Indicator-Based Evolutionary Level Set Approximation: Mixed Mutation Strategy and Extended Analysis

  • Lai-Yee Liu
  • Vitor Basto-Fernandes
  • Iryna Yevseyeva
  • Joost Kok
  • Michael Emmerich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10337)


The aim of evolutionary level set approximation is to find a finite representation of a level set of a given black box function. The problem of level set approximation plays a vital role in solving problems, for instance in fault detection in water distribution systems, engineering design, parameter identification in gene regulatory networks, and in drug discovery. The goal is to create algorithms that quickly converge to feasible solutions and then achieve a good coverage of the level set. The population based search scheme of evolutionary algorithms makes this type of algorithms well suited to target such problems. In this paper, the focus is on continuous black box functions and we propose a challenging benchmark for this problem domain and propose dual mutation strategies, that balance between global exploration and local refinement. Moreover, the article investigates the role of different indicators for measuring the coverage of the level set approximation. The results are promising and show that even for difficult problems in moderate dimension the proposed evolutionary level set approximation algorithm (ELSA) can serve as a versatile and robust meta-heuristic.


  1. [Bra98]
    Branke, J.: Creating robust solutions by means of evolutionary algorithms. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 119–128. Springer, Heidelberg (1998). doi: 10.1007/BFb0056855 CrossRefGoogle Scholar
  2. [CZ06]
    Coelho, G.P., Von Zuben, F.J.: omni-aiNet: an immune-inspired approach for omni optimization. In: Bersini, H., Carneiro, J. (eds.) ICARIS 2006. LNCS, vol. 4163, pp. 294–308. Springer, Heidelberg (2006). doi: 10.1007/11823940_23 CrossRefGoogle Scholar
  3. [EBN05]
    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
  4. [EDK13]
    Emmerich, M.T.M., Deutz, A.H., Kruisselbrink, J.W.: On quality indicators for black-box level set approximation. In: Tantar, E., Tantar, A.-A., Bouvry, P., Del Moral, P., Legrand, P., Coello, C.A.C., Schütze, O. (eds.) EVOLVE-A Bridge Between Probability, pp. 157–185. Set Oriented Numerics and Evolutionary Computation. Springer, Heidelberg (2013)Google Scholar
  5. [Kru12]
    Kruisselbrink, J.W.: Evolution strategies for robust optimization. Ph.D. thesis, Leiden Institute of Advanced Computer Science (LIACS), Faculty of Science, Leiden University (2012)Google Scholar
  6. [NE15]
    Nezhinsky, A., Emmerich, M.T.M.: Parameter identification of stochastic gene regulation models by indicator-based evolutionary level set approximation. In: Proceedings of EVOLVE - A Bridge Between Probability, Set-Oriented Numerics, and Evolutionary Computation, Iasi, June 2015. Springer, Heidelberg (2015, in print)Google Scholar
  7. [PCWB00]
    Parmee, I.C., Cvetković, D., Watson, A.H., Bonham, C.R.: Multiobjective satisfaction within an interactive evolutionary design environment. Evol. Comput. 8(2), 197–222 (2000)CrossRefGoogle Scholar
  8. [Set99]
    Sethian, J.A.: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, vol. 3. Cambridge University Press, Cambridge (1999)MATHGoogle Scholar
  9. [SPB93]
    Solow, A., Polasky, S., Broadus, J.: On the measurement of biological diversity. J. Environ. Econ. Manag. 24(1), 60–68 (1993)CrossRefGoogle Scholar
  10. [UBT10]
    Ulrich, T., Bader, J., Thiele, L.: Defining and optimizing indicator-based diversity measures in multiobjective search. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN 2010. LNCS, vol. 6238, pp. 707–717. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-15844-5_71 Google Scholar
  11. [UT11]
    Ulrich, T., Thiele, L.: Maximizing population diversity in single-objective optimization. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, pp. 641–648. ACM (2011)Google Scholar
  12. [vdB13]
    van der Burgh, B.: An evolutionary algorithm for finding diverse sets of molecules with user-defined properties. Technical report (2013)Google Scholar
  13. [vdGSB08]
    van der Goes, V., Shir, O.M., Bäck, T.: Niche radius adaptation with asymmetric sharing. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 195–204. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-87700-4_20 CrossRefGoogle Scholar
  14. [ZR07]
    Zechman, E.M., Ranjithan, R.S.: Generating alternatives using evolutionary algorithms for water resources and environmental management problems. J. Water Resour. Plan. Manag. 133(2), 156–165 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Lai-Yee Liu
    • 1
  • Vitor Basto-Fernandes
    • 2
    • 3
  • Iryna Yevseyeva
    • 4
  • Joost Kok
    • 1
  • Michael Emmerich
    • 1
  1. 1.Leiden Institute of Advanced Computer ScienceLeiden UniversityLeidenThe Netherlands
  2. 2.Instituto Universitário de Lisboa (ISCTE-IUL), University Institute of Lisbon, ISTAR-IULLisboaPortugal
  3. 3.School of Technology and Management, Computer Science and Communications Research CentrePolytechnic Institute of LeiriaLeiriaPortugal
  4. 4.Faculty of TechnologyDe Montfort UniversityLeicesterUK

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