Linear Search Mechanism for Multi- and Many-Objective Optimisation

  • Heiner ZilleEmail author
  • Sanaz Mostaghim
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11411)


This article proposes a search mechanism based on linear combinations of population members to increase the solution quality of multi-objective and many-objective optimisation algorithms. Our approach makes use of the inherent knowledge in the solution population at a given time step, and forms new solutions through linear combinations of the existing ones. A population of coefficient vectors is formed and optimised by a metaheuristic to explore and exploit promising areas of the search space. In addition, our proposed method provides a reduction of dimensionality for large search spaces. The concept is formally introduced and implemented into a generic algorithm structure to be used in arbitrary metaheuristics. The experimental evaluation uses four multi- and many-objective algorithms (NSGA-II, GDE3, NSGA-III and RVEA) and is performed on a total of 60 test instances from three benchmark families with 2 to 5 objective functions and 30 to 514 decision variables. The results indicate that the performance of existing methods can be significantly improved by the proposed search strategy, especially in high-dimensional search spaces and for many-objective problems.


Multi-objective optimisation Many-objective optimisation Large-scale optimisation Evolutionary algorithm Exploration Linear combination Dimensionality reduction 


  1. 1.
    Antonio, L.M., Coello Coello, C.A.: Use of cooperative coevolution for solving large scale multiobjective optimization problems. In: IEEE Congress on Evolutionary Computation (CEC), pp. 2758–2765 (2013)Google Scholar
  2. 2.
    Cheng, R., Jin, Y., Olhofer, M., Sendhoff, B.: A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans. Evol. Comput. 20(5), 773–791 (2016). Scholar
  3. 3.
    Cheng, R., Jin, Y., Olhofer, M., Sendhoff, B.: Test problems for large-scale multiobjective and many-objective optimization. IEEE Trans. Cybern. 47(12), 4108–4121 (2017)CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    Deb, K., Srinivasan, A.: Innovization: innovating design principles through optimization. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 1629–1636. ACM (2006)Google Scholar
  6. 6.
    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
  7. 7.
    Gaur, A., Deb, K.: Effect of size and order of variables in rules for multi-objective repair-based innovization procedure. In: 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 2177–2184. IEEE (2017)Google Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    Kukkonen, S., Lampinen, J.: GDE3: the third evolution step of generalized differential evolution. In: IEEE Congress on Evolutionary Computation (CEC), vol. 1, pp. 443–450. IEEE (2005).
  10. 10.
    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). Scholar
  11. 11.
    Ma, X., et al.: A multiobjective evolutionary algorithm based on decision variable analyses for multiobjective optimization problems with large-scale variables. IEEE Trans. Evol. Comput. 20(2), 275–298 (2016)CrossRefGoogle Scholar
  12. 12.
    Mostaghim, S., Halter, W., Wille, A.: Linear multi-objective particle swarm optimization. In: Abraham, A., Grosan, C., Ramos, V. (eds.) Stigmergic Optimization. Studies in Computational Intelligence, vol. 31, pp. 209–238. Springer, Heidelberg (2006). Scholar
  13. 13.
    Sander, F., Zille, H., Mostaghim, S.: Transfer strategies from single- to multi-objective grouping mechanisms. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2018, pp. 729–736. ACM, New York (2018).
  14. 14.
    Singh, H.K., Isaacs, A., Ray, T.: A pareto corner search evolutionary algorithm and dimensionality reduction in many-objective optimization problems. IEEE Trans. Evol. Comput. 15(4), 539–556 (2011). Scholar
  15. 15.
    Tian, Y., Cheng, R., Zhang, X., Jin, Y.: Platemo: a MATLAB platform for evolutionary multi-objective optimization. CoRR abs/1701.00879 (2017).
  16. 16.
    While, L., Hingston, P., Barone, L., Huband, S.: A faster algorithm for calculating hypervolume. IEEE Trans. Evol. Comput. 10(1), 29–38 (2006)CrossRefGoogle Scholar
  17. 17.
    Zhang, X., Tian, Y., Jin, Y., Cheng, R.: A decision variable clustering-based evolutionary algorithm for large-scale many-objective optimization. IEEE Trans. Evol. Comput. 22(1), 97–112 (2018). Scholar
  18. 18.
    Zille, H., Ishibuchi, H., Mostaghim, S., Nojima, Y.: Mutation operators based on variable grouping for multi-objective large-scale optimization. In: 2016 IEEE Symposium Series on Computational Intelligence (SSCI) (2016)Google Scholar
  19. 19.
    Zille, H., Ishibuchi, H., Mostaghim, S., Nojima, Y.: Weighted optimization framework for large-scale multi-objective optimization. In: Companion of Genetic and Evolutionary Computation Conference - GECCO. ACM (2016)Google Scholar
  20. 20.
    Zille, H., Ishibuchi, H., Mostaghim, S., Nojima, Y.: A framework for large-scale multi-objective optimization based on problem transformation. IEEE Trans. Evol. Comput. 22(2), 260–275 (2018). Scholar
  21. 21.
    Zille, H., Mostaghim, S.: Comparison study of large-scale optimisation techniques on the LSMOP benchmark functions. In: 2017 IEEE Symposium Series on Computational Intelligence (SSCI), November 2017Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute for Intelligent Cooperative SystemsOtto von Guericke UniversityMagdeburgGermany

Personalised recommendations