Indicator-Based Evolutionary Level Set Approximation: Mixed Mutation Strategy and Extended Analysis
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.
- [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
- [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
- [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
- [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
- [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
- [vdB13]van der Burgh, B.: An evolutionary algorithm for finding diverse sets of molecules with user-defined properties. Technical report (2013)Google Scholar