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Dynamic Multi-modal Multi-objective Optimization: A Preliminary Study

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Parallel Problem Solving from Nature – PPSN XVII (PPSN 2022)

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Abstract

Many real-world multi-modal multi-objective optimization problems are subject to continuously changing environments, which requires the optimizer to track multiple equivalent Pareto sets in the decision space. To the best of our knowledge, this type of optimization problems has not been studied in the literature. To fill the research gap in this area, we provide a preliminary study on dynamic multi-modal multi-objective optimization. We give a formal definition of dynamic multi-modal multi-objective optimization problems and point out some key challenges in solving them. To facilitate algorithm development, we suggest a systematic approach to construct benchmark problems. Furthermore, we provide a feature-rich test suite containing 10 novel dynamic multi-modal multi-objective test problems.

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Notes

  1. 1.

    The supplementary file can be found at https://github.com/Yiming-Peng-Official/dMMOP.

References

  1. Azzouz, R., Bechikh, S., Said, L.B.: A dynamic multi-objective evolutionary algorithm using a change severity-based adaptive population management strategy. Soft Comput. 21(4), 885–906 (2015). https://doi.org/10.1007/s00500-015-1820-4

    Article  Google Scholar 

  2. Cao, L., Xu, L., Goodman, E.D., Bao, C., Zhu, S.: Evolutionary dynamic multiobjective optimization assisted by a support vector regression predictor. IEEE Trans. Evol. Comput. 24(2), 305–309 (2020)

    Article  Google Scholar 

  3. Coello Coello, C.A., Reyes Sierra, M.: A study of the parallelization of a coevolutionary multi-objective evolutionary algorithm. In: Monroy, R., Arroyo-Figueroa, G., Sucar, L.E., Sossa, H. (eds.) MICAI 2004. LNCS (LNAI), vol. 2972, pp. 688–697. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24694-7_71

    Chapter  Google Scholar 

  4. Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms. Wiley, New York (2001)

    Google Scholar 

  5. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  6. Deb, K., Rao N., U.B., Karthik, S.: Dynamic multi-objective optimization and decision-making using modified NSGA-II: a case study on hydro-thermal power scheduling. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 803–817. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70928-2_60

  7. Deb, K., Tiwari, S.: Omni-optimizer: a generic evolutionary algorithm for single and multi-objective optimization. Eur. J. Oper. Res. 185(3), 1062–1087 (2008)

    Article  MathSciNet  Google Scholar 

  8. Farina, M., Deb, K., Amato, P.: Dynamic multiobjective optimization problems: test cases, approximations, and applications. IEEE Trans. Evol. Comput. 5(8), 425–442 (2004)

    Article  Google Scholar 

  9. Goh, C., Tan, K.C.: A competitive-cooperative coevolutionary paradigm for dynamic multiobjective optimization. IEEE Trans. Evol. Comput. 13(1), 103–127 (2008)

    Google Scholar 

  10. Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the Second International Conference on Genetic Algorithms and Their Application, pp. 41–49 (1987)

    Google Scholar 

  11. Greeff, M., Engelbrecht, A.P.: Solving dynamic multi-objective problems with vector evaluated particle swarm optimisation. In: IEEE Congress on Evolutionary Computation, pp. 2917–2924 (2008)

    Google Scholar 

  12. Ishibuchi, H., Matsumoto, T., Masuyama, N., Nojima, Y.: Many-objective problems are not always difficult for Pareto dominance-based evolutionary algorithms. In: Proceedings of the 24th European Conference on Artificial Intelligence (2020)

    Google Scholar 

  13. Jaszkiewicz, A.: On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - a comparative experiment. IEEE Trans. Evol. Comput. 6(4), 402–412 (2002)

    Article  Google Scholar 

  14. Jiang, S., Yang, S.: A steady-state and generational evolutionary algorithm for dynamic multiobjective optimization. IEEE Trans. Evol. Comput. 21(1), 65–82 (2016)

    Article  Google Scholar 

  15. Li, Q., Zou, J., Yang, S., Zheng, J., Ruan, G.: A predictive strategy based on special points for evolutionary dynamic multi-objective optimization. Soft Comput. 23(11), 3723–3739 (2018). https://doi.org/10.1007/s00500-018-3033-0

    Article  Google Scholar 

  16. Lin, Q., Lin, W., Zhu, Z., Gong, M., Li, J., Coello, C.A.C.: Multimodal multi-objective evolutionary optimization with dual clustering in decision and objective spaces. IEEE Trans. Evol. Comput. 25(1), 130–144 (2021)

    Article  Google Scholar 

  17. Liu, Y., Ishibuchi, H., Nojima, Y., Masuyama, N., Shang, K.: A double-niched evolutionary algorithm and its behavior on polygon-based problems. In: Proceedings of the Parallel Problem Solving from Nature - PPSN XV, pp. 262–273 (2018)

