Abstract
In this paper we propose a Diversity-Indicator based Multi-Objective Evolutionary Algorithm (DI-MOEA) for fast computation of evenly spread Pareto front approximations. Indicator-based optimization has been a successful principle for multi-objective evolutionary optimization algorithm (MOEA) design. The idea is to guide the search for approximating the Pareto front by a performance indicator. Ideally, the indicator captures both convergence to the Pareto front and a high diversity, and it does not require a priori knowledge of the Pareto front shape and location. It is, however, so far difficult to define indicators that scale well in computation time for high dimensional objective spaces, and that distribute points evenly on the Pareto front. Moreover, the behavior of commonly applied indicators depends on additional information, such as reference points or sets. The proposed DI-MOEA adopts a hybrid search scheme for combining the advantages of Pareto dominance-based approaches to ensure fast convergence to the Pareto front, with indicator based approaches to ensure convergence to an evenly distributed, diverse set. In addition, it avoids the use of complex structure and parameters in decomposition-based approaches. The Euclidean distance-based geometric mean gap is used as diversity indicator. Experimental results show that the new algorithm can find uniformly spaced Pareto fronts without the involvement of any reference points or sets. Most importantly, our algorithm performs well on both the hypervolume indicator and IGD when comparing with state-of-the-art MOEAs (NSGA-II, SMS-EMOA, MOEA/D and NSGA-III).
This work is part of the research programme Smart Industry SI2016 with project name CIMPLO and project number 15465, which is (partly) financed by the Netherlands Organisation for Scientific Research (NWO).
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
Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181(3), 1653–1669 (2007)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577–601 (2014)
Emmerich, M.T.M., Deutz, A.H., Kruisselbrink, J.W.: On quality indicators for black-box level set approximation. In: Tantar, E., et al. (eds.) EVOLVE - A Bridge Between Probability, Set Oriented Numerics and Evolutionary Computation. SCI, vol. 447, pp. 157–185. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-32726-1_4
Ghosh, J.B.: Computational aspects of the maximum diversity problem. Oper. Res. Lett. 19(4), 175–181 (1996)
Giagkiozis, I., Purshouse, R.C., Fleming, P.J.: Generalized decomposition and cross entropy methods for many-objective optimization. Inf. Sci. 282, 363–387 (2014)
Hajela, P., Lin, C.-Y.: Genetic search strategies in multicriterion optimal design. Struct. Optim. 4(2), 99–107 (1992)
Hanne, T.: On the convergence of multiobjective evolutionary algorithms. Eur. J. Oper. Res. 117(3), 553–564 (1999)
Liu, L.-Y., Basto-Fernandes, V., Yevseyeva, I., Kok, J., Emmerich, M.: Indicator-based evolutionary level set approximation: mixed mutation strategy and extended analysis. In: Ferrández Vicente, J.M., Álvarez-Sánchez, J.R., de la Paz López, F., Toledo Moreo, J., Adeli, H. (eds.) IWINAC 2017. LNCS, vol. 10337, pp. 146–159. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-59740-9_15
Ulrich, T., Bader, J., Thiele, L.: Defining and optimizing indicator-based diversity measures in multiobjective search. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010. LNCS, vol. 6238, pp. 707–717. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15844-5_71
Vaidya, P.M.: An o(n log n) algorithm for the all-nearest-neighbors problem. Discrete Comput. Geom. 4(2), 101–115 (1989)
Wessing, S.: Two-stage methods for multimodal optimization. Ph.D. thesis. Universitätsbibliothek Dortmund (2015)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30217-9_84
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Wang, Y., Emmerich, M., Deutz, A., Bäck, T. (2019). Diversity-Indicator Based Multi-Objective Evolutionary Algorithm: DI-MOEA. In: Deb, K., et al. Evolutionary Multi-Criterion Optimization. EMO 2019. Lecture Notes in Computer Science(), vol 11411. Springer, Cham. https://doi.org/10.1007/978-3-030-12598-1_28
Download citation
DOI: https://doi.org/10.1007/978-3-030-12598-1_28
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-12597-4
Online ISBN: 978-3-030-12598-1
eBook Packages: Computer ScienceComputer Science (R0)