Abstract
Decomposition based evolutionary approaches such as MOEA/D and its variants have been quite successful in solving various classes of two and three objective optimization problems. While there have been some attempts to modify the dominance based approaches such as NSGA-II and SPEA2 to deal with many-objective optimization, there are few attempts to extend the capability of decomposition based approaches. The performance of a decomposition based approach is dependent on (a) the mechanism of reference points generation i.e. one which needs to be scalable and computationally efficient (b) the method to simultaneously deal with conflicting requirements of convergence and diversity and finally (c) the means to use the information of neighboring subproblems efficiently. In this paper, we introduce a decomposition based evolutionary algorithm, wherein the reference points are generated via systematic sampling and an adaptive epsilon scheme is used to manage the balance between convergence and diversity. To deal with constraints efficiently, an adaptive epsilon formulation is adopted. The performance of the algorithm is highlighted using standard benchmark problems i.e. DTLZ1 and DTLZ2 for 3, 5, 8, 10 and 15 objectives, the car side impact problem, the water resource management problem and the constrained ten-objective general aviation aircraft (GAA) design problem. The study clearly highlights that the proposed algorithm is better or at par with recent reference direction based approaches.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
References
Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: A short review. In: Proc. IEEE World Congress Computational Intelligence, pp. 2419–2426 (2008)
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)
Singh, H.K., Isaacs, A., Ray, T., Smith, W.: A Study on the Performance of Substitute Distance Based Approaches for Evolutionary Many Objective Optimization. In: Li, X., Kirley, M., Zhang, M., Green, D., Ciesielski, V., Abbass, H.A., Michalewicz, Z., Hendtlass, T., Deb, K., Tan, K.C., Branke, J., Shi, Y. (eds.) SEAL 2008. LNCS, vol. 5361, pp. 401–410. Springer, Heidelberg (2008)
Kachroudi, S., Grossard, M.: Average rank domination relation for NSGA-II and SMPSO algorithms for many-objective optimization. In: Proc. Second World Congress Nature and Biologically Inspired Computing (NaBIC), pp. 19–24 (2010)
Wang, G., Wu, J.: A new fuzzy dominance GA applied to solve many-objective optimization problem. In: Proc. Second Int. Conf. Innovative Computing, Information and Control (ICICIC 2007), pp. 617–621 (2007)
Zou, X., Chen, Y., Liu, M., Kang, L.: A new evolutionary algorithm for solving many-objective optimization problems. IEEE Transactions on Systems, Man, and Cybernetics-Part B 38(5), 1402–1412 (2008)
Hadka, D., Reed, P.M., Simpson, T.W.: Diagnostic assessment of the Borg MOEA for many-objective product family design problems. In: IEEE World Congress on Computational Intelligence, Brisbane, Australia, pp. 10–15 (June 2012)
Aguirre, H., Tanaka, K.: Adaptive ε-ranking on MNK-landscapes. In: Proc. IEEE Symposium Computational Intelligence in Miulti-Criteria Decision-Making (MCDM 2009), pp. 104–111 (2009)
Saxena, D.K., Deb, K.: Dimensionality reduction of objectives and constraints in multi-objective optimization problems: A system design perspective. In: IEEE Congress on Evolutionary Computation (2008)
Singh, H.K., Isaacs, A., Ray, T.: A Pareto corner search evolutionary algorithm and dimensionality reduction in many-objective optimization problems. IEEE Transactions on Evolutionary Computation 15(4), 539–556 (2011)
Deb, K., Sinha, A., Korhonen, P.J., Wallenius, J.: An interactive evolutionary multi-objective optimization method based on progressively approximated value functions. IEEE Transactions on Evolutionary Computation 14, 723–739 (2010)
Wagner, T., Beume, N., Naujoks, B.: Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 742–756. Springer, Heidelberg (2007)
Hughes, E.J.: MSOPS-II: A general-purpose many-objective optimiser. In: Proc. IEEE Congress Evolutionary Computation, pp. 3944–3951 (2007)
Bader, J., Zitzler, E.: Hype: An algorithm for fast hypervolume-based many-objective optimization. Evolutionary Computation 19, 45–76 (2011)
Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation 11(6), 712–731 (2007)
Das, I., Dennis, J.E.: Normal-bounday intersection: A new method for generating Pareto optimal points in multicriteria optimization problems. SIAM J. Optim. 8(3), 631–657 (1998)
Deb, K., Jain, H.: Handling many-objective problems using an improved NSGA-II procedure. In: IEEE World Congress on Computational Intelligence, Brisbane, Australia, pp. 10–15 (June 2012)
Tan, Y.Y., Jiao, Y.C., Lib, H., Wang, X.K.: MOEA/D + uniform design: A new version of MOEA/D for optimization problems with many objectives. Computers & Operations Research (January 2012)
Takahama, T., Sakai, S.: Constrained optimization by applying the α constrained method to the nonlinear simplex method with mutations. IEEE Transactions on Evolutionary Computation 9(5), 437–451 (2005)
Deb, K., Agarwal, R.B.: Simulated binary crossover for continuous search space. Complex Systems 9(2), 115–148 (1995)
Asafuddoula, M., Ray, T., Sarker, R., Alam, K.: An adaptive constraint handling approach embedded MOEA/D. In: IEEE World Congress on Computational Intelligence, June 10-15, pp. 1–8 (2012)
Deb, K., Jain, H.: An improved NSGA-II procedure for many-objective optimization, Part I: Solving problems with box constraints. KanGAL Report No. 2012009 (June 2012)
Lili, Z., Wenhua, Z.: Research on performance measures of multi-objective optimization evolutionary algorithms. In: Proc. 3rd Int. Conf. Intelligent System and Knowledge Engineering (ISKE), vol. 1, pp. 502–507 (2008)
Deb, K., Jain, H.: An improved NSGA-II procedure for many-objective optimization, Part II: Handling constraints and extending to an adaptive approach. KanGAL Report No. 2012010 (June 2012)
Ray, T., Tai, K., Seow, K.C.: An evolutionary algorithm for multiobjective optimization. Engineering Optimization 33(3), 399–424 (2001)
Durillo, J., Nebro, A.: jMetal: a java framework for multi-objective optimization. Advances in Engineering Software 42, 760–771 (2011)
Simpson, T.W., Chen, W., Allen, J.K., Mistree, F.: Conceptual design of a family of products through the use of the robust concept exploration method. In: 6th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, vol. 2, pp. 1535–1545 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Asafuddoula, M., Ray, T., Sarker, R. (2013). A Decomposition Based Evolutionary Algorithm for Many Objective Optimization with Systematic Sampling and Adaptive Epsilon Control. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds) Evolutionary Multi-Criterion Optimization. EMO 2013. Lecture Notes in Computer Science, vol 7811. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37140-0_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-37140-0_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37139-4
Online ISBN: 978-3-642-37140-0
eBook Packages: Computer ScienceComputer Science (R0)