Few for Many: Tchebycheff Set Scalarization for Many-Objective Optimization
Xi Lin Yilu Liu Xiaoyuan Zhang Fei Liu Zhenkun Wang Qingfu Zhang
Multi-objective optimization can be found in many real-world applications where some conflicting objectives can not be optimized by a single solution. Existing optimization methods often focus on finding a set of Pareto solutions with different optimal trade-offs among the objectives. However, the required number of solutions to well approximate the whole Pareto optimal set could be exponentially large with respect to the number of objectives, which makes these methods unsuitable for handling many optimization objectives. In this work, instead of finding a dense set of Pareto solutions, we propose a novel Tchebycheff set scalarization method to find a few representative solutions (e.g., 5) to cover a large number of objectives (e.g., $>100$) in a collaborative and complementary manner. In this way, each objective can be well addressed by at least one solution in the small solution set. In addition, we further develop a smooth Tchebycheff set scalarization approach for efficient optimization with good theoretical guarantees. Experimental studies on different problems with many optimization objectives demonstrate the effectiveness of our proposed method.
multi-objective optimization, many-objective optimization, Tchebycheff scalarization
We propose a novel Tchebycheff set scalarization approach to find a small set of solutions to tackle a large number of optimization objectives.