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旅行商问题


TravelingSalesmanProblem

旅行商问题是图论中的一个问题,要求销售员通过 n 个城市的最有效率的(即总距离最短的)哈密顿回路。目前还没有通用的解法,该问题是 NP-hard 问题。

Wolfram 语言命令FindShortestTour[g] 尝试找到最短路径,对于 哈密顿图 G,如果它返回的列表的第一个元素等于 顶点数,则该最短路径是一个哈密顿回路(初始顶点在末尾重复)。

在电视剧《数字追凶》(NUMB3RS) 第二季的剧集“Rampage”(2006 年)中,角色拉里·弗莱恩哈特提到了旅行商问题。


另请参阅

蚁群算法, 中国邮递员问题, 树枝状体, 哈密顿回路, 最长路径, 优化, 普拉托问题, 道路着色问题, 旅行商常数

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参考文献

Applegate, D.; Bixby, R.; Chvatal, V.; and Cook, W. "Finding Cuts in the TSP (a Preliminary Report)." Technical Report 95-05, DIMACS. Piscataway NJ: Rutgers University, 1995.Applegate, D.; Bixby, R.; Chvatal, V.; and Cook, W. "Solving Traveling Salesman Problems." http://www.tsp.gatech.edu/.Hoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, pp. 168-169, 1998.Kruskal, J. B. "On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem." Proc. Amer. Math. Soc. 7, 48-50, 1956.Lawler, E.; Lenstra, J.; Rinnooy Kan, A.; and Shmoys, D. The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization. New York: Wiley, 1985.Lin, S. "Computer Solutions of the Traveling Salesman Problem." Bell System Tech. J. 44, 2245-2269, 1965.Platzman, L. K. and Bartholdi, J. J. "Spacefilling Curves and the Planar Travelling Salesman Problem." J. Assoc. Comput. Mach. 46, 719-737, 1989.Reinelt, G. "TSPLIB--A Traveling Salesman Problem Library." ORSA J. Comput. 3, 376-384, 1991.Rosenkrantz, D. J.; Stearns, R. E.; and Lewis, P. M. "An Analysis of Several Heuristics for the Traveling Salesman Problem." SIAM J. Comput. 6, 563-581, 1977.Skiena, S. "Traveling Salesman Tours." §5.3.5 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 199-202, 1990.Skiena, S. S. "Traveling Salesman Problem." §8.5.4 in The Algorithm Design Manual. New York: Springer-Verlag, pp. 319-322, 1997.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, pp. 120-121, 1999.

请引用为

Weisstein, Eric W. "旅行商问题。" 来自 MathWorld--Wolfram Web 资源。 https://mathworld.net.cn/TravelingSalesmanProblem.html

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