Abstract
Differential Evolution (DE) is a simple yet powerful evolutionary algorithm, whose performance highly depends on the setting of some parameters. In this paper, we propose an adaptive DE algorithm for multi-objective optimization problems. Firstly, a novel tree neighborhood density estimator is proposed to enforce a higher spread between the non-dominated solutions, while the Pareto dominance strength is used to promote a higher convergence to the Pareto front. These two metrics are then used by an original replacement mechanism based on a three-step comparison procedure; and also to port two existing adaptive mechanisms to the multi-objective domain, one being used for the autonomous selection of the operators, and the other for the adaptive control of DE parameters CR and F. Experimental results confirm the superior performance of the proposed algorithm, referred to as Adap-MODE, when compared to two state-of-the-art baseline approaches, and to its static and partially-adaptive variants.
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
Preview
Unable to display preview. Download preview PDF.
References
Brest, J., Greiner, S., Boskovic, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10, 646–657 (2006)
Das, S., Suganthan, P.N.: Differential evolution – a survey of the state-of-the-art. IEEE Trans. Evol. Comput. (in press)
Davis, L.: Adapting operator probabilities in genetic algorithms. In: Proc. ICGA, pp. 61–69 (1989)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2002)
Deb, K., Thiele, L., Laummans, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Abraham, A., et al. (eds.) Evolutionary Multiobjective Optimization, pp. 105–145. Springer, Heidelberg (2005)
Eiben, A.E., Hinterding, R., Michalewicz, Z.: Parameter control in evolutionary algorithms. IEEE Trans. Evol. Comput. 3, 124–141 (1999)
Fialho, Á., Ros, R., Schoenauer, M., Sebag, M.: Comparison-based adaptive strategy selection with bandits in differential evolution. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G., et al. (eds.) PPSN XI. LNCS, vol. 6238, pp. 194–203. Springer, Heidelberg (2010)
Fialho, Á., Da Costa, L., Schoenauer, M., Sebag, M.: Extreme value based adaptive operator selection. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 175–184. Springer, Heidelberg (2008)
Gong, W., Fialho, A., Cai, Z.: Adaptive strategy selection in differential evolution. In: Branke, J., et al. (eds.) Proc. GECCO. ACM, New York (2010)
Huang, V.L., Zhao, S.Z., Mallipeddi, R., Suganthan, P.N.: Multi-objective optimization using self-adaptive differential evolution algorithm. In: Proc. CEC, pp. 190–194. IEEE, Los Alamitos (2009)
Jia, L., Gong, W., Wu, H.: An improved self-adaptive control parameter of differential evolution for global optimization. In: Cai, Z., Li, Z., Kang, Z., Liu, Y. (eds.) Computational Intelligence and Intelligent Systems. CCIS, vol. 51, pp. 215–224. Springer, Heidelberg (2009)
Kukkonen, S., Lampinen, J.: GDE3: The third evolution step of generalized differential evolution. In: Proc. CEC, pp. 443–450. IEEE, Los Alamitos (2005)
Li, M., Zheng, J., Xiao, G.: Uniformity assessment for evolutionary multi-objective optimization. In: Proc. CEC, pp. 625–632. IEEE, Los Alamitos (2008)
Maturana, J., Lardeux, F., Saubion, F.: Autonomous operator management for evolutionary algorithms. J. Heuristics (2010)
Price, K.V.: An introduction to differential evolution. In: Corne, D., et al. (eds.) New Ideas in Optimization, pp. 79–108. McGraw-Hill, New York (1999)
Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13, 398–417 (2009)
Robič, T., Filipič, B.: DEMO: Differential evolution for multiobjective optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 520–533. Springer, Heidelberg (2005)
Thierens, D.: An adaptive pursuit strategy for allocating operator probabilities. In: Beyer, H.-G., et al. (eds.) Proc. GECCO, pp. 1539–1546. ACM, New York (2005)
Whitacre, J., Pham, T., Sarker, R.: Use of statistical outlier detection method in adaptive evolutionary algorithms. In: Proc. GECCO, pp. 1345–1352. ACM, New York (2006)
Zhang, J., Sanderson, A.C.: Self-adaptive multi-objective differential evolution with direction information provided by archived inferior solutions. In: Proc. CEC, pp. 2806–2815. IEEE, Los Alamitos (2008)
Zhang, J., Sanderson, A.C.: JADE: Adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput. 13, 945–958 (2009)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evol. Comput. 8, 173–195 (2000)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K.C., et al. (eds.) Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems, pp. 95–100. CIMNE (2002)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evol. Comput. 3, 257–271 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, K., Fialho, Á., Kwong, S. (2011). Multi-Objective Differential Evolution with Adaptive Control of Parameters and Operators. In: Coello, C.A.C. (eds) Learning and Intelligent Optimization. LION 2011. Lecture Notes in Computer Science, vol 6683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25566-3_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-25566-3_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25565-6
Online ISBN: 978-3-642-25566-3
eBook Packages: Computer ScienceComputer Science (R0)