A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 8 Issue 6
Jun.  2021

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 7.847, Top 10% (SCI Q1)
    CiteScore: 13.0, Top 5% (Q1)
    Google Scholar h5-index: 64, TOP 7
Turn off MathJax
Article Contents
Qinqin Fan and Okan K. Ersoy, "Zoning Search With Adaptive Resource Allocating Method for Balanced and Imbalanced Multimodal Multi-Objective Optimization," IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1163-1176, June 2021. doi: 10.1109/JAS.2021.1004027
Citation: Qinqin Fan and Okan K. Ersoy, "Zoning Search With Adaptive Resource Allocating Method for Balanced and Imbalanced Multimodal Multi-Objective Optimization," IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1163-1176, June 2021. doi: 10.1109/JAS.2021.1004027

Zoning Search With Adaptive Resource Allocating Method for Balanced and Imbalanced Multimodal Multi-Objective Optimization

doi: 10.1109/JAS.2021.1004027
Funds:  This work was partially supported by the Shandong Joint Fund of the National Nature Science Foundation of China (U2006228), and the National Nature Science Foundation of China (61603244)
More Information
  • Maintaining population diversity is an important task in the multimodal multi-objective optimization. Although the zoning search (ZS) can improve the diversity in the decision space, assigning the same computational costs to each search subspace may be wasteful when computational resources are limited, especially on imbalanced problems. To alleviate the above-mentioned issue, a zoning search with adaptive resource allocating (ZS-ARA) method is proposed in the current study. In the proposed ZS-ARA, the entire search space is divided into many subspaces to preserve the diversity in the decision space and to reduce the problem complexity. Moreover, the computational resources can be automatically allocated among all the subspaces. The ZS-ARA is compared with seven algorithms on two different types of multimodal multi-objective problems (MMOPs), namely, balanced and imbalanced MMOPs. The results indicate that, similarly to the ZS, the ZS-ARA achieves high performance with the balanced MMOPs. Also, it can greatly assist a “regular” algorithm in improving its performance on the imbalanced MMOPs, and is capable of allocating the limited computational resources dynamically.

     

