The Weighted Linear Ordering Problem

Jessica Hautz (), Philipp Hungerländer (), Tobias Lechner (), Kerstin Maier () and Peter Rescher ()
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Jessica Hautz: Alpen-Adria-Universität Klagenfurt
Philipp Hungerländer: Alpen-Adria-Universität Klagenfurt
Tobias Lechner: Alpen-Adria-Universität Klagenfurt
Kerstin Maier: Alpen-Adria-Universität Klagenfurt
Peter Rescher: Alpen-Adria-Universität Klagenfurt

A chapter in Operations Research Proceedings 2019, 2020, pp 223-229 from Springer

Abstract: Abstract In this work, we introduce and analyze an extension of the Linear Ordering Problem ( LOP) . The LOP aims to find a simultaneous permutation of rows and columns of a given weight matrix such that the sum of the weights in the upper triangle is maximized. We propose the weighted Linear Ordering Problem ( wLOP) that additionally considers individual node weights. First, we argue that in several applications of the LOP the optimal ordering obtained by the wLOP is a worthwhile alternative to the optimal solution of the LOP. Additionally, we show that the wLOP constitutes a generalization of the well-known Single Row Facility Layout Problem. We introduce an Integer Linear Programming formulation as well as a Variable Neighborhood Search for solving the wLOP. Finally, we provide a benchmark library and examine the efficiency of our exact and heuristic approaches on the proposed instances in a computational study.

Keywords: Integer linear programming; Variable neighborhood search; Ordering problem (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-030-48439-2_27

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DOI: 10.1007/978-3-030-48439-2_27

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