A multicriteria generalization of Bayesian global optimization

Michael Emmerich, Kaifeng Yang, André Deutz, Hao Wang, Carlos M. Fonseca

Research output: Contribution to journalArticlepeer-review

49 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)229-242
Number of pages14
JournalSpringer Optimization and Its Applications
Publication statusPublished - 2016


  • Bayesian global optimization
  • Computation complexity
  • Expected hypervolume improvement


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