【摘要】：城市交通是城市發(fā)展和進(jìn)步的決定性因素,與社會(huì)經(jīng)濟(jì)的發(fā)展相輔相成。交通超前于社會(huì)經(jīng)濟(jì)的發(fā)展,是發(fā)達(dá)國(guó)家保持經(jīng)濟(jì)長(zhǎng)期快速發(fā)展的一個(gè)重要因素,反之交通問(wèn)題則會(huì)成為制約經(jīng)濟(jì)發(fā)展的主要瓶頸。為此,如何做好交通規(guī)劃是我國(guó)當(dāng)前急需解決的迫切問(wèn)題,也是保障未來(lái)發(fā)展不可忽視的重要問(wèn)題。交通調(diào)查作為交通規(guī)劃的主要內(nèi)容之一,是獲取交通數(shù)據(jù)的基本方法和必要手段。通過(guò)交通調(diào)查獲得的數(shù)據(jù)是未來(lái)需求預(yù)測(cè)、規(guī)劃方案制定的主要依據(jù),其真實(shí)性和可靠性直接決定著規(guī)劃結(jié)果。由于交通源的數(shù)量巨大,交通調(diào)查一般以交通小區(qū)作為空間統(tǒng)計(jì)單元,要求確定合理的統(tǒng)計(jì)單元,不能過(guò)細(xì)而造成資源浪費(fèi),又不能過(guò)粗而影響后續(xù)的規(guī)劃結(jié)果,這就要求使用科學(xué)的方法制定這些統(tǒng)計(jì)單元。有鑒于此,本文以城市交通規(guī)劃為研究背景,運(yùn)用整數(shù)規(guī)劃建模求解理論與方法,分別針對(duì)交通小區(qū)劃分問(wèn)題的數(shù)據(jù)抽象和最優(yōu)化建模、空間鄰接約束的建模、分區(qū)個(gè)數(shù)已知的交通小區(qū)劃分問(wèn)題(基本交通小區(qū)劃分問(wèn)題)以及考慮分區(qū)個(gè)數(shù)決策的交通小區(qū)劃分問(wèn)題(擴(kuò)展的交通小區(qū)劃分問(wèn)題)的建模與求解開(kāi)展了系統(tǒng)的研究,主要研究工作如下文所述。(1)圍繞交通規(guī)劃中交通小區(qū)的實(shí)際劃分方法、理論研究中最優(yōu)交通小區(qū)劃分問(wèn)題的數(shù)據(jù)抽象過(guò)程、優(yōu)化目標(biāo)的選擇與建立以及優(yōu)化框架與求解方法等幾個(gè)方面,開(kāi)展了較全面的綜述研究工作,并在此基礎(chǔ)上針對(duì)空間單元的鄰接矩陣構(gòu)造方法、空間單元的可達(dá)性計(jì)算方法以及基于可達(dá)性的交通小區(qū)劃分的優(yōu)化目標(biāo)建立等問(wèn)題開(kāi)展了算法設(shè)計(jì)與建模工作。該項(xiàng)研究工作的具體內(nèi)容包括：針對(duì)交通活動(dòng)實(shí)踐中的交通小區(qū),以文獻(xiàn)資料為依據(jù)闡述了優(yōu)化劃分交通小區(qū)的意義,并概述了交通規(guī)劃管理實(shí)踐中交通小區(qū)劃分的原則及方法；從微觀角度,針對(duì)交通小區(qū)劃分問(wèn)題的理論研究,重點(diǎn)圍繞使用優(yōu)化技術(shù)解決交通小區(qū)劃分問(wèn)題時(shí)設(shè)立何種優(yōu)化目標(biāo)以及如何抽象構(gòu)建優(yōu)化目標(biāo)的問(wèn)題,分別針對(duì)建立優(yōu)化目標(biāo)前對(duì)連續(xù)的空間研究區(qū)域進(jìn)行離散化的方法、離散化后面狀空間單元的可達(dá)性度量方法、現(xiàn)實(shí)與文獻(xiàn)中劃分交通小區(qū)最優(yōu)目標(biāo)的內(nèi)容與形式以及基于可達(dá)性構(gòu)建的交通小區(qū)劃分最優(yōu)目標(biāo)的內(nèi)容與表達(dá)形式四個(gè)方面,開(kāi)展了文獻(xiàn)綜述工作；在此基礎(chǔ)上分別提出了基于Z型順序編碼的基本地理單元鄰接矩陣的構(gòu)造算法、使用路段局部深度值度量基本地理單元可達(dá)性的方法以及兩個(gè)交通小區(qū)劃分優(yōu)化目標(biāo)的數(shù)學(xué)表達(dá)形式—最小化總區(qū)內(nèi)加權(quán)出行費(fèi)用目標(biāo)和最小化總區(qū)內(nèi)可達(dá)性差異目標(biāo)；從宏觀角度,針對(duì)交通小區(qū)劃分問(wèn)題研究中的理論優(yōu)化框架與方法,綜述了最優(yōu)交通小區(qū)劃分問(wèn)題的相關(guān)研究成果,將其優(yōu)化問(wèn)題的框架概括為分區(qū)依據(jù)數(shù)據(jù)、最優(yōu)目標(biāo)、基本分區(qū)約束、問(wèn)題約束、算法以及評(píng)價(jià)分區(qū)解的指標(biāo)這五個(gè)要素；并分別從不同類(lèi)型的分區(qū)依據(jù)數(shù)據(jù)和求解方法兩個(gè)方面對(duì)交通小區(qū)劃分問(wèn)題的理論研究進(jìn)行了進(jìn)一步的綜述。(2)圍繞使用整數(shù)規(guī)劃技術(shù)對(duì)最優(yōu)交通小區(qū)空間鄰接約束建模的方法,針對(duì)文獻(xiàn)中保障最優(yōu)交通小區(qū)分區(qū)解滿足空間鄰接約束的方法進(jìn)行了簡(jiǎn)要的綜述,在此基礎(chǔ)上,針對(duì)空間鄰接約束整數(shù)規(guī)劃建模方法以及不同建模方法對(duì)問(wèn)題求解效率的影響這兩個(gè)方面的問(wèn)題開(kāi)展了建模求解與算例分析等研究工作。該項(xiàng)研究工作的具體內(nèi)容包括：在綜述最優(yōu)交通小區(qū)空間鄰接約束建模的方法的基礎(chǔ)上,修正文獻(xiàn)中鄰接約束整數(shù)規(guī)劃建模的方法以適用于交通小區(qū)劃分問(wèn)題,給出了最小生成樹(shù)表示、順序路徑表示以及網(wǎng)絡(luò)流表示三種對(duì)空間鄰接約束建模的方法；提出了基于鄰接矩陣表示的保障分區(qū)一階鄰接約束的一種新建模方法；分別從模型的決策變量規(guī)模與模型的約束規(guī)模兩個(gè)角度,給出了四種模型的變量、約束數(shù)量的推算過(guò)程以及理論計(jì)算表達(dá)式；基于對(duì)四種模型決策變量與約束規(guī)模的理論值估算,討論并比較與分析了四種模型的求解復(fù)雜度；基于兩個(gè)小規(guī)模仿真算例對(duì)四種模型的求解過(guò)程及原理、求解效率進(jìn)行了比較與分析,并簡(jiǎn)要探討了本文所提出的基于鄰接矩陣的建模方法的適用范圍。(3)圍繞基本交通小區(qū)劃分問(wèn)題,研究了在分區(qū)個(gè)數(shù)已知的情景下,基于P中位問(wèn)題模型的交通小區(qū)劃分問(wèn)題的0-1整數(shù)規(guī)劃建模及求解方法。