A Multicriteria Generalization of Bayesian Global Optimization

  • Michael Emmerich
  • Kaifeng Yang
  • André DeutzEmail author
  • Hao Wang
  • Carlos M. Fonseca
Part of the Springer Optimization and Its Applications book series (SOIA, volume 107)


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.


Bayesian Global Optimization Expected Hypervolume Improvement Computation Complexity 



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.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Michael Emmerich
    • 1
  • Kaifeng Yang
    • 1
  • André Deutz
    • 1
    Email author
  • Hao Wang
    • 1
  • Carlos M. Fonseca
    • 2
  1. 1.Multiobjective Optimization and Decision Analysis (MODA) Research Group, LIACS, Faculty of ScienceLeiden UniversityLeidenThe Netherlands
  2. 2.CISUC, Department of Informatics EngineeringUniversity of CoimbraCoimbraPortugal

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