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最优灾情巡视路线模型

时间:2017-08-11 数学毕业论文 我要投稿

摘要

本文依据某县的公路网示意图,求解不同条件下的灾情巡视路线,1为定组巡视,2位限时巡视,并总结出1些在这类图中求最优回路的有效法则。文中首先将县城公路示意图转化为赋权连通图,并通过最小生成树将原权图分为若干子图,分析并给出在这些子图中寻找最佳回路的若干原则:扩环策略、增环策略、换枝策略,依据这些原则,求得不同条件下的巡视路线。
当巡视人员分为3组时,在要求总路线最短且尽可能均衡的条件下各组巡视路线分别为:159.3km,239.8km,186.4km。当要求在24小时完成巡视,各乡(镇)停留时间为2小时,各村停留时间为1小时时,至少需要分为4组,巡视完成时间为:22.4小时。
分析T,t和V的改变对最佳路线的影响不但于T,t和V的改变方式有关,而且与最佳路线均衡度的精度要求有关。

关键词:最优方法;最小生成树;连通图;Kruskal算法

ABSTRACT

On the basis of highway sketch map in a county, In this paper, the author tries to find out catastrophic scouting routes on different conditions. One is scouting in settled groups, the other is scouting in fixed time. And also summarizes effective principles about the most favorable circuit in this category of charts. The county highway sketch maps was transformed into value-endowed connected charts firstly, and divided the original value maps into several child charts through Minimum Cost Spanning Tree. By analyzing these child charts, several principles of the best circuit was found out, which was expanding strategy, circle strategy, branch-exchange. And on the basis of these strategies, scouting routes on different occasions was tried to find out. 
Under the situation of dividing the scouting personnel into 3 groups, the shortest total route and as equilibrium as possible, each group of scouting route respectively is: 159.3km, 239.8km, 186.4km. If it was required to be finished scouting within 24 hours, they can be stayed at each county for about two hours and one hour in each village. The whole personnel must be divided into at least 4 groups and thus the required finishing time is: 22.4 hours.
The changes of T, t, V influence the most favorable route in the following ways: the relationship between T, t, V and the most favorable route is: it is  not only related with the changing way of T, t and V, but also related with the precision requirement of the most favorable routes equilibrium.

Keywords: the best favorable method;Minimum Cost Spanning Tree;Connected chart;Kruskal arithmetic

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