  • loading
  • [1]
    K. Deb, “Multi-objective genetic algorithms: Problem difficulties and construction of test problems,” Evolutionary Computation, vol. 7, no. 3, pp. 205–230, 1999. doi: 10.1162/evco.1999.7.3.205
    [2]
    P. Kerschke, H. Wang, and M. Preuss et al., “Search dynamics on multimodal multiobjective problems,” Evolutionary Computation, vol. 27, no. 4, pp. 577–609, 2019.
    [3]
    W. Gong, Y. Wang, Z. Cai et al., “Finding multiple roots of nonlinear equation systems via a repulsion-based adaptive differential evolution,” IEEE Trans. Systems, Man, and Cybernetics: Systems, vol. 50, no. 4, pp. 1499–1513, 2020.
    [4]
    W. Gao, G. Li, Q. Zhang, et al., “Solving nonlinear equation systems by a two-phase evolutionary algorithm,” IEEE Trans. Systems, Man, and Cybernetics: Systems, 2019. DOI: 10.1109/TSMC.2019.2957324.
    [5]
    Q. Kang, X. Song, M. Zhou, and L. Li, “A collaborative resource allocation strategy for decomposition-based multiobjective evolutionary algorithms,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 49, pp. 2416–2423, 2018.
    [6]
    Z. Lv, L. Wang, Z. Han, J. Zhao, and W. Wang, “Surrogate-assisted particle swarm optimization algorithm with Pareto active learning for expensive multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 6, pp. 838–849, 2019. doi: 10.1109/JAS.2019.1911450
    [7]
    L. Huang, M. Zhou, and K. Hao, “Non-dominated immune-endocrine short feedback algorithm for multi-robot maritime patrolling,” IEEE Trans. Intelligent Transportation Systems, vol. 21, pp. 362–373, 2019.
    [8]
    X. Guo, M. Zhou, S. Liu, and L. Qi, “Lexicographic multiobjective scatter search for the optimization of sequence-dependent selective disassembly subject to multiresource constraints,” IEEE Trans. Cybernetics, vol. 50, no. 7, pp. 3307–3317, 2020. doi: 10.1109/TCYB.2019.2901834
    [9]
    Y. Fu, M. Zhou, X. Guo, and L. Qi, “Scheduling dual-objective stochastic hybrid flow shop with deteriorating jobs via bi-population evolutionary algorithm,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 50, no. 12, pp. 5037–5048, 2020. doi: 10.1109/TSMC.2019.2907575
    [10]
    B. Qu, J. Liang, and Z. Wang et al., “Novel benchmark functions for continuous multimodal optimization with comparative results,” Swarm and Evolutionary Computation, vol. 26, pp. 23–34, 2016.
    [11]
    Q. Fan and X. Yan, “Solving multimodal multiobjective problems through zoning search,” IEEE Trans. Systems, Man, and Cybernetics: Systems, 2019. DOI: 10.1109/TSMC.2019.2944338.
    [12]
    Y. Tian, C. He, R. Cheng, et al., “A multistage evolutionary algorithm for better diversity preservation in multiobjective optimization,” IEEE Trans. Systems, Man, and Cybernetics: Systems, 2019. DOI: 10.1109/TSMC.2019.2956288.
    [13]
    Y. Liu, H. Ishibuchi, and G. Yen et al., “Handling imbalance between convergence and diversity in the decision space in evolutionary multi-modal multi-objective optimization,” IEEE Trans. Evolutionary Computation, vol. 24, no. 3, pp. 551–565, 2020.
    [14]
    C. Yue, B. Qu, and J. Liang, “A multiobjective particle swarm optimizer using ring topology for solving multimodal multiobjective problems,” IEEE Trans. Evolutionary Computation, vol. 22, no. 5, pp. 805–817, 2018. doi: 10.1109/TEVC.2017.2754271
    [15]
    K. Miettinen, Nonlinear Multiobjective Optimization: Springer, 1999.
    [16]
    K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms: John Wiley & Sons, 2001.
    [17]
    B. Wang, H. Li, Q. Zhang, et al., “Decomposition-based multiobjective optimization for constrained evolutionary optimization,” IEEE Trans. Systems, Man, and Cybernetics: Systems, 2018. DOI: 10.1109/TSMC.2018.2876335.
    [18]
    Y. Liu, G. Yen, and D. Gong, “A multi-modal multi-objective evolutionary algorithm using two-archive and recombination strategies,” IEEE Trans. Evolutionary Computation, vol. 23, pp. 660–674, 2018.
    [19]
    K. Deb and S. Tiwari, “Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization,” European Journal of Operational Research, vol. 185, no. 3, pp. 1062–1087, 2008. doi: 10.1016/j.ejor.2006.06.042
    [20]
    G. Rudolph, B. Naujoks, and M. Preuss, “Capabilities of EMOA to detect and preserve equivalent Pareto subsets.” in Proc. Int. Conf. Evolutionary Multi-Criterion Optimization. Springer, Berlin, Heidelberg, pp. 36–50, 2007.
