Truncated expected hypervolume improvement: Exact computation and application

Kaifeng Yang, Andre Deutz, Zhiwei Yang, Thomas Back, Michael Emmerich

Research output: Chapter in Book/Report/Conference proceedingsConference contributionpeer-review

19 Citations (Scopus)

Abstract

In optimization with expensive black box evaluations, the expected improvement algorithm (also called efficient global optimization) is a commonly applied method. It uses Gaussian Processes (or Kriging) to build a model of the objective function and uses the expected improvement as an infill criterion, taking into account both - predictive mean and variance. It has been generalized to multi-objective optimization using the expected hypervolume improvement, which measures the expected gain in the hypervolume indicator of a Pareto front approximation. However, this criterion assumes an unbounded objective space even if it is often known a-priori that the objective function values are within a prescribed range, e.g., lower bounded by zero. To take advantage of such a-priori knowledge, this paper introduces the truncated expected hypervolume improvement and a multiobjective efficient global optimization method that is based on it. In this paper it is shown how to compute the truncated expected hypervolume improvement exactly and efficiently. Then it is tested as an infill criterion in efficient global optimization. It is shown that it can effectively make use of a-priori knowledge and achieve better results in cases where such knowledge is given. The usefulness of the new approach is demonstrated in benchmark examples and applications from robust PID (proportionalintegral-derivative) controller optimization. The empirical studies in this paper are confined to the bi-objective case.

Original languageEnglish
Title of host publication2016 IEEE Congress on Evolutionary Computation, CEC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4350-4357
Number of pages8
ISBN (Electronic)9781509006229
DOIs
Publication statusPublished - 14 Nov 2016
Event2016 IEEE Congress on Evolutionary Computation, CEC 2016 - Vancouver, Canada
Duration: 24 Jul 201629 Jul 2016

Publication series

Name2016 IEEE Congress on Evolutionary Computation, CEC 2016

Conference

Conference2016 IEEE Congress on Evolutionary Computation, CEC 2016
Country/TerritoryCanada
CityVancouver
Period24.07.201629.07.2016

Keywords

  • Efficient Global Optimization
  • Expected Hypervolume Improvement
  • Robust PID Parameter Tuning
  • Truncated Normal Distribution

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