Abstract
In almost all cases the performance of a multi-objective evolutionary algorithm (MOEA) is measured in terms of its approximation quality in objective space. As a consequence, most MOEAs focus on such approximations while neglecting the distribution of the individuals in decision space. This, however, represents a potential shortcoming in certain applications as in many cases one can obtain the same or a very similar qualities (measured in objective space) in several ways (measured in decision space) which may be very valuable information for the decision maker for the realization of a project.
In this work, we propose the variable-NSGA-III (vNSGA-III) an algorithm that performs an exploration both in objective and decision space. The idea behind this algorithm is the so-called variation rate, a heuristic that can easily be integrated into other MOEAs as it is free of additional design parameters. We demonstrate the effectiveness of our approach on several benchmark problems, where we show that, compared to other methods, we significantly improve the approximation quality in decision space without any loss in the quality in objective space.
The authors acknowledge support for CONACyT project No. 285599.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Castillo, J.C., Segura, C., Aguirre, A.H., Miranda, G., León, C.: A multi-objective decomposition-based evolutionary algorithm with enhanced variable space diversity control. In: Proceedings of GECCO 2017, pp. 1565–1571. ACM, New York (2017)
Coello, C.A.C., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-objective Problems, vol. 242. Springer, Berlin (2002). https://doi.org/10.1007/978-0-387-36797-2
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)
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)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: 2002 Proceedings of the 2002 Congress on Evolutionary Computation. CEC 2002, vol. 1, pp. 825–830. IEEE (2002)
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)
Dilettoso, E., Rizzo, S.A., Salerno, N.: A weakly pareto compliant quality indicator. Math. Comput. Appl. 22(1), 25 (2017)
Huband, S., Barone, L., While, L., Hingston, P.: A scalable multi-objective test problem toolkit. In: Coello, C.A.C., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 280–295. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31880-4_20
Horn, J., Nafpliotis, N., Goldberg, D.E.: Multiobjective optimization using the niched Pareto genetic algorithm. IlliGAL report (93005), 61801–2296 (1993)
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., Esquivel, X., Lara, A., Coello, C.A.C.: Using the averaged Hausdorff distance as a performance measure in evolutionary multiobjective optimization. IEEE Trans. Evol. Comput. 16(4), 504–522 (2012)
Schütze, O., Witting, K., Ober-Blöbaum, S., Dellnitz, M.: Set oriented methods for the numerical treatment of multiobjective optimization problems. In: Tantar, E., et al. (eds.) EVOLVE - A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation. SCI, vol. 447, pp. 187–219. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-32726-1_5
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)
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
Cuate, O., Schütze, O. (2019). Variation Rate: An Alternative to Maintain Diversity in Decision Space for Multi-objective Evolutionary Algorithms. 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_17
Download citation
DOI: https://doi.org/10.1007/978-3-030-12598-1_17
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)