhenkun Wang, Qingfu
  Zhang},
    journal={arXiv preprint arXiv:2402.19078},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.19078},
    primaryClass={cs.LG cs.AI cs.NE math.OC}
}