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A Multicriteria Generalization of Bayesian Global Optimization

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Book cover Advances in Stochastic and Deterministic Global Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 107))

Abstract

This chapter discusses a generalization of the expected improvement used in Bayesian global optimization to the multicriteria optimization domain, where the goal is to find an approximation to the Pareto front. The expected hypervolume improvement (EHVI) measures improvement as the gain in dominated hypervolume relative to a given approximation to the Pareto front. We will review known properties of the EHVI, applications in practice and propose a new exact algorithm for computing EHVI. The new algorithm has asymptotically optimal time complexity O(nlogn). This improves existing computation schemes by a factor of n∕logn. It shows that this measure, at least for a small number of objective functions, is as fast as other simpler measures of multicriteria expected improvement that were considered in recent years.

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Acknowledgements

Hao Wang gratefully acknowledges support by the Netherlands Organisation for Scientific Research, NWO ICT PPP Project Grant “Process mining for multi-objective online control (PROMIMOOC)”. Kaifeng Yang acknowledges financial support from China Scholarship Council (CSC), CSC No. 201306370037.

Author information

Authors and Affiliations

  1. Multiobjective Optimization and Decision Analysis (MODA) Research Group, LIACS, Faculty of Science, Leiden University, Leiden, The Netherlands

    Michael Emmerich, Kaifeng Yang, André Deutz & Hao Wang

  2. CISUC, Department of Informatics Engineering, University of Coimbra, Polo II, Pinhal de Marrocos, P-3030 290, Coimbra, Portugal

    Carlos M. Fonseca

Authors
  1. Michael Emmerich
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  2. Kaifeng Yang
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  3. André Deutz
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  4. Hao Wang
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  5. Carlos M. Fonseca
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Corresponding author

Correspondence to André Deutz .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Cardiff School of Mathematics, Cardiff University, Cardiff, United Kingdom

    Anatoly Zhigljavsky

  3. Institute of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

    Julius Žilinskas

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Emmerich, M., Yang, K., Deutz, A., Wang, H., Fonseca, C.M. (2016). A Multicriteria Generalization of Bayesian Global Optimization. In: Pardalos, P., Zhigljavsky, A., Žilinskas, J. (eds) Advances in Stochastic and Deterministic Global Optimization. Springer Optimization and Its Applications, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-29975-4_12

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