該項(xiàng)研究工作的具體內(nèi)容包括：根據(jù)P中位問(wèn)題模型,在假設(shè)分區(qū)決策參數(shù)已知的條件下,建立了以最小異質(zhì)性為優(yōu)化目標(biāo),滿足空間鄰接約束的整數(shù)規(guī)劃模型的基本形式—最優(yōu)交通小區(qū)劃分問(wèn)題的P中位問(wèn)題模型(TAZ-PMP模型),并分析與探討了模型的性質(zhì)；將空間鄰接約束與TAZ-PMP模型分離,由此將最優(yōu)交通小區(qū)劃分問(wèn)題分解為構(gòu)造列池以及求解最優(yōu)下料問(wèn)題兩個(gè)過(guò)程,基于此,將鄰接約束作為隱枚舉規(guī)則,給出了通過(guò)構(gòu)造TAZ-PMP模型主問(wèn)題的初始化列池進(jìn)而將TAZ-PMP模型轉(zhuǎn)化為求解最優(yōu)下料問(wèn)題的精確求解算法(TAZ-IE算法)；使用拉格朗日替代松弛技術(shù)對(duì)TAZ-PMP模型進(jìn)行分解,結(jié)合近似求解拉格朗日對(duì)偶問(wèn)題的搜索算法、優(yōu)化求解拉格朗日對(duì)偶問(wèn)題的下降梯度算法以及TAZH算法給出了基于拉格朗日替代松弛的局部搜索啟發(fā)式算法(TAZ-LSLSH算法)；通過(guò)識(shí)別、推導(dǎo)拉格朗日替代松弛和下降花費(fèi)問(wèn)題中的共同優(yōu)化的子問(wèn)題,將拉格朗日替代松弛與列生成過(guò)程相結(jié)合,給出了基于拉格朗日替代松弛方法的主問(wèn)題與價(jià)格子問(wèn)題的分解過(guò)程,并基于此設(shè)計(jì)了基于拉格朗日替代松弛技術(shù)的列生成算法(TAZ-LSCG算法)：使用基于OR-Library和Pcb3038修改的仿真數(shù)值算例對(duì)三種算法的求解過(guò)程及求解效率進(jìn)行了比較與分析。(4)對(duì)基本交通小區(qū)劃分問(wèn)題進(jìn)行擴(kuò)展,圍繞考慮分區(qū)個(gè)數(shù)未知的情景下,交通小區(qū)劃分問(wèn)題的非線性混合整數(shù)規(guī)劃建模、模型的解析求解特征以及模型的求解算法等內(nèi)容,開(kāi)展了建模、算法設(shè)計(jì)與算例分析等研究工作。該項(xiàng)研究工作的具體內(nèi)容包括：考慮分區(qū)組成、分區(qū)中心設(shè)置以及分區(qū)個(gè)數(shù)三個(gè)決策變量,建立了以最小地理誤差為目標(biāo),以各分區(qū)空間可達(dá)性同質(zhì)、各分區(qū)面積同質(zhì)為主要約束條件的最優(yōu)交通小區(qū)劃分問(wèn)題的混合整數(shù)規(guī)劃模型(K-TAZ模型)；在分析了基本地理單元設(shè)置與最優(yōu)分區(qū)問(wèn)題之間關(guān)系的基礎(chǔ)上給出了影響區(qū)的定義,給出了構(gòu)造影響區(qū)的三個(gè)核心要素為鄰接關(guān)系謂詞、同質(zhì)性度量的劃分謂詞以及影響區(qū)構(gòu)成規(guī)則,設(shè)計(jì)了構(gòu)造影響區(qū)的啟發(fā)式搜索算法；將最優(yōu)交通小區(qū)劃分問(wèn)題的求解空間離散單元由基本地理單元改為影響區(qū),對(duì)提出的K-TAZ模型進(jìn)行了改進(jìn),使最優(yōu)分區(qū)問(wèn)題更容易求解；對(duì)K-TAZ模型進(jìn)行了解析推導(dǎo),給出了關(guān)于模型最優(yōu)分區(qū)個(gè)數(shù)解下界的引理與定理,以縮小分區(qū)個(gè)數(shù)取值范圍為目標(biāo),提出了確定最大分區(qū)個(gè)數(shù)下界的方法；基于K-TAZ模型中與分區(qū)個(gè)數(shù)決策變量相關(guān)的同質(zhì)性約束,作為搜索可行分區(qū)個(gè)數(shù)的限制條件,結(jié)合引理給出了可行分區(qū)個(gè)數(shù)的隱枚舉算法；分析了K-TAZ模型無(wú)解情景以及導(dǎo)致K-TAZ模型無(wú)解的理論原因；設(shè)計(jì)了包含兩個(gè)階段的聚合式聚類(lèi)啟發(fā)式算法以重構(gòu)求解空間使K-TAZ模型可解；通過(guò)對(duì)比僅包含一階段的聚合式聚類(lèi)啟發(fā)過(guò)程與所提出算法的啟發(fā)式過(guò)程中求解空間結(jié)構(gòu)的變化,說(shuō)明了所提出算法的有效性；將最大Kmin域縮減方法與約束規(guī)劃模型求解過(guò)程結(jié)合,給出了求解K-TAZ模型的約束規(guī)劃方法；將可行分區(qū)個(gè)數(shù)隱枚舉域縮減方法與P中位問(wèn)題模型求解過(guò)程結(jié)合,給出了求解K-TAZ模型的P中位模型方法；使用基于Pcb3038修改的仿真數(shù)值算例對(duì)兩種算法的求解過(guò)程及求解效率進(jìn)行了比較與分析。(5)結(jié)合蘇州工業(yè)園區(qū)公交規(guī)劃中最優(yōu)交通小區(qū)劃分的實(shí)際案例,開(kāi)展了抽象建模與算例分析等應(yīng)用研究。該項(xiàng)研究工作的具體內(nèi)容包括：基于本文提出的抽象建模與計(jì)算方法,給出了案例的數(shù)據(jù)模型及其建立過(guò)程；考慮分區(qū)個(gè)數(shù)固定的情景,將案例的最優(yōu)交通小區(qū)劃分問(wèn)題抽象為最小化分區(qū)異質(zhì)性的TAZ-PMP模型；分別使用IE算法、LSLSH算法以及LSCG算法給出了案例最小化分區(qū)異質(zhì)性TAZ-PMP模型的最優(yōu)交通小區(qū)劃分方案,并對(duì)算法求解實(shí)例的效率進(jìn)行了討論與分析；考慮分區(qū)個(gè)數(shù)未知的情景,將案例的最優(yōu)交通小區(qū)劃分問(wèn)題抽象為最小化地理誤差的K-TAZ模型；分別使用CP方法以及PMP方法給出了最小化地理誤差K-TAZ模型的最優(yōu)交通小區(qū)劃分方案,并對(duì)算法求解實(shí)例的效率進(jìn)行了相關(guān)的討論與分析。
