Decision making in multiobjective optimization problems under uncertainty : balancing between robustness and quality
Zhou-Kangas, Y., & Miettinen, K. (2019). Decision making in multiobjective optimization problems under uncertainty : balancing between robustness and quality. OR Spektrum, 41(2), 391-413. https://doi.org/10.1007/s00291-018-0540-4
Published inOR Spektrum
© The Authors, 2018.
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. ...
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Shavazipour, Babooshka; Kwakkel, Jan H.; Miettinen, Kaisa (Elsevier BV, 2021)This paper proposes a novel optimization approach for multi-scenario multi-objective robust decision making, as well as an alternative way for scenario discovery and identifying vulnerable scenarios even before any solution ...
Zhou-Kangas, Yue (Jyväskylän yliopisto, 2018)Practical optimization problems usually have multiple objectives, and they also involve uncertainty from different sources. Various robustness concepts have been proposed to handle multiple objectives and the involved ...
Zhou-Kangas, Yue; Miettinen, Kaisa; Sindhya, Karthik (Springer, 2019)We propose an interactive approach to support a decision maker to find a most preferred robust solution to multiobjective optimization problems with decision uncertainty. A new robustness measure that is understandable for ...
Zhou-Kangas, Yue; Miettinen, Kaisa; Sindhya, Karthik (Springer, 2018)In this paper, we introduce the MuRO-NIMBUS method for solving multiobjective optimization problems with uncertain parameters. The concept of set-based minmax robust Pareto optimality is utilized to tackle the uncertainty ...
The price of multiobjective robustness : Analyzing solution sets to uncertain multiobjective problems Schöbel, Anita; Zhou-Kangas, Yue (Elsevier BV, 2021)Defining and finding robust efficient solutions to uncertain multiobjective optimization problems has been an issue of growing interest recently. Different concepts have been published defining what a “robust efficient” ...