Decision uncertainty in multiobjective optimization

Gabriele Eichfelder (), Corinna Krüger () and Anita Schöbel ()
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Gabriele Eichfelder: Technische Universität Ilmenau
Corinna Krüger: University of Goettingen
Anita Schöbel: University of Goettingen

Journal of Global Optimization, 2017, vol. 69, issue 2, No 9, 485-510

Abstract: Abstract In many real-world optimization problems, a solution cannot be realized in practice exactly as computed, e.g., it may be impossible to produce a board of exactly 3.546 mm width. Whenever computed solutions are not realized exactly but in a perturbed way, we speak of decision uncertainty. We study decision uncertainty in multiobjective optimization problems and we propose the concept of decision robust efficiency for evaluating the robustness of a solution in this case. This solution concept is defined by using the framework of set-valued maps. We prove that convexity and continuity are preserved by the resulting set-valued maps. Moreover, we obtain specific results for particular classes of objective functions that are relevant for solving the set-valued problem. We furthermore prove that decision robust efficient solutions can be found by solving a deterministic problem in case of linear objective functions. We also investigate the relationship of the proposed concept to other concepts in the literature.

Keywords: Decision uncertainty; Multiobjective optimization; Robust optimization; Set-valued optimization (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s10898-017-0518-9

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