A Branch & Cut Algorithm for the Asymmetric Traveling Salesman Problem with Precedence Constraints
Please always quote using this URN: urn:nbn:de:0297-zib-3391
- In this paper we consider a variant of the classical ATSP, namely the asymmetric Hamiltonian path problem (or equivalently ATSP) with precedence constraints. In this problem precedences among the nodes are present, stating that a certain node has to precede others in any feasible sequence. This problem occurs as a basic model in scheduling and routing and has a wide range of applications varying from helicopter routing[Timlin89], sequencing in flexible manufacturing [AscheuerEscuderoGroetschelStoer90,AscheuerEscuderoGroetschelStoer93], to stacker crane routing in an automatic storage system[Ascheuer95]. We give an integer programming model and summarize known classes of valid inequalities. We describe in detail the implementation of a branch&-cut algorithm and give computational results on real world instances and benchmark problems from TSPLIB. The results we achieve indicate that our implementation outperforms other implementations found in the literature. Real world instances up to 174 nodes could be solved to optimality within a few minutes of CPU-time. As a side product we obtained a branch&cut-algorithm for the ATSP. All instances in TSPLIB could be solved to optimality in a reasonable amount of computing time.
Author: | Norbert Ascheuer, Michael Jünger, Gerhard Reinelt |
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Document Type: | ZIB-Report |
Date of first Publication: | 1997/12/19 |
Series (Serial Number): | ZIB-Report (SC-97-70) |
ZIB-Reportnumber: | SC-97-70 |
Published in: | Appeared in: Computational Optimization and Applications, 17(1):61-84 (2000) |