Integer programming formulations for the elementary shortest path problem

•We compare integer programming formulations for the elementary shortest path problem.•We describe IP formulations with exponentially-many SECs and MIP extended formulations of polynomial size.•We study the polyhedral structure of the two strongest formulations and prove their LP bounds are equivale...

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Vydané v:European journal of operational research Ročník 252; číslo 1; s. 122 - 130
Hlavný autor: Taccari, Leonardo
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.07.2016
Elsevier Sequoia S.A
Predmet:
Branch-and-cut
Comparative analysis
Computation
Costs
Effectiveness studies
Elementary shortest path
Extended formulations
Formulations
Graph theory
Graphs
Inequalities
Integer programming
Linear programming
Mathematical analysis
Mathematical problems
Polyhedra
Shortest path algorithms
Shortest-path problems
Subtour elimination constraints
Integer programming
Subtour elimination constraints
Extended formulations
Branch-and-cut
Elementary shortest path
ISSN:0377-2217, 1872-6860
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Popis
Shrnutí:•We compare integer programming formulations for the elementary shortest path problem.•We describe IP formulations with exponentially-many SECs and MIP extended formulations of polynomial size.•We study the polyhedral structure of the two strongest formulations and prove their LP bounds are equivalent.•We report computational results for the LP relaxations and for the full branch-and-cut.•Formulation with dynamically generated cutset inequalities is the most effective. Given a directed graph G=(V,A) with arbitrary arc costs, the Elementary Shortest Path Problem (ESPP) consists of finding a minimum-cost path between two nodes s and t such that each node of G is visited at most once. If negative costs are allowed, the problem is NP-hard. In this paper, several integer programming formulations for the ESPP are compared. We present analytical results based on a polyhedral study of the formulations, and computational experiments where we compare their linear programming relaxation bounds and their behavior within a branch-and-cut framework. The computational results show that a formulation with dynamically generated cutset inequalities is the most effective.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2016.01.003