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实际应用中，不同目标间往往相互冲突，无法通过单个最优解实现统一优化。过去数十年间，研究者提出了众多方法以获取能体现目标间最优权衡的帕累托解集，但现有方法在求解一般可微多目标优化问题时，存在计算复杂度较高或缺乏良好理论性质的问题。本文通过引入平滑优化技术，提出了一种新颖且轻量级的平滑切比雪夫标量化方法，用于梯度驱动的多目标优化。该方法在寻求具有有效权衡偏好的全体帕累托解时兼具优良理论性质，同时计算复杂度显著低于其他方法。在多个实际应用问题上的实验结果表明，所提方法具有显著有效性。