Abstract
This paper proposes a novel decomposition-based evolutionary algorithm for multi-modal multi-objective optimization, which is the problem of locating as many as possible (almost) equivalent Pareto optimal solutions. In the proposed method, two or more individuals can be assigned to each decomposed subproblem to maintain the diversity of the population in the solution space. More precisely, a child is assigned to a subproblem whose weight vector is closest to its objective vector, in terms of perpendicular distance. If the child is close to one of individuals that have already been assigned to the subproblem in the solution space, the replacement selection is performed based on their scalarizing function values. Otherwise, the child is newly assigned to the subproblem, regardless of its quality. The effectiveness of the proposed method is evaluated on seven problems. Results show that the proposed algorithm is capable of finding multiple equivalent Pareto optimal solutions.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms. Wiley, Hoboken (2001)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE TEVC 6(2), 182–197 (2002)
Deb, K., Tiwari, S.: Omni-optimizer: a generic evolutionary algorithm for single and multi-objective optimization. EJOR 185(3), 1062–1087 (2008)
Durillo, J.J., Nebro, A.J.: jMetal: a Java framework for multi-objective optimization. Adv. Eng. Softw. 42(10), 760–771 (2011)
Gong, M., Liu, F., Zhang, W., Jiao, L., Zhang, Q.: Interactive MOEA/D for multi-objective decision making. In: GECCO, pp. 721–728 (2011)
Kramer, O., Danielsiek, H.: DBSCAN-based multi-objective niching to approximate equivalent pareto-subsets. In: GECCO, pp. 503–510 (2010)
Kudo, F., Yoshikawa, T., Furuhashi, T.: A study on analysis of design variables in Pareto solutions for conceptual design optimization problem of hybrid rocket engine. In: IEEE CEC, pp. 2558–2562 (2011)
Li, X., Epitropakis, M.G., Deb, K., Engelbrecht, A.P.: Seeking multiple solutions: an updated survey on niching methods and their applications. IEEE TEVC 21(4), 518–538 (2017)
Liang, J.J., Yue, C.T., Qu, B.Y.: Multimodal multi-objective optimization: a preliminary study. In: IEEE CEC, pp. 2454–2461 (2016)
Preuss, M., Naujoks, B., Rudolph, G.: Pareto set and EMOA behavior for simple multimodal multiobjective functions. In: Runarsson, T.P., Beyer, H.-G., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 513–522. Springer, Heidelberg (2006). https://doi.org/10.1007/11844297_52
Rudolph, G., Naujoks, B., Preuss, M.: Capabilities of EMOA to detect and preserve equivalent pareto subsets. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 36–50. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-70928-2_7
Schütze, O., Vasile, M., Coello, C.A.C.: Computing the set of epsilon-efficient solutions in multiobjective space mission design. JACIC 8(3), 53–70 (2011)
Shir, O.M., Preuss, M., Naujoks, B., Emmerich, M.: Enhancing decision space diversity in evolutionary multiobjective algorithms. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, J.-K., Sevaux, M. (eds.) EMO 2009. LNCS, vol. 5467, pp. 95–109. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01020-0_12
Trivedi, A., Srinivasan, D., Sanyal, K., Ghosh, A.: A survey of multiobjective evolutionary algorithms based on decomposition. IEEE TEVC 21(3), 440–462 (2017)
Ulrich, T., Bader, J., Zitzler, E.: Integrating decision space diversity into hypervolume-based multiobjective search. In: GECCO, pp. 455–462 (2010)
Yuan, Y., Xu, H., Wang, B., Zhang, B., Yao, X.: Balancing convergence and diversity in decomposition-based many-objective optimizers. IEEE TEVC 20(2), 180–198 (2016)
Yue, C., Qu, B., Liang, J.: A multi-objective particle swarm optimizer using ring topology for solving multimodal multi-objective problems. IEEE TEVC (2017, in press)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE TEVC 11(6), 712–731 (2007)
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 TEVC 13(5), 1167–1189 (2009)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE TEVC 7(2), 117–132 (2003)
Acknowledgments
This work was supported by the Science and Technology Innovation Committee Foundation of Shenzhen (Grant No. ZDSYS201703031748284).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Tanabe, R., Ishibuchi, H. (2018). A Decomposition-Based Evolutionary Algorithm for Multi-modal Multi-objective Optimization. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11101. Springer, Cham. https://doi.org/10.1007/978-3-319-99253-2_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-99253-2_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99252-5
Online ISBN: 978-3-319-99253-2
eBook Packages: Computer ScienceComputer Science (R0)