Integer programming formulations for the elementary shortest path problem - Taccari, Leonardo (European journal of operational research, 2016)
•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.