[Abstract]:Urban traffic is the decisive factor of urban development and progress, and is mutually reinforcing with the development of social economy. The development of the traffic ahead of the social economy is an important factor for the developed countries to maintain the long-term and fast development of the economy. To this end, how to do well the traffic planning is the urgent problem to be solved urgently in our country, and it is also an important issue to guarantee the future development. As one of the main contents of the traffic planning, the traffic survey is the basic method and necessary means for obtaining the traffic data. The data obtained through the traffic investigation is the main basis for future demand forecast and planning, and its authenticity and reliability directly determine the planning result. because the number of the traffic sources is large, the traffic survey is generally used as a space statistical unit in a traffic cell, a reasonable statistical unit is required to be determined, the resource waste can not be caused to be too thin, and the subsequent planning result can not be influenced by rough, This requires the use of scientific methods for the development of these statistical units. In view of the above, this paper uses the urban traffic planning as the research background, and uses the integer programming modeling to solve the theory and the method, respectively the data abstraction and optimization modeling of the traffic cell division problem, the modeling of the space adjacency constraint, The model and solution of the traffic cell division problem (the basic traffic cell division problem) and the traffic cell division problem (extended traffic cell division problem) considering the number decision of the division are studied in this paper. The main research work is as follows. (1) The comprehensive review and research work is carried out in the aspects of the actual division method of the traffic cell in the traffic planning, the data abstraction process of the optimal traffic cell division problem in the theoretical study, the selection and establishment of the optimization target, the optimization framework and the solution method, and the like. On the basis of this, the algorithm design and modeling of the space unit's neighbor matrix construction method, the reachability calculation method of the space unit and the optimization target establishment based on the accessibility of the traffic cell are carried out. The concrete contents of this research include: for the traffic district in the practice of traffic activity, the paper expounds the significance of the optimization of the traffic district based on the literature, and outlines the principle and method of the traffic cell division in the traffic planning management practice; from the micro angle, In order to solve the problem of traffic cell division, this paper focuses on how to use the optimization technique to solve the problem of the optimization goal and how to abstract and construct the optimization target. a method for discretizing a continuous space research area before an optimization target is established, and a reachability measurement method for the discretized back space unit, The paper reviews the content and form of the optimal target of the traffic cell and the content and the expression form of the optimal target for the traffic subdistrict based on the accessibility. On the basis of this, the structure algorithm of the