Arc flow formulations based on dynamic programming: Theoretical foundations and applications

Vinícius L. de Lima, Cláudio Alves, François Clautiaux, Manuel Iori and José M. Valério de Carvalho

European Journal of Operational Research, 2022, vol. 296, issue 1, 3-21

Abstract: Network flow formulations are among the most successful tools to solve optimization problems. Such formulations correspond to determining an optimal flow in a network. One particular class of network flow formulations is the arc flow, where variables represent flows on individual arcs of the network. For NP-hard problems, polynomial-sized arc flow models typically provide weak linear relaxations and may have too much symmetry to be efficient in practice. Instead, arc flow models with a pseudo-polynomial size usually provide strong relaxations and are efficient in practice. The interest in pseudo-polynomial arc flow formulations has grown considerably in the last twenty years, in which they have been used to solve many open instances of hard problems. A remarkable advantage of pseudo-polynomial arc flow models is the possibility to solve practical-sized instances directly by a Mixed Integer Linear Programming solver, avoiding the implementation of complex methods based on column generation.

Keywords: Combinatorial optimization; Arc flow; Dynamic programming; Acyclic network; Pseudo-polynomial (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:296:y:2022:i:1:p:3-21

DOI: 10.1016/j.ejor.2021.04.024

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