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.

翻译：多目标优化问题广泛存在于现实应用中，其目标函数往往相互冲突，无法通过单一解实现全局优化。过去几十年间，研究者提出了大量方法以寻找能够反映目标间最优权衡的帕累托解。然而，现有方法在求解一般可微多目标优化问题时，或存在较高计算复杂度，或缺乏完善的理论性质。本研究通过引入光滑优化技术，提出了一种轻量高效的光滑切比雪夫标量化方法，适用于基于梯度的多目标优化。该方法在理论上能够以有效权衡偏好找到所有帕累托解，同时相比其他方法显著降低了计算复杂度。在多个实际应用问题上的实验结果充分证明了所提方法的有效性。