本文關(guān)鍵詞：基于魯棒優(yōu)化的城市交通網(wǎng)絡(luò)設(shè)計(jì)模型與算法研究　出處：《北京交通大學(xué)》2014年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 交通網(wǎng)絡(luò)設(shè)計(jì)問題 魯棒優(yōu)化 可調(diào)整的魯棒優(yōu)化 元胞傳輸模型 最壞風(fēng)險(xiǎn)值 最壞條件風(fēng)險(xiǎn)值 分布式魯棒聯(lián)合機(jī)會(huì)約束

【摘要】：城市交通網(wǎng)絡(luò)設(shè)計(jì)問題是城市綜合規(guī)劃的核心問題,也是關(guān)系到城市經(jīng)濟(jì)長(zhǎng)期、快速、和諧和穩(wěn)定發(fā)展的基本問題。當(dāng)前,隨著城市的高速發(fā)展,城市交通擁堵現(xiàn)象日益嚴(yán)重,交通供需矛盾日益突出,緩解和預(yù)防交通擁堵已經(jīng)成為城市發(fā)展當(dāng)務(wù)之急。另一方面,城市交通網(wǎng)絡(luò)中存在著大量的不確定因素,如果在交通網(wǎng)絡(luò)設(shè)計(jì)中忽視這些不確定性因素,可能會(huì)導(dǎo)致交通網(wǎng)絡(luò)更加嚴(yán)重的擁堵。因此,不確定的交通網(wǎng)絡(luò)設(shè)計(jì)問題的研究是必不可少的。當(dāng)前,不確定城市交通網(wǎng)絡(luò)設(shè)計(jì)的研究方法主要有隨機(jī)規(guī)劃和魯棒優(yōu)化兩種,其中隨機(jī)規(guī)劃的方法需要事先假定不確定參數(shù)滿足某種概率分布。然而,在現(xiàn)實(shí)中,由于缺少大量數(shù)據(jù)去校準(zhǔn)這種概率分布,這種假定的概率分布可能不能用。而魯棒優(yōu)化的方法則不需要事先假定不確定參數(shù)滿足某種概率分布。因此,應(yīng)用魯棒優(yōu)化的方法研究不確定交通網(wǎng)絡(luò)設(shè)計(jì)問題具有更加實(shí)際的意義。 本論文基于魯棒優(yōu)化的方法,研究不確定的城市交通網(wǎng)絡(luò)設(shè)計(jì)問題,探討不確定交通網(wǎng)絡(luò)設(shè)計(jì)問題的建模和求解算法。具體來講,本論文研究工作主要有以下幾個(gè)方面： (1)運(yùn)用魯棒非線性優(yōu)化方法研究了基于用戶均衡下不確定需求的連續(xù)交通網(wǎng)絡(luò)設(shè)計(jì)問題,其中不確定需求屬于一個(gè)橢球集合。通過運(yùn)用魯棒優(yōu)化的思想和靈敏度分析的方法,我們將連續(xù)交通網(wǎng)絡(luò)設(shè)計(jì)問題的魯棒對(duì)應(yīng)(Robust Counterpart,RC)模型轉(zhuǎn)化為一系列帶互補(bǔ)約束的數(shù)學(xué)規(guī)劃問題(Mathematical Programms with Complementarity Problem, MPCC),并運(yùn)用一種松弛算法求解這一系列的MPCC。另外,我們將它和Yin和Lawphongpanich[1]提出的魯棒對(duì)應(yīng)模型進(jìn)行了比較。數(shù)值實(shí)驗(yàn)的結(jié)果表明,我們提出的魯棒對(duì)應(yīng)模型比Yin和Lawphongpanich[1]的魯棒對(duì)應(yīng)模型更加靈活,沒那么保守。 (2)探討了不確定需求下的魯棒可靠性用戶均衡模型,其中模型并不要求知道不確定需求的準(zhǔn)確的概率分布,而僅需知道它的前m階矩�；谧顗娘L(fēng)險(xiǎn)值(Worst-case Value-at-Risk, WVaR)和最壞條件風(fēng)險(xiǎn)值(Worst-Case Conditional Value-at-Risk, WCVaR)[2],我們定義了魯棒分位走行時(shí)問和魯棒均值-超量走行時(shí)問,并證明了兩種走行時(shí)間在需求一般分布情況下是等價(jià)的。基于這種等價(jià)的走行時(shí)問提出了魯棒分位用戶均衡(魯棒均值-超量交通均衡)模型,模型被表示為一個(gè)非線性互補(bǔ)問題(Nonlinear Complementarity Problem, NCP),并證明了模型的等價(jià)性和解的存在性。然后一種基于間隙函數(shù)的方法被用來求解這個(gè)非線性互補(bǔ)問題�；谔岢龅木饽Ｐ�,我們進(jìn)一步研究了帶分布式魯棒聯(lián)合機(jī)會(huì)約束的連續(xù)交通網(wǎng)絡(luò)設(shè)計(jì)模型,通過利用Bonferroni不等式,模型中的分布式魯棒聯(lián)合機(jī)會(huì)約束被近似為非線性約束,我們應(yīng)用積極集的算法求解近似后的模型,數(shù)值實(shí)驗(yàn)的結(jié)果驗(yàn)證了提出的模型和算法的有效性。 (3)運(yùn)用可調(diào)整的魯棒優(yōu)化方法研究了基于元胞傳輸模型(Cell Transimission Model, CTM)[3-4]的單層動(dòng)態(tài)交通網(wǎng)絡(luò)設(shè)計(jì)模型,其中不確定需求被假定屬于一個(gè)多面體集合。