A Hierarchical Decomposition-Based Evolutionary Many-Objective Algorithm

  • Fangqing Gu
  • Hai-Lin LiuEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10593)


The evolutionary multiobjective algorithms have been demonstrated the effectiveness in dealing with multiobjective optimization problems. However, when solving the problems with many objectives, i.e., the number of objectives is greater than three, it needs a large population size to maintain population diversity and provide a good approximation to the Pareto front. The dilemma between limited computational resources and the exponentially increasing population size is a big challenge. Thus, we suggest a hierarchical decomposition-based evolutionary algorithm for solving many-objective optimization problems in this paper. Specifically, it constructs a binary tree on a set of large-scale uniform weight vectors. We only compare a candidate solutions with the solutions on the path from root to a leaf node of the tree to assign it into an appropriate node. The proposed algorithm has lower time complexity. Theoretical analysis shows the complexity of the proposed algorithm is \(\mathcal {O}(Mlog(\mathbb {N}))\) for dealing with a new candidate solution. Empirical results fully demonstrate the effectiveness and competitiveness of the proposed algorithm.


Decomposition Evolutionary algorithm Multiobjective optimization Binary tree 


  1. 1.
    Asafuddoula, M., Ray, T., Sarker, R.: A decomposition based evolutionary algorithm for many objective optimization. IEEE Trans. Evol. Comput. 19(3), 445–460 (2015)CrossRefGoogle Scholar
  2. 2.
    Bader, J., Zitzler, E.: HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol. Comput. 19(1), 45–76 (2011)CrossRefGoogle Scholar
  3. 3.
    Bosman, P.A., Thierens, D.: The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Trans. Evol. Comput. 7(2), 174–188 (2003)CrossRefGoogle Scholar
  4. 4.
    Cheung, Y.M., Gu, F., Liu, H.L.: Objective extraction for many-objective optimization problems: algorithm and test problems. IEEE Trans. Evol. Comput. 20(5), 755–772 (2016)CrossRefGoogle Scholar
  5. 5.
    Deb, K.: Multiobjective Optimization Using Evolutionary Algorithms. Wiley, New York (2001)zbMATHGoogle Scholar
  6. 6.
    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)CrossRefGoogle Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Eckart, Z., Marco, L., Lothar, T.: SPEA2: improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Proceedings of Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, pp. 95–100 (2001)Google Scholar
  9. 9.
    Emmerich, M., Beume, N., Naujoks, B.: An EMO algorithm using the hypervolume measure as selection criterion. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 62–76. Springer, Heidelberg (2005). doi: 10.1007/978-3-540-31880-4_5 CrossRefGoogle Scholar
  10. 10.
    Gu, F., Cheung, Y.M.: Self-organizing map-based weight design for decomposition-based many-objective evolutionary algorithm. IEEE Trans. Evolutionary Computation (2017). doi: 10.1109/TEVC20172695579
  11. 11.
    Hadka, D., Reed, P.: Diagnostic assessment of search controls and failure modes in many-objective evolutionary optimization. Evol. Comput. 20(3), 423–452 (2012)CrossRefGoogle Scholar
  12. 12.
    Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. IEEE Trans. Evol. Comput. 10(5), 477–506 (2006)CrossRefzbMATHGoogle Scholar
  13. 13.
    Ishibuchi, H., Masuda, H., Nojima, Y.: Pareto fronts of many-objective degenerate test problems. IEEE Trans. Evol. Comput. (2015) doi: 10.1109/TEVC20152505784
  14. 14.
    Li, B., Li, J., Tang, K., Yao, X.: Many-objective evolutionary algorithms: a survey. ACM Comput. Surv. 48(1), 13:1–13:35 (2015)Google Scholar
  15. 15.
    Li, B., Tang, K., Li, J., Yao, X.: Stochastic ranking algorithm for many-objective optimization based on multiple indicators. IEEE Trans. Evol. Comput. 20(6), 924–938 (2016)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Nicola, B., Naujoks, B., Emmerich, M.: SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur. J. Oper. Res. 181(3), 1653–1669 (2007)CrossRefzbMATHGoogle Scholar
  18. 18.
    Schutze, O., Lara, A., Coello Coello, C.A.: On the influence of the number of objectives on the hardness of a multiobjective optimization problem. IEEE Trans. Evol. Comput. 15(4), 444–455 (2011)CrossRefGoogle Scholar
  19. 19.
    Trivedi, A., Srinivasan, D., Sanyal, K., Ghosh, A.: A survey of multiobjective evolutionary algorithms based on decomposition. IEEE Trans. Evol. Comput. (2016). doi: 10.1109/TEVC.2016.2608507
  20. 20.
    Wagner, M., Neumann, F.: A fast approximation-guided evolutionary multi-objective algorithm. In: Proceedings of 2013 Conference on Genetic and Evolutionary Computation, pp. 687–694 (2013)Google Scholar
  21. 21.
    Wang, H., Jiao, L., Yao, X.: Two_Arch2: an improved two-archive algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 19(4), 524–541 (2015)CrossRefGoogle Scholar
  22. 22.
    Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)CrossRefGoogle Scholar
  23. 23.
    Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-30217-9_84 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Guangdong University of TechnologyGuangzhouChina

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