A class of lifted path and flow-based formulations for the asymmetric traveling salesman problem with and without precedence constraints

Authors:
Hanif D. Sherali;Subhash C. Sarin;Pei-Fang Tsai
Affiliations:
Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA 24061, United States;Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA 24061, United States;Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA 24061, United States
Venue:
Discrete Optimization
Year:
2006

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Abstract

In this paper, we present a new class of polynomial length formulations for the asymmetric traveling salesman problem (ATSP) by lifting an ordered path-based model using logical restrictions in concert with the Reformulation-Linearization Technique (RLT). We show that a relaxed version of this formulation is equivalent to a flow-based ATSP model, which in turn is tighter than the formulation based on the exponential number of Dantzig-Fulkerson-Johnson (DFJ) subtour elimination constraints. The proposed lifting idea is applied to derive a variety of new formulations for the ATSP, and we explore several dominance relationships among these. We also extend these formulations to include precedence constraints in order to enforce a partial order on the sequence of cities to be visited in a tour. Computational results are presented to exhibit the relative tightness of our formulations and the efficacy of the proposed lifting process.