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2020 | OriginalPaper | Chapter

Bayesian Optimization Approaches for Massively Multi-modal Problems

Authors : Ibai Roman, Alexander Mendiburu, Roberto Santana, Jose A. Lozano

Published in: Learning and Intelligent Optimization

Publisher: Springer International Publishing

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Abstract

The optimization of massively multi-modal functions is a challenging task, particularly for problems where the search space can lead the optimization process to local optima. While evolutionary algorithms have been extensively investigated for these optimization problems, Bayesian Optimization algorithms have not been explored to the same extent. In this paper, we study the behavior of Bayesian Optimization as part of a hybrid approach for solving several massively multi-modal functions. We use well-known benchmarks and metrics to evaluate how different variants of Bayesian Optimization deal with multi-modality.

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Literature
1.
go back to reference Brochu, E., Cora, V.M., de Freitas, N.: A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning, December 2010. arXiv:1012.2599 Brochu, E., Cora, V.M., de Freitas, N.: A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning, December 2010. arXiv:​1012.​2599
2.
go back to reference Fieldsend, J.E.: Running up those hills: multi-modal search with the niching migratory multi-swarm optimiser. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp. 2593–2600. IEEE (2014) Fieldsend, J.E.: Running up those hills: multi-modal search with the niching migratory multi-swarm optimiser. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp. 2593–2600. IEEE (2014)
4.
go back to reference Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multi-modal function optimisation. In: Proceedings of the of Second International Conference on Genetic Algorithms and Their Applications, pp. 41–49 (1987) Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multi-modal function optimisation. In: Proceedings of the of Second International Conference on Genetic Algorithms and Their Applications, pp. 41–49 (1987)
5.
6.
go back to reference Guhaniyogi, R., Li, C., Savitsky, T.D., Srivastava, S.: A divide-and-conquer Bayesian approach to large-scale kriging, December 2017. arXiv:1712.09767 Guhaniyogi, R., Li, C., Savitsky, T.D., Srivastava, S.: A divide-and-conquer Bayesian approach to large-scale kriging, December 2017. arXiv:​1712.​09767
17.
go back to reference Rasmussen, C.E., Williams, C.K.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)MATH Rasmussen, C.E., Williams, C.K.: Gaussian Processes for Machine Learning. MIT Press, Cambridge (2006)MATH
19.
go back to reference Sareni, B., Krahenbuhl, L.: Fitness sharing and niching methods revisited. IEEE Trans. Evol. Comput. 2(3), 97–106 (1998)CrossRef Sareni, B., Krahenbuhl, L.: Fitness sharing and niching methods revisited. IEEE Trans. Evol. Comput. 2(3), 97–106 (1998)CrossRef
20.
go back to reference Silverman, B.W.: Some aspects of the spline smoothing approach to non-parametric regression curve fitting. J. Roy. Stat. Soc. Series B (Method.) 47(1), 1–52 (1985)MathSciNetMATH Silverman, B.W.: Some aspects of the spline smoothing approach to non-parametric regression curve fitting. J. Roy. Stat. Soc. Series B (Method.) 47(1), 1–52 (1985)MathSciNetMATH
21.
go back to reference Singh, G., Deb, K.: Comparison of multi-modal optimization algorithms based on evolutionary algorithms. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, GECCO 2006, pp. 1305–1312. ACM, New York (2006). https://doi.org/10.1145/1143997.1144200 Singh, G., Deb, K.: Comparison of multi-modal optimization algorithms based on evolutionary algorithms. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, GECCO 2006, pp. 1305–1312. ACM, New York (2006). https://​doi.​org/​10.​1145/​1143997.​1144200
22.
go back to reference Srinivas, N., Krause, A., Kakade, S., Seeger, M.: Gaussian process optimization in the bandit setting: no regret and experimental design. In: Proceedings of the 27th International Conference on Machine Learning (ICML 2010), Haifa, 21–24 June 2010, pp. 1015–1022 (2010). http://www.icml2010.org/papers/422.pdf Srinivas, N., Krause, A., Kakade, S., Seeger, M.: Gaussian process optimization in the bandit setting: no regret and experimental design. In: Proceedings of the 27th International Conference on Machine Learning (ICML 2010), Haifa, 21–24 June 2010, pp. 1015–1022 (2010). http://​www.​icml2010.​org/​papers/​422.​pdf
23.
go back to reference Wang, H., van Stein, B., Emmerich, M., Bäck, T.: Time complexity reduction in efficient global optimization using cluster kriging. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2017, pp. 889–896. ACM, New York (2017). https://doi.org/10.1145/3071178.3071321 Wang, H., van Stein, B., Emmerich, M., Bäck, T.: Time complexity reduction in efficient global optimization using cluster kriging. In: Proceedings of the Genetic and Evolutionary Computation Conference, GECCO 2017, pp. 889–896. ACM, New York (2017). https://​doi.​org/​10.​1145/​3071178.​3071321
24.
go back to reference Wong, K.C., Leung, K.S., Wong, M.H.: Protein structure prediction on a lattice model via multimodal optimization techniques. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, GECCO 2010, pp. 155–162. ACM, New York (2010). https://doi.org/10.1145/1830483.1830513 Wong, K.C., Leung, K.S., Wong, M.H.: Protein structure prediction on a lattice model via multimodal optimization techniques. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, GECCO 2010, pp. 155–162. ACM, New York (2010). https://​doi.​org/​10.​1145/​1830483.​1830513
Metadata
Title
Bayesian Optimization Approaches for Massively Multi-modal Problems
Authors
Ibai Roman
Alexander Mendiburu
Roberto Santana
Jose A. Lozano
Copyright Year
2020
DOI
https://doi.org/10.1007/978-3-030-38629-0_31

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