    [21]
    M. Preuss, B. Naujoks, and G. Rudolph, “Pareto set and EMOA behavior for simple multimodal multiobjective functions,” Parallel Problem Solving from Nature-PPSN IX, pp. 513–522: Springer, 2006.
    [22]
    C. Yue, B. Qu, and K. Yu et al., “A novel scalable test problem suite for multimodal multiobjective optimization,” Swarm and Evolutionary Computation, vol. 48, pp. 62–71, 2019.
    [23]
    H. Ishibuchi, Y. Peng, and K. Shang, “A scalable multimodal multiobjective test problem.” in Proc. IEEE Int. Conf. Evolutionary Computation, pp. 310–317, 2019.
    [24]
    O. Shir, M. Preuss, B. Naujoks, et al., “Enhancing decision space diversity in evolutionary multiobjective algorithms.” in Proc. IEEE Int. Conf. Evolutionary Multi-criterion Optimization, pp. 95–109, 2009.
    [25]
    J. Liang, Q. Guo, C. Yue, et al., “A self-organizing multi-objective particle swarm optimization algorithm for multimodal multi-objective problems.” in Proc. Int. Conf. Swarm Intelligence, Springer, Cham, pp. 550–560, 2018.
    [26]
    R. Tanabe and H. Ishibuchi, “A decomposition-based evolutionary algorithm for multi-modal multi-objective optimization.” in Proc. Int. Conf. Parallel Problem Solving from Nature, Springer, Cham, pp. 249–261, 2018.
    [27]
    Y. Liu, H. Ishibuchi, Y. Nojima, et al., “A double-niched evolutionary algorithm and its behavior on polygon-based problems.” in Proc. Int. Conf. Parallel Problem Solving from Nature, Springer, Cham, pp. 262–273, 2018.
    [28]
    M. Pal and S. Bandyopadhyay, “Differential evolution for multi-modal multi-objective problems.” in Proc. Genetic and Evolutionary Computation Conf. Companion, pp. 1399–1406. 2019.
    [29]
    S. Maree, T. Alderliesten, and P. Bosman, “Real-valued evolutionary multi-modal multi-objective optimization by hill-valley clustering.” in Proc. Genetic and Evolutionary Computation Conf., pp. 568–576, 2019.
    [30]
    R. Tanabe and H. Ishibuchi, “A review of evolutionary multi-modal multi-objective optimization,” IEEE Trans. Evolutionary Computation, vol. 24, pp. 193–200, 2020. doi: 10.1109/TEVC.2019.2909744
    [31]
    D. Liang, B. Qu, D. Gong, and C. Yue, “Problem definitions and evaluation criteria for the CEC 2019 special session on multimodal multiobjective optimization,” Computational Intelligence Laboratory, Zhengzhou University, 2019. DOI: 10.13140/RG.2.2.33423.64164.
    [32]
    K. Deb and S. Tiwari, “Omni-optimizer: A procedure for single and multi-objective optimization.” in Proc. Int. Conf. Evolutionary Multi-Criterion Optimization. pp. 47–61, 2005.
    [33]
    J. Liang, C. Yue, and B. Qu, “Multimodal multi-objective optimization: A preliminary study.” in Proc. IEEE Int. Conf. Evolutionary Computation, pp. 2454–2461, 2016.
    [34]
    K. Deb, A. Pratap, and S. Agarwal et al., “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evolutionary Computation, vol. 6, no. 2, pp. 182–197, 2002.
    [35]
    F. Wilcoxon, “Individual comparisons by ranking methods,” Biometrics Bulletin, vol. 1, no. 6, pp. 80–83, 1945. doi: 10.2307/3001968
    [36]
    M. Friedman, “The use of ranks to avoid the assumption of normality implicit in the analysis of variance,” Journal of the American Statistical Association, vol. 32, no. 200, pp. 675–701, 1937. doi: 10.1080/01621459.1937.10503522
    [37]
    Q. Fan, X. Yan, Y. Zhang, et al., “A variable search space strategy based on sequential trust region determination technique,” IEEE Trans. Cybernetics, 2019. DOI: 10.1109/TCYB.2019.2914060.
    [38]
    Q. Fan, N. Li, and Y. Zhang et al., “Zoning search using a hyper-heuristic algorithm,” Science China Information Sciences, vol. 62, no. 9, pp. 199102, 2019.

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(9)  / Tables(4)

    Article Metrics

    Article views (1795) PDF downloads(27) Cited by()

    Highlights

    • The ZS-SRA can allocate different computational resources among all subspaces
    • The ZS-SRA can assist “regular” MMOEA in finding more equivalent solutions on imbalanced MMOPs
    • The ZS-SRA outperforms “special” and “regular” MMOEAs on imbalanced and balanced MMOPs

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return