Decision uncertainty in multiobjective optimization
Eichfelder G, Krueger C, Schoebel A (2017)
Publication Type: Journal article
Publication year: 2017
Journal
Book Volume: 69
Pages Range: 485-510
Journal Issue: 2
DOI: 10.1007/s10898-017-0518-9
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.
Involved external institutions
Germany (DE)How to cite
APA:
Eichfelder, G., Krueger, C., & Schoebel, A. (2017). Decision uncertainty in multiobjective optimization. Journal of Global Optimization, 69(2), 485-510. https://dx.doi.org/10.1007/s10898-017-0518-9
MLA:
Eichfelder, Gabriele, Corinna Krueger, and Anita Schoebel. "Decision uncertainty in multiobjective optimization." Journal of Global Optimization 69.2 (2017): 485-510.
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