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A reference vector adaptive strategy for balancing diversity and convergence in many-objective evolutionary algorithms

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Abstract

Decomposition-based multiobjective evolutionary algorithms (MOEA/D) have achieved great success in the field of evolutionary multiobjective optimization, and their outstanding performance in solving for the Pareto-optimal solution set has attracted attention. This type of algorithm uses reference vectors to decompose the multiobjective problem into multiple single-objective problems and searches them collaboratively, hence the choice of reference vectors is particularly important. However, predefined reference vectors may not be suitable for dealing with many-objective optimization problems with complex Pareto fronts (PFs), which can affect the performance of MOEA/D. To solve this problem, we introduce a reference vector initialization strategy, namely, scaling of the reference vectors (SRV), and also propose a new reference vector adaptation strategy, that is, transformation of the solution positions (TSP) based on the ideal point solution, to deal with irregular PFs. The TSP strategy can adaptively redistribute the reference vectors through periodic adjustment to endow that the solution set with better convergence and a better distribution. Both strategies are introduced into a representative MOEA/D, called 𝜃-DEA-TSP, which is compared with five state-of-the-art algorithms to verify the effectiveness of the proposed TSP strategy.

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Acknowledgements

This work was supported in part by Natural Science Foundation of Zhejiang Province (LQ20F020014), in part by the National Natural Science Foundation of China (61472366, 61379077), in part by the Natural Science Foundation of Zhejiang Province (LY17F020022), in part by Key Projects of Science and Technology Development Plan of Zhejiang Province (2018C01080).

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Authors and Affiliations

  1. College of Computer Science and Technology, College of software, Zhejiang University of Technology, Hangzhou, 310023, China

    Lin Zhang, Liping Wang & Xiaotian Pan

  2. Zhejiang Lab, Hangzhou, 310023, China

    Qicang Qiu

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  1. Lin Zhang
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  2. Liping Wang
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  3. Xiaotian Pan
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  4. Qicang Qiu
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Correspondence to Liping Wang or Qicang Qiu.

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Zhang, L., Wang, L., Pan, X. et al. A reference vector adaptive strategy for balancing diversity and convergence in many-objective evolutionary algorithms. Appl Intell 53, 7423–7438 (2023). https://doi.org/10.1007/s10489-022-03545-w

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