On expected-improvement criteria for model-based multi-objective optimization

Authors:
Tobias Wagner;Michael Emmerich;André Deutz;Wolfgang Ponweiser
Affiliations:
Institute of Machining Technology, Technische Universität Dortmund, Dortmund, Germany;Leiden Institute of Advanced Computer Science, Universiteit Leiden, Leiden, The Netherlands;Leiden Institute of Advanced Computer Science, Universiteit Leiden, Leiden, The Netherlands;Automation and Control Institute, Vienna University of Technology, Vienna, Austria
Venue:
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Year:
2010

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Abstract

Surrogate models, as used for the Design and Analysis of Computer Experiments (DACE), can significantly reduce the resources necessary in cases of expensive evaluations. They provide a prediction of the objective and of the corresponding uncertainty, which can then be combined to a figure of merit for a sequential optimization. In singleobjective optimization, the expected improvement (EI) has proven to provide a combination that balances successfully between local and global search. Thus, it has recently been adapted to evolutionary multi-objective optimization (EMO) in different ways. In this paper, we provide an overview of the existing EI extensions for EMO and propose new formulations of the EI based on the hypervolume. We set up a list of necessary and desirable properties, which is used to reveal the strengths and weaknesses of the criteria by both theoretical and experimental analyses.