数学建模课程设计---闭路电视监控系统的优化设计

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1、 闭路电视监控系统的优化设计闭路电视监控系统的优化设计 摘要摘要: 本题主要解决的问题是选择安装摄像头的位置， 并且在保证所有区域被监控的条件下安 装摄像头数目最少。 我们首先将这一问题转化为 01 整数规划问题， 并用 LINDO 软件求解。 由于每条街道的两端基本 （也有极少数街道只有一端可以安装摄像头） 都是可以安装摄像头 的位置，我们可以把街道看做线段，安装摄像头的位置看作点，这样工业区的布局图就转化 为一个图论模型， 本题就转化为求图的最小点覆盖的问题了。 利用图的关联矩阵求出最小覆 盖的点，这些点就是安装摄像头的位置！ 关关键字键字：01 整数规划 关联矩阵 最小点覆盖 Abstr

2、act : The aim of this term is to choose the places of fixing web-cameras，and make sure the whole aeras are under the control .Under this condition ,we should make sure that the number of fixed web-cameras is minimal. Firstly ,we convert this problem to the case of zero one integer programming ,and L

3、INDO can solve this changing case .Secondly,we can change our idea to think about this problem .Because the two points of each street are available places for fixing web-cameras (only a very few streets have one available point to fix web-cameras ),we can respond the streets to line segments ,at the

4、 same time ,the place of fixing web-cameras responding to vertices ,then the layout of this industrial park becames a model of graph theory .Hence the original term transforms to solve the minimal vertex covering problems of graph .We can use the correlative matrix to find out the minimal vertex covering concourse, the solving points are the final places for fixing KeywordsKeywords: zeroone integral layout correlative matrix minimal vertex covering 1.1. 问题重述问题重述 某市的工业区发生多起夜间入室