基于加权Voronoi图的小学优化配置模型

发布时间：2018-04-10 22:40

本文选题：加权Voronoi图 + GIS适龄儿童人口密度　；参考：《河北师范大学》2013年硕士论文

【摘要】：目前中国处于快速城市化发展阶段，城市公共服务设施优化配置是城镇化健康发展的重要保障。在应用数学中，公共资源配置问题属于计算几何学问题，在地理学中，小学校址优化配置属于公共资源优化配置问题。借助地理信息系统，实现城市建城区的小学校址优化配置，能方便群众生活，降低资源损耗。是推动公共设施均等化配置的一种有益的尝试。城市地理学一直致力于公共设施区位优化配置研究。1960年代以来，城市公共服务设施区位布局广泛应用运筹学方法，运筹学已成为城市公共设施优化配置模型的量化模型基础，以此为基础，发展起来三类城市公共服务设施优化配置模型，即基于经济地理学的区位分析模型；基于运筹学规划技术的区位模型；基于GIS的公共服务设施空间布局模型。其中，GIS模型综合了前两类模型，并融合了Voronoi图等计算几何算法。本文以石家庄市建城区小学优化配置为目标，利用ArcGIS的Python语言，基于石家庄市的小学现状数据、城市路网图和教育适龄人口密度，根据公共服务设施“均等化”与“公平性”原则，采用加权Voronoi图算法，构建了基于教育适龄人口密度的小学优化配置模型。通过有限次迭代计算，评价了当前小学的布局合理性，提出来小学空间优化方案和小学规模设置方案。研究表明，利用加权Voronoi图，能够有效地构建小学优化配置模型；模型计算结果显示：石家庄市建城区小学数量偏多，建议由211所减少到155所，石家庄市需要减去56所小型的学校，主要分布在城市郊区附近；部分强势学校规模仍需扩大，主要包括：中山西路小学、振头小学、留营小学、河北师大附属小学、东马路小学等20所小学。石家庄目前的小学优化配置任务重点在压缩规模小、效益差的学校数量，同时要把具有优质师资资源的小学进一步做大。随着教育适龄儿童的不断递减，，部分城区存在删减小学校址的可能，本文设计的小学优化配置模型仅仅是Voronoi图理论的初步应用探索，有待进一步完善。例如：为把握教育适龄人口动态变化特征，有必要将教育适龄人口预测模型整合进来；为实现增加或删减学校的功能，有必要将动态加权Voronoi图算法融合进来；为与城市交通存在的阻障问题相适应，有必要研究阻障条件下的加权Voronoi图算法；为了充分发挥GIS系统提供的点集非加权Voronoi算法，有必要在GIS系统中研究任意发生元的加权Voronoi算法。可以预见，随着Voronoi图理论和方法的不断完善和GIS技术的不断进步，Voronoi图将在公共设施优化配置领域发挥更大作用。
[Abstract]:At present, China is in the stage of rapid urbanization, and the optimal allocation of urban public service facilities is an important guarantee for the healthy development of urbanization.In applied mathematics, the problem of allocation of public resources belongs to the problem of computational geometry, and in geography, the optimal allocation of primary school sites belongs to the problem of optimal allocation of public resources.With the help of geographic information system (GIS), the optimal allocation of primary school sites in urban areas can be realized, which can facilitate the life of the masses and reduce the loss of resources.It is a useful attempt to promote the equalization of public facilities.Urban Geography has been devoted to the study of location optimal allocation of public facilities since 1960s, the location layout of urban public service facilities has been widely used in operational research, and operational research has become the basis of the quantitative model of the optimal allocation of urban public facilities.On this basis, three kinds of optimal allocation models of urban public service facilities are developed, that is, the location analysis model based on economic geography, the location model based on operational research planning technology, and the spatial layout model of public service facilities based on GIS.The first two kinds of models are integrated and the computational geometry algorithms such as Voronoi diagrams are fused.This paper aims at optimizing the allocation of primary schools in Jiancheng District of Shijiazhuang City, using the Python language of ArcGIS, based on the current situation data of primary schools in Shijiazhuang City, the map of urban road network and the population density of educational age.According to the principle of "equalization" and "fairness" of public service facilities, the optimal allocation model of primary school based on the population density of education age is constructed by using weighted Voronoi graph algorithm.Through finite iteration calculation, the rationality of the layout of primary school is evaluated, and the optimization scheme of primary school space and the scheme of primary school scale setting are put forward.The results show that the number of primary schools in Jiancheng District of Shijiazhuang City is on the high side, and it is suggested that the number of primary schools should be reduced from 211 to 155.Shijiazhuang needs to subtract 56 small schools, mainly located near the outskirts of the city; some of the most powerful schools still need to be expanded, including: Zhongshan West Road Primary School, Zhentou Primary School, Liuying Primary School, and Hebei normal University affiliated Primary School.East Road Primary School and other 20 primary schools.At present, the task of optimizing the allocation of primary schools in Shijiazhuang is to reduce the number of schools with small scale and low efficiency, and at the same time, to further enlarge the primary schools with high quality teacher resources.With the decline of school-age children, there is the possibility of deleting primary school sites in some urban areas. The optimal allocation model of primary schools designed in this paper is only a preliminary exploration of the application of Voronoi diagram theory, which needs to be further improved.For example, it is necessary to integrate the educational age population prediction model to grasp the characteristics of the dynamic change of the school-age population, to add or delete the functions of schools, and to integrate the algorithm of dynamically weighted Voronoi diagrams.In order to adapt to the obstacle problem existing in urban traffic, it is necessary to study the weighted Voronoi graph algorithm under obstacle condition, and to give full play to the point set unweighted Voronoi algorithm provided by GIS system.It is necessary to study the weighted Voronoi algorithm of arbitrary generator in GIS system.It can be predicted that with the continuous improvement of the theory and method of Voronoi diagram and the continuous progress of GIS technology, Voronoi diagram will play a more important role in the field of public facilities optimization.
【学位授予单位】：河北师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TU984.14;P208

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