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Stochastic multi-objective optimization: a survey on non-scalarizing methods

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  • Walter Gutjahr
  • Alois Pichler

Abstract

Currently, stochastic optimization on the one hand and multi-objective optimization on the other hand are rich and well-established special fields of Operations Research. Much less developed, however, is their intersection: the analysis of decision problems involving multiple objectives and stochastically represented uncertainty simultaneously. This is amazing, since in economic and managerial applications, the features of multiple decision criteria and uncertainty are very frequently co-occurring. Part of the existing quantitative approaches to deal with problems of this class apply scalarization techniques in order to reduce a given stochastic multi-objective problem to a stochastic single-objective one. The present article gives an overview over a second strand of the recent literature, namely methods that preserve the multi-objective nature of the problem during the computational analysis. We survey publications assuming a risk-neutral decision maker, but also articles addressing the situation where the decision maker is risk-averse. In the second case, modern risk measures play a prominent role, and generalizations of stochastic orders from the univariate to the multivariate case have recently turned out as a promising methodological tool. Modeling questions as well as issues of computational solution are discussed. Copyright Springer Science+Business Media New York 2016

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  • Walter Gutjahr & Alois Pichler, 2016. "Stochastic multi-objective optimization: a survey on non-scalarizing methods," Annals of Operations Research, Springer, vol. 236(2), pages 475-499, January.
  • Handle: RePEc:spr:annopr:v:236:y:2016:i:2:p:475-499:10.1007/s10479-013-1369-5
    DOI: 10.1007/s10479-013-1369-5
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    6. Yue Zhou-Kangas & Kaisa Miettinen, 2019. "Decision making in multiobjective optimization problems under uncertainty: balancing between robustness and quality," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(2), pages 391-413, June.
    7. Milford, James & Henrion, Max & Hunter, Chad & Newes, Emily & Hughes, Caroline & Baldwin, Samuel F., 2022. "Energy sector portfolio analysis with uncertainty," Applied Energy, Elsevier, vol. 306(PA).
    8. Ahmadi-Javid, Amir & Fallah-Tafti, Malihe, 2019. "Portfolio optimization with entropic value-at-risk," European Journal of Operational Research, Elsevier, vol. 279(1), pages 225-241.
    9. Young Gwan Lee & Kihyun Park & Hyun Jae Kim & Seong-Hoon Cho, 2023. "Creating portfolios of firm-specific energy R&D investment under market uncertainty," Energy & Environment, , vol. 34(5), pages 1548-1563, August.
    10. Juan Ribes & Jacinto González-Pachón, 2021. "Risk Attitude in Multicriteria Decision Analysis: A Compromise Approach," IJERPH, MDPI, vol. 18(12), pages 1-14, June.
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