## Optimization of a 532-city symmetric traveling salesman problem by branch and cut.(English)Zbl 0618.90082

We report the solution to optimality of a 532-city symmetric traveling salesman problem involving the optimization over 141 246 zero-one variables. The results of an earlier study by H. Crowder and M. Padberg [Manage. Sci. 26, 495-509 (1980; Zbl 0444.90068)] are cross- validated. In this note we briefly outline the methodology, algorithms and software system that we developed to obtain these results.

### MSC:

 90C27 Combinatorial optimization 90C35 Programming involving graphs or networks 65K05 Numerical mathematical programming methods

Zbl 0444.90068
Full Text:

### References:

 [1] Crowder, H.; Padberg, M., Solving large-scale symmetric travelling salesman problems to optimality, Management science, 26, 495-509, (1980) · Zbl 0444.90068 [2] Dantzig, G.; Fulkerson, R.; Johnson, S., Solution of a large-scale traveling salesman problem, Operations research, 2, 393-410, (1954) · Zbl 1414.90372 [3] Dantzig, G.; Fulkerson, R.; Johnson, S., On a linear programming combinatorial approach to the traveling salesman problem, Operations research, 7, 58-66, (1959) · Zbl 1414.90211 [4] Grötschel, M., On the symmetric travelling salesman problem: solution of 120-city problem, Mathematical programming studies, 12, 61-77, (1980) · Zbl 0435.90070 [5] Grötschel, M.; Padberg, M., Polyhedral theory, (), 251-305 · Zbl 0587.90073 [6] Held, M.; Karp, R., The traveling salesman problem and minimum spanning trees: part II, Mathematical programming, 1, 6-26, (1971) · Zbl 0232.90038 [7] Lin, S.; Kernighan, B., An effective heuristic algorithm for the traveling salesman problem, Operations research, 21, 498-516, (1973) · Zbl 0256.90038 [8] Marsten, R., The design of the XMP linear programming libary, ACM transactions of mathematical software, 7, 481-497, (1981) [9] Padberg, M.; Grötschel, M., Polyhedral computations, (), 307-360 · Zbl 0587.90074 [10] Padberg, M.; Hong, S., On the symmetric traveling salesman problem: A computational study, Mathematical programming studies, 12, 78-107, (1980) · Zbl 0435.90071 [11] M. Padberg and G. Rinaldi, “An LP-based algorithm for the resolution of large-scale traveling salesman problems”, Preprint, New York University, New York, in preparation. · Zbl 0734.90060 [12] Rinaldi, G.; Padberg, M., An efficient algorithm for the minimum capacity cut problem in large sparse graphs, (1985), IASI-CNR Rome, Preprint [13] Rinaldi, G.; Yarrow, L.A., Optimizing a 48-city traveling salesman problem: A case study in combinatorial problem solving, (1985), IASI-CNR Rome, Preprint R.122
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