通過運(yùn)用仿射決策準(zhǔn)則和線性規(guī)劃的對(duì)偶,我們構(gòu)建了相應(yīng)的仿射可調(diào)整的魯棒對(duì)應(yīng)模型,同時(shí)將它與傳統(tǒng)的魯棒對(duì)應(yīng)模型進(jìn)行了比較,數(shù)值算例的結(jié)果顯示,可調(diào)整的魯棒對(duì)應(yīng)模型比傳統(tǒng)的魯棒對(duì)應(yīng)模型更加靈活。 (4)基于元胞傳輸模型,研究了單層動(dòng)態(tài)交通網(wǎng)絡(luò)設(shè)計(jì)問題的分布式魯棒聯(lián)合機(jī)會(huì)約束模型,模型假定OD需求的概率分布是未知的,僅知道它的期望和方差。首先,我們將模型中的分布式魯棒聯(lián)合機(jī)會(huì)約束近似為最壞條件風(fēng)險(xiǎn)值約束,然后,利用錐對(duì)偶原理,將最壞條件風(fēng)險(xiǎn)值約束等價(jià)的轉(zhuǎn)化為半定規(guī)劃約束。另外,這種基于半定規(guī)劃的近似被用來和基于Bonferroni不等式的近似以及基于二階錐優(yōu)化(Second-Order Cone Programming,SOCP)的近似進(jìn)行比較。數(shù)值算例的結(jié)果證實(shí)了基于半定規(guī)劃(Semidefinite Programming, SDP)的近似方法更加靈活,沒那么保守,比基于Bonferroni不等式和基于SOCP的近似有更優(yōu)的目標(biāo)函數(shù)值 (5)基于元胞傳輸模型,通過利用最壞條件風(fēng)險(xiǎn)值,我們建立了不確定需求下的雙層動(dòng)態(tài)交通網(wǎng)絡(luò)設(shè)計(jì)模型,其中不確定需求的概率分布被假定屬于由幾種已知概率分布所組成的多面體集合�；谙聦拥挠脩糇顑�(yōu)的最優(yōu)性條件,我們將雙層動(dòng)態(tài)交通網(wǎng)絡(luò)設(shè)計(jì)模型等價(jià)轉(zhuǎn)化為帶互補(bǔ)約束的數(shù)學(xué)規(guī)劃模型。一種松弛的算法被用來求解轉(zhuǎn)化后的模型,通過數(shù)值實(shí)驗(yàn)的結(jié)果證實(shí)了模型和算法的有效性。
[Abstract]:City traffic network design problem is the core problem of city comprehensive planning of the city, but also related to the long-term economic, rapid, harmonious and stable development of the basic problem. At present, with the rapid development of city, city traffic congestion has become more serious, the contradiction between supply and demand have become increasingly prominent, mitigation and prevention of traffic congestion has become a pressing matter of the moment. Another city development and there are many uncertain factors in city traffic network, if we ignore these uncertain factors in traffic network design, network traffic may lead to more serious congestion. Therefore, transportation network design problem of uncertainty is essential. At present, the research of uncertain methods of city traffic network design major there are two kinds of stochastic programming and robust optimization method, the stochastic programming need to assume the uncertain parameters satisfy a certain probability distribution. However, in reality, due to the lack of large amounts of data to calibrate the probability distribution, the probability distribution of possible this assumption can not be used. The robust optimization method is not required to assume the uncertain parameters satisfy a certain probability distribution. So it has more practical significance to design problem of robust optimization application of uncertain network traffic.
