本文選題：覆蓋問(wèn)題 + 連續(xù)選址�。� 參考：《清華大學(xué)》2013年碩士論文

【摘要】：選址問(wèn)題是指確定設(shè)施位置來(lái)提供所需服務(wù)，在經(jīng)濟(jì)活動(dòng)領(lǐng)域和公共服務(wù)領(lǐng)域有著較為廣泛的應(yīng)用。經(jīng)濟(jì)活動(dòng)領(lǐng)域的選址問(wèn)題多以最小化設(shè)施建設(shè)成本或運(yùn)營(yíng)成本為優(yōu)化目標(biāo)，比如工業(yè)生產(chǎn)中工廠以及倉(cāng)庫(kù)的選址、物流領(lǐng)域中配送中心的選址；而公共服務(wù)領(lǐng)域的選址問(wèn)題則是以最大化受益人群或最小化財(cái)產(chǎn)損失為優(yōu)化目標(biāo)的，比如臺(tái)風(fēng)預(yù)警裝置、消防中心的選址。經(jīng)濟(jì)活動(dòng)設(shè)施的選址失誤將導(dǎo)致企業(yè)運(yùn)作的高成本低效率，而應(yīng)急服務(wù)設(shè)施的選址失誤將為社會(huì)帶來(lái)巨大的財(cái)產(chǎn)損失甚至是災(zāi)難，而且也會(huì)降低城市居民對(duì)政府或城市建設(shè)者的信任，所以應(yīng)對(duì)應(yīng)急服務(wù)設(shè)施選址問(wèn)題給予高度重視。 基本選址問(wèn)題包括P-中值問(wèn)題、P-中心問(wèn)題以及覆蓋問(wèn)題。覆蓋問(wèn)題在公共服務(wù)設(shè)施領(lǐng)域應(yīng)用較為廣泛，，其目標(biāo)是將需求區(qū)域置于設(shè)施所能提供服務(wù)范圍之內(nèi)，比如臺(tái)風(fēng)預(yù)警裝置，其目的是將報(bào)警聲音傳到任何存在人類活動(dòng)的區(qū)域，同時(shí)其設(shè)施也可在城市區(qū)域內(nèi)任意位置建立（山脈、河流除外）。而解決此類問(wèn)題的傳統(tǒng)方法是將連續(xù)區(qū)域轉(zhuǎn)化為離散點(diǎn)集來(lái)表示需求和設(shè)施候選位置，這樣可簡(jiǎn)化覆蓋模型并快速獲得最優(yōu)解，但使用不同離散間隔或離散規(guī)則所得點(diǎn)集求得的設(shè)施最優(yōu)位置以及需求覆蓋率存在較大誤差。產(chǎn)生誤差的原因有二：一是離散覆蓋模型的優(yōu)化目標(biāo)是將需求點(diǎn)覆蓋；二是離散的固定位置可能根本不包含設(shè)施的最優(yōu)位置。 針對(duì)離散覆蓋模型誤差產(chǎn)生的原因，本文分別找到了對(duì)應(yīng)的解決辦法。為了將覆蓋問(wèn)題的優(yōu)化目標(biāo)轉(zhuǎn)化為最大化被覆蓋的需求區(qū)域，使用GIS的量算功能獲得被覆蓋區(qū)域的面積；為了實(shí)現(xiàn)設(shè)施在整個(gè)候選區(qū)域內(nèi)選址，將設(shè)施朝著未被覆蓋需求區(qū)域移動(dòng)以期獲得更高的覆蓋率。本文設(shè)計(jì)了一種優(yōu)化算法，首先使用離散最大覆蓋模型獲得設(shè)施的初始位置，然后使用GIS的多邊形疊加功能來(lái)識(shí)別未被覆蓋需求區(qū)域，將設(shè)施朝該區(qū)域移動(dòng)并使用GIS的量算功能衡量設(shè)施移動(dòng)效果的好壞，這樣便實(shí)現(xiàn)了需求連續(xù)分布的設(shè)施連續(xù)選址。最后，給出詳細(xì)的算例分析來(lái)證明優(yōu)化算法的有效性，最大限度的減少了離散覆蓋模型引入的誤差。
[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.
【學(xué)位授予單位】：清華大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：P208;TU99

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本文編號(hào)：1951889