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校园最佳游览路线问题的数学模型分析

         

摘要

将某高校的校园示意图转化为赋权连通图,求得该连通图的邻接矩阵,利用Floyd算法及图论软件包构造一个最短路径矩阵,得到一个赋权完全图,将求校园最佳游览路线问题归结为图论中的最佳推销员回路问题,建立混合整数线性规划模型,并利用优化软件求得最优解.从而解决了校园开放日游览计划中提出的关于校园最佳游览路线和校园游览车最优配置问题.%A campuses sketch map is transfered into connected graph with weight and its adjacency matrix is gotten. The shortest path matrix is constructed and a completed graph with weight is gotten by Floyed arithmetic and the software package of graph. The best tourist route of campus problem is regarded as TSP problem, i. e. , find the best similar Hamilton circle in the completed graph with weight. It is solved three problems in the opening day of campus: 1. For visitors to choose the main buildings, spots or sites. 2. According to the sketch map, design the shortest four tourist paths. 3. Get the minimal number of sightseeing bus in the opening day of campus.

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