Based on the robust optimization method, this paper studies the design problem of uncertain urban transportation network, and discusses the modeling and solving algorithm of uncertain transportation network design.
(1) based on the robust of continuous transportation network design problem of user equilibrium under uncertain demand based on nonlinear optimization method, which belongs to an uncertain demand. By analyzing the ellipsoid set robust optimization thought and sensitivity of use, we will continuous transportation network design problem of robust counterpart (Robust Counterpart, RC) model into a series of mathematical programming problems with complementarity constraints (Mathematical Programms with Complementarity Problem, MPCC), and the use of a relaxation algorithm to solve this series of MPCC. also, we will model and corresponding robust Yin and Lawphongpanich[1] is proposed. By comparing the results of numerical experiments show that the proposed model than the corresponding robust robust Yin and Lawphongpanich[1] corresponding to the model is more flexible and less conservative.
(2) discuss the robust reliability of user equilibrium model under demand, the model does not require the exact probability distribution of demand uncertainty, and only need to know the first m moments. It's the worst value based risk (Worst-case Value-at-Risk, WVaR) and the worst condition risk value (Worst-Case Conditional Value-at-Risk. WCVaR [2]), we define a robust walking time and robust mean excess travel time, and proves that two kinds of walking time distribution in general demand are equivalent. Based on the equivalent time walking into a robust user equilibrium (robust mean excess traffic equilibrium) model, the model is formulated as a nonlinear complementarity problem (Nonlinear Complementarity, Problem, NCP), and proved the existence of equivalent model of reconciliation. Then a method based on gap functions are used to solve the non line Complementarity problems. Equilibrium model based on the proposed continuous transportation network design model we further studied with the distributed robust joint chance constraint, by using the Bonferroni inequality, a robust distributed joint chance constraints in the model is similar to the algorithm for solving the nonlinear constraints, we apply the active set approximation of the model, the results of numerical experiments validate the effectiveness of the proposed model and algorithm.
(3) the use of adjustable robust optimization method based on the cell transmission model (Cell Transimission Model, CTM) - dynamic traffic network design model of [3-4], the demand uncertainty is assumed to belong to a polytope. By using the dual affine set of decision criteria and linear programming, we construct the corresponding robust model the affine adjustable, and it corresponds with the traditional robust model were compared. The numerical results show that the robust model can adjust the corresponding than the traditional robust corresponding model is more flexible.
(4) the cell transmission model based on distributed robust design problem of single joint chance constraint model of dynamic traffic network, the probability distribution model assumes that the demand of OD is unknown, only know the expectation and variance of it. First, we will model the distributed robust joint chance constraint approximation for the worst conditional value at risk then, by using the cone constraint, duality principle, the conditional value at risk transformation constraints as semidefinite programming constraints. In addition, this approximation based on semidefinite programming is used to approximate and based on the Bonferroni inequality and is based on two order cone optimization (Second-Order Cone Programming, SOCP) were compared with the numerical approximation. The results proved that based on semidefinite programming (Semidefinite Programming SDP) approximation method is more flexible and less conservative than the Bonferroni inequality and the SOCP approximation based on better. Standard function
(5) based on cell transmission model, through the use of the worst condition value at risk, we established a double uncertain dynamic traffic network design model under demand uncertainty, the probability distribution of demand is assumed to be set by several known probability distribution composed of polyhedra. The optimality conditions based on the underlying user optimum. We will double the dynamic traffic network design model is transformed into a mathematical programming model with complementary constraints. A relaxation algorithm is used to solve the transformed model, the validity of the model and algorithm is verified by numerical experiments.

【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：F224;F572

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本文編號(hào)：1369003