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2015 | OriginalPaper | Buchkapitel

A Bayesian Approach to Constrained Multi-objective Optimization

verfasst von : Paul Feliot, Julien Bect, Emmanuel Vazquez

Erschienen in: Learning and Intelligent Optimization

Verlag: Springer International Publishing

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Abstract

This paper addresses the problem of derivative-free multi-objective optimization of real-valued functions under multiple inequality constraints. Both the objective and constraint functions are assumed to be smooth, nonlinear, expensive-to-evaluate functions. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited. The method we propose to overcome this difficulty has its roots in the Bayesian and multi-objective optimization literatures. More specifically, we make use of an extended domination rule taking both constraints and objectives into account under a unified multi-objective framework and propose a generalization of the expected improvement sampling criterion adapted to the problem. A proof of concept on a constrained multi-objective optimization test problem is given as an illustration of the effectiveness of the method.

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Vorheriges Kapitel A Practical Case of the Multiobjective Knapsack Problem: Design, Modelling, Tests and Analysis

Nächstes Kapitel Solving Large MultiZenoTravel Benchmarks with Divide-and-Evolve

Au, S.K., Beck, J.L.: Estimation of small failure probabilities in high dimensions by subset simulation. Probab. Eng. Mech. 16(4), 263–277 (2001)CrossRef

Bader, J., Zitzler, E.: Hype: An algorithm for fast hypervolume-based many-objective optimization. Evol. Comput. 19(1), 45–76 (2011)CrossRef

Benassi, R., Bect, J., Vazquez, E.: Bayesian optimization using sequential Monte Carlo. In: Hamadi, Y., Schoenauer, M. (eds.) LION 2012. LNCS, vol. 7219, pp. 339–342. Springer, Heidelberg (2012) CrossRef

Emmerich, M.T.M., Giannakoglou, K.C., Naujoks, B.: Single- and multi-objective evolutionary optimization assisted by Gaussian random field metamodels. IEEE Trans. Evol. Comput. 10(4), 421–439 (2006)CrossRef

Emmerich, M., Klinkenberg, J.W.: The computation of the expected improvement in dominated hypervolume of Pareto front approximations. Leiden University, Rapport Technique (2008)

Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation. IEEE Trans. Syst. Man Cybern. B Cybern. Part A: Syst. Hum. 28(1), 26–37 (1998)

Gramacy, R.L., Lee, H.: Optimization under unknown constraints. In: Bayesian Statistics 9. In: Proceedings of the Ninth Valencia International Meeting, pp. 229–256. Oxford University Press (2011)

Hupkens, I., Emmerich, M., Deutz, A.: Faster computation of expected hypervolume improvement. arXiv preprint arXiv:1408.7114 (2014)

Jeong, S., Minemura, Y., Obayashi, S.: Optimization of combustion chamber for diesel engine using kriging model. J. Fluid Sci. Technol. 1(2), 138–146 (2006)CrossRef

10.

Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Global Optim. 13(4), 455–492 (1998)CrossRefMATHMathSciNet

11.

Li, L., Bect, J., Vazquez, E.: Bayesian Subset Simulation: a kriging-based subset simulation algorithm for the estimation of small probabilities of failure. In: Proceedings of PSAM 2011 & ESREL 2012, 25–29 June 2012, Helsinki, Finland. IAPSAM (2012)

12.

Liu, J.S.: Monte Carlo strategies in scientific computing. Springer, Heidelberg (2008)

13.

Mockus, J.: Application of bayesian approach to numerical methods of global and stochastic optimization. J. Global Optim. 4(4), 347–365 (1994)CrossRefMATHMathSciNet

14.

Osyczka, A., Kundu, S.: A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm. Struct. Optim. 10(2), 94–99 (1995)CrossRef

15.

Oyama, A., Shimoyama, K., Fujii, K.: New constraint-handling method for multi-objective and multi-constraint evolutionary optimization. Trans. Jpn. Soc. Aeronaut. Space Sci. 50(167), 56–62 (2007)CrossRef

16.

Parr, J.M., Keane, A.J., Forrester, A.I.J., Holden, C.M.E.: Infill sampling criteria for surrogate-based optimization with constraint handling. Eng. Optim. 44(10), 1147–1166 (2012)CrossRef

17.

Picheny, V.: Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction. Stat. Comput. 16 p. (2014). doi:10.1007/s11222-014-9477-x

18.

Picheny, V.: A stepwise uncertainty reduction approach to constrained global optimization. In: Proceedings of the 17th International Conference on Artificial Intelligence and Statistics (AISTATS), Reykjavik, Iceland. vol. 33, pp. 787–795. JMLR: W&CP (2014)

19.

Ray, T., Tai, K., Seow, K.C.: Multiobjective design optimization by an evolutionary algorithm. Eng. Optim. 33(4), 399–424 (2001)CrossRef

20.

Sasena, M.J., Papalambros, P., Goovaerts, P.: Exploration of metamodeling sampling criteria for constrained global optimization. Eng. Optim. 34(3), 263–278 (2002)CrossRef

21.

Schonlau, M., Welch, W.J., Jones, D.R.: Global versus local search in constrained optimization of computer models. In: New Developments and Applications in Experimental Design: Selected Proceedings of a 1997 Joint AMS-IMS-SIAM Summer Conference. IMS Lecture Notes-Monographs Series, vol. 34, pp. 11–25. Institute of Mathematical Statistics (1998)

22.

Shimoyama, K., Sato, K., Jeong, S., Obayashi, S.: Updating kriging surrogate models based on the hypervolume indicator in multi-objective optimization. J. Mech. Des. 135(9), 094503 (2013)CrossRef

23.

Wagner, T., Emmerich, M., Deutz, A., Ponweiser, W.: On expected-improvement criteria for model-based multi-objective optimization. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 718–727. Springer, Heidelberg (2010)

Titel: A Bayesian Approach to Constrained Multi-objective Optimization
verfasst von: Paul Feliot
Julien Bect
Emmanuel Vazquez
Verlag: Springer International Publishing
Buch: Learning and Intelligent Optimization
Print ISBN: 978-3-319-19083-9

Electronic ISBN: 978-3-319-19084-6

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-19084-6_24

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