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 different 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 novel and lightweight 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.

翻译：多目标优化问题广泛存在于现实应用中，此类问题的各目标间往往相互冲突，无法通过单一解进行优化。近几十年来，研究者提出了大量方法以获取能够表征各目标间最优折衷关系的Pareto解。然而，现有方法在求解一般的可微多目标优化问题时，可能面临计算复杂度较高或缺乏良好理论性质的问题。本研究通过引入光滑优化技术，提出了一种新颖且轻量化的平滑切比雪夫标量化方法用于梯度驱动的多目标优化。该方法在保持有效偏好折衷特性以寻找所有Pareto解的同时，计算复杂度显著低于其他方法。在多个真实应用问题上的实验结果充分验证了所提方法的有效性。