Abstract
The Precedence Constrained Line Traveling Salesman is a variant of the Traveling Salesman Problem, where the cities to be visited lie on a line, the distance between two cities is the absolute difference between their abscissae and a partial ordering is given on the set of cities. Such a problem is encountered on linear construction schemes for instance. Using key dominance properties and lower bounds, we design a call-based dynamic program able to solve instances with up to 450 cities.
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de la Banda, M.G., Stuckey, P.J.: Dynamic programming to minimize the maximum number of open stacks. INFORMS Journal on Computing 19(4), 607–617 (2007)
Brightwell, G.: Models of random partial orders, pp. 53–84. Cambridge University Press (1993)
Charikar, M., Motwani, R., Raghavan, P., Silverstein, C.: Constrained tsp and low-power computing. In: Dehne, F., Rau-Chaplin, A., Sack, J.-R., Tamassia, R. (eds.) WADS 1997. LNCS, vol. 1272, pp. 104–115. Springer, Heidelberg (1997)
Cutler, M.: Efficient special case algorithms for the n-line planar traveling salesman problem. Networks 10(3), 183–195 (1980)
Deineko, V.G., van Dal, R., Rote, G.: The convex-hull-and-line traveling salesman problem: A solvable case. Information Processing Letters 51(3), 141–148 (1994)
Deineko, V.G., Woeginger, G.J.: The convex-hull-and-k-line travelling salesman problem. Inf. Process. Lett. 59(6), 295–301 (1996)
Held, M., Karp, R.M.: A dynamic programming approach to sequencing problems. In: Proceedings of the 1961 16th ACM National Meeting, pp. 71.201–71.204. ACM, New York (1961)
Jeanjean, A.: Resource scheduling optimization in mass transportation problems. In: 12th International Conference on Project Management and Scheduling, PMS 2010 (2010)
Jeanjean, A.: Recherche locale pour l’optimisation en variables mixtes: Méthodologie et applications industrielles. Ph.D. thesis, Laboratoire d’informatique de Polytechnique (2011)
Johnson, D.S., Mcgeoch, L.A.: The Traveling Salesman Problem: A Case Study in Local Optimization. John Wiley and Sons, Chichester (1997)
Rosenkrantz, D.J., Stearns, R.E., Lewis II, P.M.: An analysis of several heuristics for the traveling salesman problem.  6(3), 563–581 (1977)
Rote, G.: The n-line traveling salesman problem. Networks 22, 91–108 (1991)
Tsitsiklis, J.N.: Special cases of traveling salesman and repairman problems with time windows. Networks 22, 263–282 (1992)
Gehrlein, V.W.: On methods for generating random partial orders. Operations Research Letters 5(6), 285–291 (1986)
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Benoist, T., Jeanjean, A., Jost, V. (2014). Call-Based Dynamic Programming for the Precedence Constrained Line Traveling Salesman. In: Simonis, H. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2014. Lecture Notes in Computer Science, vol 8451. Springer, Cham. https://doi.org/10.1007/978-3-319-07046-9_1
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DOI: https://doi.org/10.1007/978-3-319-07046-9_1
Publisher Name: Springer, Cham
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