摘要
对１９９８ 年全国数学建模竞赛的Ｂ组题进行了讨论。将问题视为图论中的旅行售货员问题。首先对顶点进行分组，采用逐次改进法求出每一组的近似最佳售货员回路。根据偏差程度的大小来衡量巡视路线的均衡性，最后得到了均衡性较好的分组路线。在所给条件下，找出完成巡视的最短时间为６．４３ 小时，在这个时间限制下，采用较为合理的分组方法，找出２２ 个组。最后，讨论了在组数一定的情况下，将Ｔ、ｔ视为时间因素Ｘ，Ｖ视为速度因素Ｙ，分析Ｘ、Ｙ变化对最佳巡视路线的影响。
The paper makes a discussion of the B-Group′s problem in the National Contest of Mathematics Model Setting of 1998. This problem is taken as the touring saleclerks′ problem in graph theory. At first, the groups division is made on the apex, then applying a successive improvement method to find out an approximate optimum return trip for saleclerks in every individual group. According to the degree of deviation to judge an inspection touring routes′ parities, at last, the dividing groups′ route is obtained, with much better parity thereon. Under given conditions, the shortest time being 6.43 hrs is to be found for touring inspection. Limited by this fixed time, much reasonable dividing groups′ method is adopted, with 22 groups found out. Finally, the paper has discussed the conditions under which the number of the groups is made certain, taking \%T,t\% as time factor \%X;V\% as speed factor \%Y\%, therein, analysis is made of \%X,Y\%, their changes, and of their influence upon the touring inspection route.
出处
《辽宁工学院学报》
1999年第4期86-91,共6页
Journal of Liaoning Institute of Technology(Natural Science Edition)
关键词
最短路
放行商问题
灾情巡视路线
哈密顿回路
network
Hamilton loop
touring clerk′s return trip
the shortest route
successive improvement method
