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The Theory of Set Tolerances
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, Unites States.
Department of Industrial and Systems Engineering, Center for Applied Optimization, University of Florida, United States.
2014 (English)In: LION 2014: Learning and Intelligent Optimization: Conference Proceedings, 2014, p. 362-377Conference paper, Published paper (Refereed)
##### Abstract [en]

The theory of single upper and lower tolerances for combinatorial minimization problems has been formalized in 2005 for the three types of cost functions sum, product and maximum, and since then shown to be rather useful in creating heuristics and exact algorithms for the Traveling Salesman Problem and related problems. In this paper for these three types of cost functions we extend this theory from single to set tolerances and the related reverse set tolerances. In particular, we characterize specific values of (reverse) set upper and lower tolerances as positive and infinite, and we present a criterion for the uniqueness of an optimal solution to a combinatorial minimization problem. Furthermore, we present formulas or bounds for computing (reverse) set upper and lower tolerances using the relation to their corresponding single tolerance counterparts. Finally, we give formulas for the minimum and maximum (reverse) set upper and lower tolerances using again their corresponding single tolerance counterparts.

2014. p. 362-377
##### Series
Lectures Notes in Computer Science ; 8426
##### National Category
Discrete Mathematics
##### Identifiers
ISBN: 978-3-319-09583-7 (print)ISBN: 978-3-319-09584-4 (electronic)OAI: oai:DiVA.org:umu-100114DiVA, id: diva2:790222
##### Conference
8th Conference on Learning and Intelligent Optimization (LION 2014), Gainesville, Florida, February 16-21, 2014
Available from: 2015-02-23 Created: 2015-02-23 Last updated: 2019-06-26Bibliographically approved

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Jäger, Gerold

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##### By organisation
Department of Mathematics and Mathematical Statistics
##### On the subject
Discrete Mathematics

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Cite
Citation style
• apa
• ieee
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