    Google Scholar 

  18. Liu, Y., Yen, G.G., Gong, D.: A multimodal multiobjective evolutionary algorithm using two-archive and recombination strategies. IEEE Trans. Evol. Comput. 23(4), 660–674 (2019)

    Article  Google Scholar 

  19. Nguyen, T.T.: Continuous Dynamic Optimization Using Evolutionary Algorithms. Ph.D. thesis, The University of Birmingham (2010)

    Google Scholar 

  20. Peng, Y., Ishibuchi, H.: A decomposition-based multi-modal multi-objective optimization algorithm. In: Proceedings of the 2020 IEEE Congress on Evolutionary Computation, pp. 1–8 (2020)

    Google Scholar 

  21. Peng, Y., Ishibuchi, H., Shang, K.: Multi-modal multi-objective optimization: problem analysis and case studies. In: Proceedings of the IEEE Symposium Series on Computational Intelligence, pp. 1865–1872 (2019)

    Google Scholar 

  22. Petrowski, A.: A clearing procedure as a niching method for genetic algorithms. In: Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 798–803 (1996)

    Google Scholar 

  23. Raquel, C., Yao, X.: Dynamic multi-objective optimization: a survey of the state-of-the-art. In: Evolutionary Computation for Dynamic Optimization Problems, pp. 85–106. Springer, Heidelberg(2013). https://doi.org/10.1007/978-3-642-38416-5_4

  24. Schütze, O., Vasile, M., Coello, C.A.C.: Computing the set of epsilon-efficient solutions in multiobjective space mission design. J. Aerosp. Comput. Inf. Commun. 8(3), 53–70 (2011)

    Article  Google Scholar 

  25. Shir, O.M.: Niching in evolutionary algorithms. In: Handbook of Natural Computing, pp. 1035–1069. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-540-92910-9_32

  26. Tian, Y., Liu, R., Zhang, X., Ma, H., Tan, K.C., Jin, Y.: A multi-population evolutionary algorithm for solving large-scale multi-modal multi-objective optimization problems. IEEE Tran. Evol. Comput. 25(3), 405–418 (2020)

    Article  Google Scholar 

  27. Yue, C., Qu, B., Liang, J.: A multiobjective particle swarm optimizer using ring topology for solving multimodal multiobjective problems. IEEE Trans. Evol. Comput. 22(5), 805–817 (2018)

    Article  Google Scholar 

  28. Yue, C., Qu, B., Yu, K., Liang, J., Li, X.: A novel scalable test problem suite for multimodal multiobjective optimization. Swarm Evol. Comput. 48, 62–71 (2019)

    Article  Google Scholar 

  29. Zhang, K., Chen, M., Xu, X., Yen, G.G.: Multi-objective evolution strategy for multi-modal multi-objective optimization. Appl. Soft Comput. 101, 107004 (2021)

    Article  Google Scholar 

  30. Zhou, A., Zhang, Q., Jin, Y.: Approximating the set of Pareto-optimal solutions in both the decision and objective spaces by an estimation of distribution algorithm. IEEE Trans. Evol. Comput. 13(5), 1167–1189 (2009)

    Article  Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61876075), Guangdong Provincial Key Laboratory (Grant No. 2020B121201001), the Program for Guangdong Introducing Innovative and Entrepre-neurial Teams (Grant No. 2017ZT07X386), The Stable Support Plan Program of Shenzhen Natural Science Fund (Grant No. 20200925174447003), Shenzhen Science and Technology Program (Grant No. KQTD2016112514355531).

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Authors and Affiliations

  1. Guangdong Provincial Key Laboratory of Brain-Inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Yiming Peng & Hisao Ishibuchi

Authors
  1. Yiming Peng
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  2. Hisao Ishibuchi
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Correspondence to Hisao Ishibuchi .

Editor information

Editors and Affiliations

  1. TU Dortmund, Dortmund, Germany

    Günter Rudolph

  2. Leiden University, Leiden, The Netherlands

    Anna V. Kononova

  3. Shinshu University, Nagano, Japan

    Hernán Aguirre

  4. Technische Universität Dresden, Dresden, Germany

    Pascal Kerschke

  5. University of Stirling, Stirling, UK

    Gabriela Ochoa

  6. Jožef Stefan Institute, Ljubljana, Slovenia

    Tea Tušar

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Peng, Y., Ishibuchi, H. (2022). Dynamic Multi-modal Multi-objective Optimization: A Preliminary Study. In: Rudolph, G., Kononova, A.V., Aguirre, H., Kerschke, P., Ochoa, G., Tušar, T. (eds) Parallel Problem Solving from Nature – PPSN XVII. PPSN 2022. Lecture Notes in Computer Science, vol 13399. Springer, Cham. https://doi.org/10.1007/978-3-031-14721-0_10

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  • DOI: https://doi.org/10.1007/978-3-031-14721-0_10

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