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Empirical Investigations of Reference Point Based Methods When Facing a Massively Large Number of Objectives: First Results

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Evolutionary Multi-Criterion Optimization (EMO 2017)

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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.

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Notes

  1. 1.

    Also known as decomposition-based method, but here we use the terminology reference point based method without loss of generality.

  2. 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

  1. Adra, S.F., Fleming, P.J.: Diversity management in evolutionary many-objective optimization. IEEE Trans. Evol. Comput. 15(2), 183–195 (2011)

    Article  Google Scholar 

  2. Auger, A., Bader, J., Brockhoff, D., Zitzler, E.: Hypervolume-based multiobjective optimization: theoretical foundations and practical implications. Theor. Comput. Sci. 425, 75–103 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bader, J., Zitzler, E.: HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol. Comput. 19(1), 45–76 (2011)

    Article  Google Scholar 

  4. 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)

    Article  MATH  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. 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)

    Article  MathSciNet  MATH  Google Scholar 

  7. 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)

    Article  Google Scholar 

  8. Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms. John Wiley & Sons Inc., New York (2001)

    MATH  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. 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)

    Article  MathSciNet  Google Scholar 

  11. 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)

    Chapter  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. Li, B., Li, J., Tang, K., Yao, X.: Many-objective evolutionary algorithms: a survey. ACM Comput. Surv. 48(1), 13 (2015)

    Article  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. 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)

    Article  MathSciNet  Google Scholar 

  16. Li, K., Kwong, S., Zhang, Q., Deb, K.: Interrelationship-based selection for decomposition multiobjective optimization. IEEE Trans. Cybern. 45(10), 2076–2088 (2015)

    Article  Google Scholar 

  17. 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)

    Article  Google Scholar 

  18. Miettinen, K.: Nonlinear Multiobjective Optimization, vol. 12. Kluwer Academic Publishers, Boston (1999)

    MATH  Google Scholar 

  19. Purshouse, R.C., Fleming, P.J.: On the evolutionary optimization of many conflicting objectives. IEEE Trans. Evol. Comput. 11(6), 770–784 (2007)

    Article  Google Scholar 

  20. 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

    Chapter  Google Scholar 

  21. 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)

    Article  Google Scholar 

  22. Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evolutionary Computation 11, 712–731 (2007)

    Article  Google Scholar 

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Acknowledgement

This work was partially supported by EPSRC (Grant No. EP/J017515/1).

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Correspondence to Ke Li .

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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

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  • DOI: https://doi.org/10.1007/978-3-319-54157-0_27

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