基于GIS的最大化区域覆盖的连续设施选址问题研究

发布时间：2018-05-29 18:08

本文选题：覆盖问题 + 连续选址　；参考：《清华大学》2013年硕士论文

【摘要】：选址问题是指确定设施位置来提供所需服务，在经济活动领域和公共服务领域有着较为广泛的应用。经济活动领域的选址问题多以最小化设施建设成本或运营成本为优化目标，比如工业生产中工厂以及仓库的选址、物流领域中配送中心的选址；而公共服务领域的选址问题则是以最大化受益人群或最小化财产损失为优化目标的，比如台风预警装置、消防中心的选址。经济活动设施的选址失误将导致企业运作的高成本低效率，而应急服务设施的选址失误将为社会带来巨大的财产损失甚至是灾难，而且也会降低城市居民对政府或城市建设者的信任，所以应对应急服务设施选址问题给予高度重视。基本选址问题包括P-中值问题、P-中心问题以及覆盖问题。覆盖问题在公共服务设施领域应用较为广泛，，其目标是将需求区域置于设施所能提供服务范围之内，比如台风预警装置，其目的是将报警声音传到任何存在人类活动的区域，同时其设施也可在城市区域内任意位置建立（山脉、河流除外）。而解决此类问题的传统方法是将连续区域转化为离散点集来表示需求和设施候选位置，这样可简化覆盖模型并快速获得最优解，但使用不同离散间隔或离散规则所得点集求得的设施最优位置以及需求覆盖率存在较大误差。产生误差的原因有二：一是离散覆盖模型的优化目标是将需求点覆盖；二是离散的固定位置可能根本不包含设施的最优位置。针对离散覆盖模型误差产生的原因，本文分别找到了对应的解决办法。为了将覆盖问题的优化目标转化为最大化被覆盖的需求区域，使用GIS的量算功能获得被覆盖区域的面积；为了实现设施在整个候选区域内选址，将设施朝着未被覆盖需求区域移动以期获得更高的覆盖率。本文设计了一种优化算法，首先使用离散最大覆盖模型获得设施的初始位置，然后使用GIS的多边形叠加功能来识别未被覆盖需求区域，将设施朝该区域移动并使用GIS的量算功能衡量设施移动效果的好坏，这样便实现了需求连续分布的设施连续选址。最后，给出详细的算例分析来证明优化算法的有效性，最大限度的减少了离散覆盖模型引入的误差。
[Abstract]:Location problem is to determine the location of facilities to provide the required services, in economic activities and public service has a relatively wide range of applications. In the field of economic activities, the optimization goal is to minimize the cost of facility construction or operation, such as the location of factories and warehouses in industrial production, and the location of distribution centers in the field of logistics. The public service location problem is to maximize the benefit of the population or minimize property losses, such as typhoon warning devices, fire center location. The failure of the location of economic facilities will lead to the high cost and low efficiency of the operation of enterprises, and the failure of the location of emergency services will bring huge property losses or even disasters to the society. It will also reduce the trust of city residents to the government or city builders, so we should attach great importance to the location of emergency services. The basic location problem includes the P-median problem and the P-center problem as well as the covering problem. Coverage is more widely used in the field of public services, with the goal of placing areas of need within the range of services that facilities can provide, such as typhoon warning devices, which aim to transmit alarm sounds to any area where human activity exists. Its facilities can also be built anywhere in urban areas (mountains, except rivers). The traditional method to solve this kind of problem is to transform the continuous region into discrete point set to represent the requirement and facility candidate position, which can simplify the covering model and obtain the optimal solution quickly. However, large errors exist in the optimal location of the facility and the requirement coverage rate obtained by using the points set obtained from different discrete intervals or discrete rules. There are two reasons for the error: one is that the optimal objective of the discrete coverage model is to cover the demand point, the other is that the discrete fixed position may not contain the optimal location of the facility at all. In this paper, the corresponding solutions are found for the error of discrete coverage model. In order to transform the optimization objective of the coverage problem into maximizing the covered requirement area, the area of the covered area is obtained using the GIS's measurement function, and the location of the facility in the entire candidate area is achieved. Move facilities towards uncovered areas of demand for higher coverage. In this paper, an optimization algorithm is designed. First, the discrete maximum coverage model is used to obtain the initial location of the facility, and then the polygon superposition function of GIS is used to identify the uncovered requirement area. The facility is moved to the area and the function of GIS is used to measure the effect of the facility movement, thus the continuous location of the facility with continuous distribution of demand is realized. Finally, a detailed example analysis is given to prove the effectiveness of the optimization algorithm, which minimizes the error introduced by the discrete cover model.
【学位授予单位】：清华大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：P208;TU99

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