adjacent matrix of the basic geographical unit based on the Z-type sequence coding is presented, the method for measuring the accessibility of the basic geographic unit by using the local depth value of the road section and the mathematical expression form of the two traffic cell division optimization targets are used to minimize the weighted travel expense target in the total area and to minimize the reachability difference target in the total area; and from the macroscopic angle, In view of the theory optimization framework and method in the research of traffic cell division, the relevant research results of the optimal traffic cell division problem are summarized, and the frame of the optimization problem is summarized as the partition basis data, the optimal objective, the basic partition constraint, the problem constraint, The five elements of the algorithm and the index for evaluating the partition solution are summarized, and the theoretical research on the division of traffic cells from different types of partitions according to the data and the method of solution is further reviewed. and (2) a method for modeling the spatial adjacent constraint of the optimal traffic cell by using an integer programming technique, In order to solve the problems of space-adjacent constrained integer programming modeling and different modeling methods, the problems in the two aspects of the problem-solving efficiency are studied, such as the modeling solution and the numerical example analysis. The specific content of the research work includes: on the basis of summarizing the method of the optimal traffic cell space adjacency constraint modeling, the method of the adjacent constrained integer programming modeling in the document is applied to the traffic cell division problem, and the minimum spanning tree representation is given, The sequential path representation and the network flow represent three methods for modeling the spatial adjacency constraint; a new modeling method for guaranteeing the first order adjacency constraint of the partition based on the adjacency matrix representation is proposed; and the two angles of the scale of the decision variables of the model and the constraint scale of the model are respectively obtained, In this paper, four model variables, the calculation process of the constraint number and the theoretical calculation expression are given, and the solution complexity of the four models is discussed and compared based on the theoretical value estimation of the four model decision variables and the constraint scale. Based on two small-scale simulation examples, the solution process and principle of four models are compared and analyzed, and the application scope of the method based on the adjacency matrix is briefly discussed. (3) The problem of the division of the basic traffic is studied, and the 0-1 integer programming model and the method for solving the traffic cell division problem based on the P-bit problem model are studied. The specific contents of the study include: according to the P-position problem model, under