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    Computationally Efficient Approximations for Distributionally Robust Optimization Under Moment and Wasserstein Ambiguity

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    Final_File_Main_08_01_2021.pdf
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    Author
    Cheramin, Meysam
    Cheng, Jianqiang
    Jiang, Ruiwei
    Pan, Kai
    Affiliation
    Department of Systems and Industrial Engineering, University of Arizona
    Issue Date
    2022-05
    Keywords
    distributionally robust optimization
    moment information
    principal component analysis
    semidefinite programming
    stochastic programming
    Wasserstein distance
    
    Metadata
    Show full item record
    Publisher
    Institute for Operations Research and the Management Sciences (INFORMS)
    Citation
    Cheramin, M., Cheng, J., Jiang, R., & Pan, K. (2022). Computationally Efficient Approximations for Distributionally Robust Optimization under Moment and Wasserstein Ambiguity. INFORMS Journal on Computing, 34(3), 1768–1794.
    Journal
    INFORMS Journal on Computing
    Rights
    Copyright © 2022, INFORMS.
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    Distributionally robust optimization (DRO) is a modeling framework in decision making under uncertainty inwhich the probability distribution of a randomparameter is unknown although its partial information (e.g., statistical properties) is available. In this framework, the unknown probability distribution is assumed to lie in an ambiguity set consisting of all distributions that are compatible with the available partial information. Although DRO bridges the gap between stochastic programming and robust optimization, one of its limitations is that its models for large-scale problems can be significantly difficult to solve, especially when the uncertainty is of high dimension. In this paper, we propose computationally efficient inner and outer approximations for DRO problems under a piecewise linear objective function and with a moment-based ambiguity set and a combined ambiguity set including Wasserstein distance and moment information. In these approximations, we split a random vector into smaller pieces, leading to smaller matrix constraints. In addition, we use principal component analysis to shrink uncertainty space dimensionality. We quantify the quality of the developed approximations by deriving theoretical bounds on their optimality gap. We display the practical applicability of the proposed approximations in a production-transportation problemand a multiproduct newsvendor problem. The results demonstrate that these approximations dramatically reduce the computational time while maintaining high solution quality. The approximations also help construct an interval that is tight for most cases and includes the (unknown) optimal value for a large-scale DRO problem, which usually cannot be solved to optimality (or even feasibility in most cases). Summary of Contribution: This paper studies an important type of optimization problem, that is, distributionally robust optimization problems, by developing computationally efficient inner and outer approximations via operations research tools. Specifically, we consider several variants of such problems that are practically important and that admit tractable yet large-scale reformulation. We accordingly utilize random vector partition and principal component analysis to derive efficient approximations with smaller sizes, which, more importantly, provide a theoretical performance guarantee with respect to low optimality gaps. We verify the significant efficiency (i.e., reducing computational time while maintaining high solution quality) of our proposed approximations in solving both production-transportation and multiproduct newsvendor problems via extensive computing experiments.
    Note
    12 month embargo; published online: 26 January 2022
    ISSN
    1091-9856
    EISSN
    1526-5528
    DOI
    10.1287/ijoc.2021.1123
    Version
    Final accepted manuscript
    ae974a485f413a2113503eed53cd6c53
    10.1287/ijoc.2021.1123
    Scopus Count
    Collections
    UA Faculty Publications

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