Abstract
Multi-objective optimization with more than three objectives has become one of the most active topics in evolutionary multi-objective optimization (EMO). However, most existing studies limit their experiments up to 15 or 20 objectives, although they claimed to be capable of handling as many objectives as possible. To broaden the insights in the behavior of EMO methods when facing a massively large number of objectives, this paper presents some preliminary empirical investigations on several established scalable benchmark problems with 25, 50, 75 and 100 objectives. In particular, this paper focuses on the behavior of the currently pervasive reference point based EMO methods, although other methods can also be used. The experimental results demonstrate that the reference point based EMO method can be viable for problems with a massively large number of objectives, given an appropriate choice of the distance measure. In addition, sufficient population diversity should be given on each weight vector or a local niche, in order to provide enough selection pressure. To the best of our knowledge, this is the first time an EMO methodology has been considered to solve a massively large number of conflicting objectives.
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
Notes
- 1.
Also known as decomposition-based method, but here we use the terminology reference point based method without loss of generality.
- 2.
Due to the page limit, the parallel coordinate plots are put in the supplementary file, which can be found in https://coda-group.github.io/publications/suppEMO.pdf.
References
Adra, S.F., Fleming, P.J.: Diversity management in evolutionary many-objective optimization. IEEE Trans. Evol. Comput. 15(2), 183–195 (2011)
Auger, A., Bader, J., Brockhoff, D., Zitzler, E.: Hypervolume-based multiobjective optimization: theoretical foundations and practical implications. Theor. Comput. Sci. 425, 75–103 (2012)
Bader, J., Zitzler, E.: HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol. Comput. 19(1), 45–76 (2011)
Beume, N., Naujoks, B., Emmerich, M.T.M.: SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181(3), 1653–1669 (2007)
Coello, C.A.C., Cortés, N.C.: Solving multiobjective optimization problems using an artificial immune system. Genet. Program. Evolvable Mach. 6(2), 163–190 (2005)
Das, I., Dennis, J.E.: Normal-boundary intersection: a new method for generating the pareto surface in nonlinear multicriteria optimization problems. SIAM J. Optim. 8, 631–657 (1998)
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.: Multi-objective Optimization Using Evolutionary Algorithms. John Wiley & Sons Inc., New York (2001)
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., Sundar, J., Bhaskara, U., Chaudhuri, S.: Reference point based multiobjective optimization using evolutionary algorithms. Int. J. Comput. Intell. Res. 2(3), 273–286 (2006)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evol. Multiobjective Optim. Advanced Information and Knowledge Processing, pp. 105–145. Springer, London (2005)
Ishibuchi, H., Setoguchi, Y., Masuda, H., Nojima, Y.: Performance of decomposition-based many-objective algorithms strongly depends on Pareto front shapes. IEEE Trans. Evol. Comput. PP(99), 1 (2016)
Li, B., Li, J., Tang, K., Yao, X.: Many-objective evolutionary algorithms: a survey. ACM Comput. Surv. 48(1), 13 (2015)
Li, K., Deb, K., Zhang, Q., Kwong, S.: An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans. Evol. Comput. 19(5), 694–716 (2015)
Li, K., Kwong, S., Cao, J., Li, M., Zheng, J., Shen, R.: Achieving balance between proximity and diversity in multi-objective evolutionary algorithm. Inf. Sci. 182(1), 220–242 (2012)
Li, K., Kwong, S., Zhang, Q., Deb, K.: Interrelationship-based selection for decomposition multiobjective optimization. IEEE Trans. Cybern. 45(10), 2076–2088 (2015)
Li, K., Zhang, Q., Kwong, S., Li, M., Wang, R.: Stable matching based selection in evolutionary multiobjective optimization. IEEE Trans. Evol. Comput. 18(6), 909–923 (2014)
Miettinen, K.: Nonlinear Multiobjective Optimization, vol. 12. Kluwer Academic Publishers, Boston (1999)
Purshouse, R.C., Fleming, P.J.: On the evolutionary optimization of many conflicting objectives. IEEE Trans. Evol. Comput. 11(6), 770–784 (2007)
Sato, H., Aguirre, H.E., Tanaka, K.: Self-controlling dominance area of solutions in evolutionary many-objective optimization. In: Deb, K., Bhattacharya, A., Chakraborti, N., Chakroborty, P., Das, S., Dutta, J., Gupta, S.K., Jain, A., Aggarwal, V., Branke, J., Louis, S.J., Tan, K.C. (eds.) SEAL 2010. LNCS, vol. 6457, pp. 455–465. Springer, Heidelberg (2010). doi:10.1007/978-3-642-17298-4_49
Wang, H., Jiao, L., Yao, X.: Two_arch2: An improved two-archive algorithm for many-objective optimization. IEEE Trans. Evolutionary Computation 19(4), 524–541 (2015)
Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evolutionary Computation 11, 712–731 (2007)
Acknowledgement
This work was partially supported by EPSRC (Grant No. EP/J017515/1).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Li, K., Deb, K., Altinoz, T., Yao, X. (2017). Empirical Investigations of Reference Point Based Methods When Facing a Massively Large Number of Objectives: First Results. In: Trautmann, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2017. Lecture Notes in Computer Science(), vol 10173. Springer, Cham. https://doi.org/10.1007/978-3-319-54157-0_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-54157-0_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54156-3
Online ISBN: 978-3-319-54157-0
eBook Packages: Computer ScienceComputer Science (R0)