the assumption that the partition decision parameter is known, the minimum heterogeneity is established as the optimization target, The basic form of an integer programming model satisfying the spatial adjacency constraint is the P center problem model (TAZ-PMP model) of the optimal traffic cell division problem, and the property of the model is analyzed and discussed; and the space adjacency constraint is separated from the TAZ-PMP model, in that method, the problem of the optimal traffic cell division is decomposed into two processes of constructing a column pool and solving the optimal blanking problem, The TAZ-PMP model is transformed into an accurate solution algorithm (TAZ-IE) for solving the optimal blanking problem by constructing the initialization column pool of the main problem of the TAZ-PMP model, and the TAZ-PMP model is decomposed using the Lagrange substitution relaxation technique, and the search algorithm for solving the Lagrange dual problem is combined with the approximate solution, In this paper, a local search heuristic algorithm (TAZ-LSLSH algorithm) based on the Lagrange's alternative relaxation is given in this paper. In this paper, the decomposition process of the main problem and the price subproblem based on the Lagrange's alternative relaxation method is given by the combination of the Lagrange's replacement relaxation and the column generation process, and the column generation algorithm (TAZ-LSCG algorithm) based on the Lagrange substitution relaxation technique is designed. A numerical example based on OR-Library and Pcb3038 is used to compare and analyze the process and efficiency of the three algorithms. (4) the basic traffic cell division problem is expanded, and the modeling is carried out around the content of the non-linear mixed integer programming modeling of the traffic cell division problem, the analysis and solving characteristics of the model and the solution algorithm of the model, The design of the algorithm and the analysis of the numerical example and so on. The specific contents of the study include: considering the composition of the partition, the setting of the center of the partition and the three decision variables of the number of the zones, the objective of the minimum geographical error is established, and the spatial accessibility of each partition is homogeneous, the mixed integer programming model (k-taz model) of the optimal traffic cell division problem with the uniform partition area as the main constraint condition is given; the definition of the influence area is given on the basis of analyzing the relation between the basic geographic unit setting and the optimal partition problem, The three core elements of the structure influence area are given as the adjacent relation predicate, the partition predicate of the homogeneity measure and the influence area constitute the rule, and the heuristic search algorithm for constructing the influence area is designed; The method for solving the problem of optimal traffic cell division is changed from the basic geographic unit to the influence