 New formulations for the elementary shortest-path problem visiting a given set of nodesRafael Castro de Andrade European Journal of Operational Research, 2016, vol. 254, issue 3, 755-768 Abstract: Consider a directed graph G=(V,A) with a set of nodes V and a set of arcs A, and let cuv denote the length of an arc uv ∈ A. Given two nodes s and t of V, we are interested in the problem of determining a shortest-path from s to t in G that must visit only once all nodes of a given set P⊆V−{s,t}. This problem is NP-hard for P=V−{s,t}. In this paper, we develop three new compact formulations for this problem. The first one is based on the spanning tree polytope. The second model is a primal-dual mixed integer model presenting a small number of variables and constraints; and the last one is obtained from a flow-based compact model for the Steiner traveling salesman problem (TSP). Numerical experiments indicate that the second compact model allows the efficient solution of randomly generated and benchmark (from the TSPLIB) instances of the problem with hundreds of nodes. Keywords: Combinatorial optimization; Shortest-path visiting given nodes; Compact extended formulation; Primal-dual formulation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:254:y:2016:i:3:p:755-768 DOI: 10.1016/j.ejor.2016.05.008 Access Statistics for this article European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati More articles in European Journal of Operational Research from Elsevier |
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