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A regularity model-based multi-objective estimation of distribution memetic algorithm with auto-controllable population diversity

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Abstract

The regularity model-based multi-objective estimation of distribution algorithm (RM-MEDA) employs the local principal component analysis to split the population into several clusters, and each cluster is used to construct an affine subspace by combing the cluster center, principal components and additional Gaussian noise. However, such affine subspace greatly limits the sampling range of trail solutions, which will lead to the rapid loss of population diversity. To address this issue, an improved RM-MEDA with auto-controllable population diversity (RM-MEDA-AcPD) is suggested in this paper. In RM-MEDA-AcPD, the simplex crossover method is employed to extend the representation range of the affine subspace, the main purpose of which is to push solutions forward along the orthogonal direction of the affine subspace. In addition, a random noise model related to the evolution process is designed to replace the original Gaussian noise model, which reduces the risk of rapid loss of population diversity. In experimental studies, we have compared eight regularity property-based multi-objective evolutionary algorithms with the RM-MEDA-AcPD on benchmark problems with disconnected Pareto fronts. The experimental results demonstrate that the performance of RM-MEDA-AcPD significantly outperforms the other nine comparison algorithms in solving these test instances.

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Notes

  1. If \(f_{i}\le 0\), \(f_{i}+M\) is employed to replace it by adding a constant M such that \(f_{i}+M>0\).

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Acknowledgements

The authors wish to thank the partial support of the National Natural Science Foundation of China (61803301, 62176146, 62272384), the Key Project of Shaanxi Key Research and Development Program (2020ZDLGR07-06), the Natural Science Foundation of Shaanxi (2022JQ-674, 2021JM-343), the Three year action plan project of Xi’an University (2021XDJH20), and the Doctoral Foundation of Xi’an University of Technology (112-256081812). They also thank Prof. Ran Cheng, Prof. Yong Wang, Prof. Aimin Zhou, Prof. Hui Li, Prof. Hanlin Liu and Prof. Yanan Sun for selflessly sharing their codes, which has greatly promoted our research work.

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Authors and Affiliations

  1. The School of Computer Science and Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Qiaoyong Jiang, Jianan Cui, Lei Wang & Xinhong Hei

  2. Shaanxi Key Laboratory of Network Computing and Security Technology, Xi’an, 710048, China

    Qiaoyong Jiang

  3. The School of Information Engineering, Xi’an University, Xi’an, 710065, China

    Yanyan Lin

  4. The School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Yali Wu

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  1. Qiaoyong Jiang
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Jiang, Q., Cui, J., Wang, L. et al. A regularity model-based multi-objective estimation of distribution memetic algorithm with auto-controllable population diversity. Memetic Comp. 15, 45–70 (2023). https://doi.org/10.1007/s12293-023-00387-y

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