area, the proposed K-TAZ model is improved, the optimal partition problem is more easily solved, and the K-TAZ model is analyzed and derived, In this paper, the lemma and the theorem of the lower bound of the number of the optimal partition of the model are given, and the method of determining the lower bound of the maximum number of partitions is put forward. Based on the homogeneity constraint associated with the number of the partition number in the K-TAZ model, In this paper, the implicit enumeration algorithm for the number of feasible partitions is given as the limit of the number of feasible partitions, and the non-solution scenarios of the K-TAZ model and the theoretical reasons leading to the non-solution of the K-TAZ model are analyzed. In this paper, a heuristic algorithm with two stages of aggregation is designed to reconstruct the solution space so that the K-TAZ model can be solved, and the validity of the proposed algorithm is explained by comparing the heuristic process of the aggregation-type clustering with only one stage and the heuristic process of the proposed algorithm. In this paper, the maximum Kmin domain reduction method is combined with the constraint planning model solving process, and a constraint planning method for solving the K-TAZ model is given, and the method for solving the K-TAZ model is given by combining the feasible partition number of the hidden enumeration domain reduction method with the P median problem model solving process, and the method for solving the P-type model of the K-TAZ model is provided. The solution process and efficiency of two algorithms are compared and analyzed using a simulation numerical example based on Pcb3038 modification. (5) In combination with the actual case of the optimal traffic cell division in the public transport planning of the Suzhou Industrial Park, the application research of the abstract modeling and an example analysis is carried out. The concrete content of this research includes: based on the abstract modeling and calculation method presented in this paper, the data model of the case and the process of establishing the case are given; considering the fixed situation of the number of the partitions, the optimal traffic cell division problem of the case is abstracted into the TAZ-PMP model which minimizes the partition heterogeneity; By using the IE algorithm, the LSLSH algorithm and the LSCG algorithm, the optimal traffic cell division scheme for the case-minimized partition heterogeneity TAZ-PMP model is given, and the efficiency of the algorithm is discussed and analyzed. The optimal traffic cell division problem of the case is abstracted as the K-TAZ model of minimizing the geographical error; the optimal traffic cell division scheme of minimizing the geographic error K-TAZ model is given by using the CP method and the PMP method, and the efficiency of the algorithm solution case is discussed and analyzed.
【學(xué)位授予單位】：東北大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類(lèi)號(hào)】：U491.12;TP301.6

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