Decision making in multiobjective optimization problems under uncertainty: balancing between robustness and quality

Yue Zhou-Kangas () and Kaisa Miettinen ()
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Yue Zhou-Kangas: University of Jyväskylä, Faculty of Information Technology
Kaisa Miettinen: University of Jyväskylä, Faculty of Information Technology

OR Spectrum: Quantitative Approaches in Management, 2019, vol. 41, issue 2, No 3, 413 pages

Abstract: Abstract As an emerging research field, multiobjective robust optimization employs minmax robustness as the most commonly used concept. Light robustness is a concept in which a parameter, tolerable degradations, can be used to control the loss in the objective function values in the most typical scenario for gaining in robustness. In this paper, we develop a lightly robust interactive multiobjective optimization method, LiRoMo, to support a decision maker to find a most preferred lightly robust efficient solution with a good balance between robustness and the objective function values in the most typical scenario. In LiRoMo, we formulate a lightly robust subproblem utilizing an achievement scalarizing function which involves a reference point specified by the decision maker. With this subproblem, we compute lightly robust efficient solutions with respect to the decision maker’s preferences. With LiRoMo, we support the decision maker in understanding the lightly robust efficient solutions with an augmented value path visualization. We use two measures ‘price to be paid for robustness’ and ‘gain in robustness’ to support the decision maker in considering the trade-offs between robustness and quality. As an example to illustrate the advantages of the method, we formulate and solve a simple investment portfolio optimization problem.

Keywords: Multiobjective robust optimization; Interactive methods; Light robust efficiency; Handling uncertainty; Trade-off between robustness and quality; Decision support (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s00291-018-0540-4

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