A dual decomposition strategy for large-scale multiobjective evolutionary optimization

Cuicui Yang, Peike Wang, Junzhong Ji

Abstract: Multiobjective evolutionary algorithms (MOEAs) have received much attention in multiobjective optimization in recent years due to their practicality. With limited computational resources, most existing MOEAs cannot efficiently solve large-scale multiobjective optimization problems (LSMOPs) that widely exist in the real world. This paper innovatively proposes a dual decomposition strategy (DDS) that can be embedded into many existing MOEAs to improve their performance in solving LSMOPs. Firstly, the outer decomposition uses a sliding window to divide large-scale decision variables into overlapped subsets of small-scale ones. A small-scale multiobjective optimization problem (MOP) is generated every time the sliding window slides. Then, once a small-scale MOP is generated, the inner decomposition immediately creates a set of global direction vectors to transform it into a set of single-objective optimization problems (SOPs). At last, all SOPs are optimized by adopting a block coordinate descent strategy, ensuring the solution’s integrity and improving the algorithm’s performance to some extent. Comparative experiments on benchmark test problems with seven state-of-the-art evolutionary algorithms and a deep learning-based algorithm framework have shown the remarkable efficiency and solution quality of the proposed DDS. Meanwhile, experiments on two real-world problems show that DDS can achieve the best performance beyond at least one order of magnitude with up to 3072 decision variables.