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A bi-layer decomposition algorithm for many-objective optimization problems

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Abstract

Decomposition-based evolutionary algorithms have shown great potential in solving many-objective optimization problems (MaOPs). However, manual parameters (e.g., neighbor size and scalarizing function) and the specified weight vector can easily degrade the performance of the algorithm, especially for MaOPs with irregular Pareto fronts. This paper presents a new decomposition-based evolutionary algorithm that adopts a bi-layer decision strategy to balance convergence and diversity of solutions for MaOPs, and it is free from neighborhood update and scalarizing methods. In the first layer decision, the well-converged solutions in each subregion form a primary population, where an adaptive fitness assignment considering the Pareto front shape is used to accelerate convergence. In the second layer decision, solutions in the primary population are ranked based on the diversity metric. The low-ranking solutions are added to the final population size until the population size is met. Further, to approximate the true PF as soon as possible, the intensity of convergence in the first layer decision and the activation frequency of the re-balance strategy are regulated. Moreover, we design a re-balance selection strategy to alleviate the dilemma of the specified weight vectors. The re-balance selection uses a clustering approach to adjust weight vectors to promote the uniform distribution of solutions. Finally, algorithms are verified on 150 test instances and one practical design problem. The experimental results show that the proposed algorithm performs better than five state-of-the-art peer algorithms on at least 64% test instances concerning hypervolume and has superiority over competitors on at least 72% test instances concerning the inverted generational distance plus.

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Notes

  1. Subproblems are determined by weight vectors, and each of them only optimizes the corresponding direction. The subregion is divided by weight vectors, and it decomposes the objective space.

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Acknowledgment

The authors would like to thank the anonymous reviewers and the Associate Editor for their constructive comments and suggestions, which greatly improve this paper. This work was supported by the NSFC (61773410).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou, 510006, China

    Chunliang Zhao & Yuren Zhou

  2. Collaborative Innovation Center of High Performance Computing, Guangzhou, China

    Chunliang Zhao

  3. School of Traffic Transportation, Beijing Jiaotong University, Beijing, 100089, China

    Yuanyuan Hao

  4. South China Agricultural University, Guangzhou, 510642, China

    Guangyu Zhang

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  1. Chunliang Zhao
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Correspondence to Yuren Zhou.

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Zhao, C., Zhou, Y., Hao, Y. et al. A bi-layer decomposition algorithm for many-objective optimization problems. Appl Intell 52, 15122–15142 (2022). https://doi.org/10.1007/s10489-021-03135-2

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