Abstract
This paper formally defines multimodality in multiobjective optimization (MO). We introduce a test-bed in which multimodal MO problems with known properties can be constructed as well as numerical characteristics of the resulting landscape. Gradient- and local search based strategies are compared on exemplary problems together with specific performance indicators in the multimodal MO setting. By this means the foundation for Exploratory Landscape Analysis in MO is provided.
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Notes
- 1.
The HIGA-MO source code is available on moda.liacs.nl/index.php?page=code.
References
Bischl, B., Mersmann, O., Trautmann, H., Preuss, M.: Algorithm selection based on exploratory landscape analysis and cost-sensitive learning. In: Proceedings of the 14th Annual Conference on Genetic and Evolutionary Computation, GECCO 2012, New York, NY, USA, pp. 313–320. ACM (2012)
Emmerich, M., Deutz, A.: Time complexity and zeros of the hypervolume indicator gradient field. In: Schuetze, O., Coello, C.A., Tantar, A.-A., Tantar, E., Bouvry, P., Moral, P.D., Legrand, P. (eds.) EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation III. SCI, vol. 500, pp. 169–193. Springer, Heidelberg (2014)
Emmerich, M.T.M., Deutz, A.H., Beume, N.: Gradient-based/evolutionary relay hybrid for computing pareto front approximations maximizing the s-metric. In: Bartz-Beielstein, T., Blesa Aguilera, M.J., Blum, C., Naujoks, B., Roli, A., Rudolph, G., Sampels, M. (eds.) HCI/ICCV 2007. LNCS, vol. 4771, pp. 140–156. Springer, Heidelberg (2007)
Kerschke, P., Preuss, M., Wessing, S., Trautmann, H.: Detecting funnel structures by means of exploratory landscape analysis. In: Proceedings of the 17th Annual Conference on Genetic and Evolutionary Computation, pp. 265–272. ACM (2015)
Kerschke, P., Preuss, M., Wessing, S., Trautmann, H.: Low-budget exploratory landscape analysis on multiple peaks models. In: Proceedings of the 18th Annual Conference on Genetic and Evolutionary Computation. ACM (2016, accepted)
Liefooghe, A., Verel, S., Daolio, F., Aguirre, H., Tanaka, K.: A feature-based performance analysis in evolutionary multiobjective optimization. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C.C. (eds.) EMO 2015. LNCS, vol. 9019, pp. 95–109. Springer, Heidelberg (2015)
Mersmann, O., Bischl, B., Trautmann, H., Preuss, M., Weihs, C., Rudolph, G.: Exploratory landscape analysis. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, GECCO 2011, New York, NY, USA, pp. 829–836. ACM (2011)
Rudolph, G., Naujoks, B., Preuss, M.: Capabilities of EMOA to detect and preserve equivalent pareto subsets. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 36–50. Springer, Heidelberg (2007)
Verel, S., Liefooghe, A., Jourdan, L., Dhaenens, C.: On the structure of multiobjective combinatorial search space: MNK-landscapes with correlated objectives. Eur. J. Oper. Res. 227(2), 331–342 (2013)
Wessing, S.: Two-stage methods for multimodal optimization. Ph.D. thesis, Technische Universität Dortmund (2015). http://hdl.handle.net/2003/34148
Acknowledgments
Heike Trautmann, Pascal Kerschke, Mike Preuss and Christian Grimme acknowledge support by the European Research Center for Information Systems (ERCIS).
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Kerschke, P. et al. (2016). Towards Analyzing Multimodality of Continuous Multiobjective Landscapes. 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_90
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DOI: https://doi.org/10.1007/978-3-319-45823-6_90
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