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A dual decomposition strategy for large-scale multiobjective evolutionary optimization

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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.

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Acknowledgements

This work is partly supported by the NSFC Research Program (61906010, 62276010) and R&D Program of Beijing Municipal Education Commission (KZ202210005009, KM202010005032).

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  1. Beijing Municipal Key Laboratory of Multimedia and Intelligent Software Technology, College of Computer Science, Faculty of Information Technology, Beijing University of Technology, Beijing, China

    Cuicui Yang, Peike Wang & Junzhong Ji

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  1. Cuicui Yang
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Yang, C., Wang, P. & Ji, J. A dual decomposition strategy for large-scale multiobjective evolutionary optimization. Neural Comput & Applic 35, 3767–3788 (2023). https://doi.org/10.1007/s00521-022-08133-0

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