A dual decomposition strategy for large-scale multiobjective evolutionary optimization

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.