Abstract
This paper proposes a novel multi-objective optimization algorithm, dual-stage nondominated sorting genetic algorithm-II (D-NSGA-II) for many-objective problems. Since the percentage of the nondominated solutions increases exponentially with the increasing number of objectives, just finding the nondominated solutions is not enough for solving many-objective problems. In other words, it is necessary to discriminate more meaningful ones from the other nondominated solutions by additionally incorporating user preference into the algorithms. The proposed D-NSGA-II can obtain not only user preference oriented, but also diverse nondominated solutions by introducing an additional stage of multi-objective optimization. The second stage employs the corresponding secondary objectives, global evaluation and crowding distance which were proposed in the previous research for representing the user’s preference to a solution and the crowdedness around a solution, respectively. To demonstrate the effectiveness of the proposed algorithm, some benchmark functions are tested and the outcomes of the proposed D-NSGA-II and the NSGA-II are empirically compared. Experimental results show that D-NSGA-II properly reflects the user’s preference in the optimization process as well as the performance in terms of the diversity and solution quality is competitive with the NSGA-II.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Coello, C., Lechuga, M.: MOPSO: A proposal for multiple objective particle swarm optimization. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1051–1056 (2002)
Hu, X., Eberhart, R.: Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1677–1681 (2002)
Coello, C., Pulido, G., Lechuga, M.: Handling multiple objectives with particle swarm optimization. IEEE Transactions on Evolutionary Computation 8(3), 256–279 (2004)
Köppen, M., Yoshida, K.: Substitute distance assignments in nsga-ii for handling many-objective optimization problems. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 727–741. Springer, Heidelberg (2007)
Bader, J., Zitzler, E.: Hype: An algorithm for fast hypervolume-based many-objective optimization. Evolutionary Computation 19(1), 45–76 (2011)
Kim, J.H., Han, J.H., Kim, Y.H., Choi, S.H., Kim, E.S.: Preference-Based Solution Selection Algorithm for Evolutionary Multiobjective Optimization. IEEE Transactions on Evolutionary Computation 16(1), 20–34 (2012)
Lee, K.B., Kim, J.H.: Multiobjective particle swarm optimization with preference-based sort and its application to path following footstep optimization for humanoid robots. IEEE Transactions on Evolutionary Computation 17(6), 755–766 (2013)
Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: A short review. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 2419–2426 (2008)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of IEEE Congress on Evolutionary Computation, vol. 1, pp. 825–830 (2002)
Raquel, C.R., Naval Jr., P.C.: An effective use of crowding distance in multiobjective particle swarm optimization. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 257–264. ACM (2005)
Agrawal, R.B., Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space (1994)
Zitzler, E.: Evolutionary algorithms for multiobjective optimization: Methods and applications. Doctoral dissertation ETH 13398, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (1999)
Li, H., Zhang, Q., Tsang, E., Ford, J.: Hybrid estimation of distribution algorithm for multiobjective knapsack problem. In: Gottlieb, J., Raidl, G.R. (eds.) EvoCOP 2004. LNCS, vol. 3004, pp. 145–154. Springer, Heidelberg (2004)
Lehmann, E., Romano, J.: Testing Statistical Hypotheses. Springer (2006)
Welch, B.L.: The generalization of ‘student’s’ problem when several different population variances are involved. Biometrika 34(1/2), 28–35 (1947)
Judge, G.G., Hill, R.C., Griffiths, W., Lutkepohl, H., Lee, T.C., Tuladhar, J., Banerjee, B., Kelly, V., Stevens, R., Stilwell, T., et al.: Introduction to the theory and practice of econometrics. Economic Development and Cultural Change 32(4), 767–780 (1984)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Lee, KB. (2015). D-NSGA-II: Dual-Stage Nondominated Sorting Genetic Algorithm-II. In: Kim, JH., Yang, W., Jo, J., Sincak, P., Myung, H. (eds) Robot Intelligence Technology and Applications 3. Advances in Intelligent Systems and Computing, vol 345. Springer, Cham. https://doi.org/10.1007/978-3-319-16841-8_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-16841-8_27
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16840-1
Online ISBN: 978-3-319-16841-8
eBook Packages: EngineeringEngineering (R0)