Abstract
Theoretical analysis of all kinds of randomised search heuristics has been and keeps being supported and facilitated by the use of simple example functions. Such functions help us understand the working principles of complicated heuristics. If the function represents some properties of practical problem landscapes these results become practically relevant. While this has been very successful in the past for optimisation in unimodal landscapes there is a need for generally accepted useful simple example functions for situations where unimodal objective functions are insufficient: multimodal optimisation and investigation of diversity preserving mechanisms are examples. A family of example landscapes is defined that comes with a limited number of parameters that allow to control important features of the landscape while all being still simple in some sense. Different expressions of these landscapes are presented and fundamental properties are explored.
The authors want to thank the organisers of the Dagstuhl Seminar 15211 ‘Theory of Evolutionary Algorithms’ for encouraging discussions that motivated this work. This article is based upon work from COST Action CA15140 ‘Improving Applicability of Nature-Inspired Optimisation by Joining Theory and Practice (ImAppNIO)’ supported by COST (European Cooperation in Science and Technology).
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Notes
- 1.
see, e.g., www.epitropakis.co.uk/cec16-niching/competition and coco.gforge.inria.fr.
- 2.
see, e.g., www.epitropakis.co.uk/ppsn2016-niching.
References
Branke, J.: Memory enhanced evolutionary algorithms for changing optimization problems. In: Proceedings of CEC, pp. 1875–1882. IEEE Press (1999)
Doerr, B., Hansen, N., Igel, C., Thiele, L.: Theory of evolutionary algorithms (Dagstuhl seminar 15211). Dagstuhl Rep. 5(5), 57–91 (2016)
Doerr, B., Winzen, C.: Ranking-based black-box complexity. Algorithmica 68(3), 571–609 (2014)
Droste, S., Jansen, T., Wegener, I.: A rigorous complexity analysis of the (1 + 1) evolutionary algorithm for linear functions with Boolean inputs. In: Proceedings of ICEC, pp. 499–504. IEEE Press (1998)
Fischer, S., Wegener, I.: The one-dimensional Ising model: mutation versus recombination. Theor. Comput. Sci. 344(2–3), 208–225 (2005)
Friedrich, T., Oliveto, P.S., Sudholt, D., Witt, C.: Analysis of diversity-preserving mechanisms for global exploration. Evol. Comput. 17(4), 455–476 (2009)
He, J., Yao, X.: Drift analysis and average time complexity of evolutionary algorithms. Artif. Intell. 127, 57–85 (2001)
Jansen, T.: Analyzing Evolutionary Algorithms. The Computer Science Perspective. Springer, Heidelberg (2013)
Jansen, T., Zarges, C.: Performance analysis of randomised search heuristics operating with a fixed budget. Theor. Comput. Sci. 545, 39–58 (2014)
Jong, K.D., Spears, W.M.: An analysis of the interacting roles of population size and crossover in genetic algorithms. In: Schwefel, H.-P., Manner, R. (eds.) Proceedings of PPSN, pp. 38–47. Springer, Heidelberg (1990)
Kennedy, J., Spears, W.M.: Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator. In: Proceedings of WCCI, pp. 78–83. IEEE Press (1998)
Kötzing, T., Lissovoi, A., Witt, C.: (1+1) EA on generalized dynamic onemax. In: Proceedings of FOGA, pp. 40–51. ACM Press (2015)
Moraglio, A., Johnson, C.G.: Geometric generalization of the Nelder-Mead algorithm. In: Cowling, P., Merz, P. (eds.) EvoCOP 2010. LNCS, vol. 6022, pp. 190–201. Springer, Heidelberg (2010)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)
Mühlenbein, H.: How genetic algorithms really work: mutation and hillclimbing. In: Proceedings of PPSN, pp. 15–26. Elsevier (1992)
Oliveto, P.S., Sudholt, D., Zarges, C.: On the runtime analysis of fitness sharing mechanisms. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds.) PPSN 2014. LNCS, vol. 8672, pp. 932–941. Springer, Heidelberg (2014)
Preuss, M.: Multimodal Optimization by Means of Evolutionary Algorithms. Springer, Heidelberg (2015)
Prügel-Bennett, A., Tayarani-Najaran, M.: Maximum satisfiability: anatomy of the fitness landscape for a hard combinatorial optimization problem. IEEE Trans. Evol. Comput. 16(3), 319–338 (2012)
Shir, O.M.: Niching in evolutionary algorithms. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds.) Handbook of Natural Computing, pp. 1035–1070. Springer, Heidelberg (2012)
Stadler, P.: Fitness landscapes. Biol. Evol. Stat. Phys. 585, 183–204 (2002)
Sudholt, D.: Crossover is provably essential for the Ising model on trees. In: Proceedings of GECCO, pp. 1161–1167. ACM Press (2005)
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Jansen, T., Zarges, C. (2016). Example Landscapes to Support Analysis of Multimodal Optimisation. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_74
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