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Bi-objective decision making in global optimization based on statistical models

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Abstract

A global optimization problem is considered where the objective functions are assumed “black box” and “expensive”. An algorithm is theoretically substantiated using a statistical model of objective functions and the theory of rational decision making under uncertainty. The search process is defined as a sequence of bi-objective selections of sites for the computation of the objective function values. It is shown that two well known (the maximum average improvement, and the maximum improvement probability) algorithms are special cases of the proposed general approach.

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Acknowledgements

The research of A. Žilinskas was supported by the Research Council of Lithuania under Grant No. P-MIP-17-61. The research of James Calvin was supported by the National Science Foundation under Grant No. CMMI-1562466.

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Authors and Affiliations

  1. Institute of Data Science and Digital Technologies, Vilnius University, Akademijos 4, 08663, Vilnius, Lithuania

    Antanas Žilinskas

  2. Department of Computer Science, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    James Calvin

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  1. Antanas Žilinskas
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  2. James Calvin
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Correspondence to Antanas Žilinskas.

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Žilinskas, A., Calvin, J. Bi-objective decision making in global optimization based on statistical models. J Glob Optim 74, 599–609 (2019). https://doi.org/10.1007/s10898-018-0622-5

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