Abstract
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.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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
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
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
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)
Kruisselbrink, J.W.: Evolution strategies for robust optimization. Ph.D. thesis, Leiden Institute of Advanced Computer Science (LIACS), Faculty of Science, Leiden University (2012)
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)
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)
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)
Solow, A., Polasky, S., Broadus, J.: On the measurement of biological diversity. J. Environ. Econ. Manag. 24(1), 60–68 (1993)
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
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)
van der Burgh, B.: An evolutionary algorithm for finding diverse sets of molecules with user-defined properties. Technical report (2013)
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
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)
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
Liu, LY., Basto-Fernandes, V., Yevseyeva, I., Kok, J., Emmerich, M. (2017). Indicator-Based Evolutionary Level Set Approximation: Mixed Mutation Strategy and Extended Analysis. In: Ferrández Vicente, J., Álvarez-Sánchez, J., de la Paz López, F., Toledo Moreo, J., Adeli, H. (eds) Natural and Artificial Computation for Biomedicine and Neuroscience. IWINAC 2017. Lecture Notes in Computer Science(), vol 10337. Springer, Cham. https://doi.org/10.1007/978-3-319-59740-9_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-59740-9_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-59739-3
Online ISBN: 978-3-319-59740-9
eBook Packages: Computer ScienceComputer Science (R0)