本文選題：基于距離擁擠收費(fèi) + 路徑成本不可加��； 參考：《東南大學(xué)》2015年碩士論文

【摘要】：目前正在實(shí)施的所有擁擠收費(fèi)都采用的是單一固定的收費(fèi)方法,比如區(qū)域通行證收費(fèi)策略。這種單一的收費(fèi)策略忽略了在收費(fèi)區(qū)域內(nèi)車輛行駛的距離和時(shí)間,同時(shí)還會(huì)引起網(wǎng)絡(luò)用戶的不公平問題。為了改善當(dāng)前收費(fèi)系統(tǒng),本文提出了基于距離擁擠收費(fèi)模式并對(duì)其進(jìn)行深入的研究。本文首先定義基于距離擁擠收費(fèi)是收費(fèi)區(qū)域內(nèi)車輛行駛距離的非線性函數(shù),并保持正的、非遞減性質(zhì)。隨后建立了基于距離擁擠收費(fèi)的用戶均衡模型并證明了模型解的存在性和唯一性。由于收費(fèi)函數(shù)的非線性數(shù)學(xué)表達(dá)形式是廣義的,因此為了能夠確定具體的收費(fèi)形式,本文利用分段線性逼近方法來重新表達(dá)非線性收費(fèi)函數(shù)。同時(shí),基于距離的非線性收費(fèi)模式還將導(dǎo)致路徑成本不可加性,即路徑成本不等于使用該路徑的各個(gè)路段成本之和,因此無法直接使用傳統(tǒng)的Frank-Wolfe算法來求解。為了解決這種路徑成本不可加性問題,本文采用基于梯度投影的路徑算法來求解,并結(jié)合k條最短路算法來尋找廣義路徑成本下的最短路徑�？紤]基于距離擁擠收費(fèi)條件下的路徑選擇行為,為了求得滿足決策者目標(biāo)期望的最優(yōu)費(fèi)率,本文建立了基于距離擁擠收費(fèi)費(fèi)率優(yōu)化雙層規(guī)劃模型。上層是多目標(biāo)優(yōu)化模型,要求網(wǎng)絡(luò)效率、網(wǎng)絡(luò)環(huán)境和網(wǎng)絡(luò)公平性三個(gè)目標(biāo)盡可能達(dá)到期望值,決策變量是基于距離收費(fèi)函數(shù)；下層是基于距離收費(fèi)下的用戶均衡模型。由于本文建立的多目標(biāo)優(yōu)化模型的各個(gè)子目標(biāo)之間是存在矛盾的,因此本文采用目標(biāo)規(guī)劃法來處理多目標(biāo)問題。由于多目標(biāo)雙層規(guī)劃模型的復(fù)雜性和基于距離收費(fèi)函數(shù)特殊的離散性,任何基于梯度的求解方法很難用來求解建立的模型,遺傳算法作為非數(shù)值優(yōu)化算法中的一種,無需考慮模型具體的數(shù)學(xué)結(jié)構(gòu),更適合用來求解建立的多目標(biāo)雙層規(guī)劃模型。最后通過一個(gè)案例驗(yàn)證了本文提出的模型和算法的合理性和可行性,證明了基于距離最優(yōu)擁擠收費(fèi)函數(shù)是高度非線性的并可以使網(wǎng)絡(luò)系統(tǒng)性能達(dá)到最優(yōu)。
[Abstract]:All congestion charges are currently implemented using a single fixed charge, such as a regional pass fee strategy. This single charging strategy neglects the distance and time of the vehicle driving in the toll area, and it also causes the unfair problem of network users. In order to improve the current toll system, this paper proposes a distance congestion pricing model and makes a deep research on it. In this paper, we first define that the distance congestion charge is a nonlinear function of the vehicle driving distance in the toll area, and maintain the positive, non-decreasing property. Then the user equilibrium model based on distance congestion pricing is established and the existence and uniqueness of the solution are proved. Because the nonlinear mathematical expression of the toll function is generalized, in order to determine the specific form of the charge, the piecewise linear approximation method is used to re-express the nonlinear toll function. At the same time, the distance based nonlinear toll collection model will lead to the path cost can not be additive, that is, the path cost is not equal to the sum of the cost of each section of the path, so the traditional Frank-Wolfe algorithm can not be directly used to solve the problem. In order to solve the problem of non-additivity of path cost, this paper uses gradient projection based path algorithm to solve the problem, and combines k shortest path algorithm to find the shortest path under generalized path cost. Considering the path selection behavior under the condition of distance congestion pricing, a bilevel programming model based on distance congestion toll rate optimization is established in order to obtain the optimal rate to meet the goal expectation of decision makers. The upper layer is a multi-objective optimization model, which requires that the three goals of network efficiency, network environment and network fairness can reach the expected value as far as possible. The decision variable is based on the distance toll function, and the lower level is the user equilibrium model based on the distance charge. Because there are contradictions among the sub-objectives of the multi-objective optimization model, the goal programming method is used to deal with the multi-objective problem in this paper. Because of the complexity of the multi-objective bilevel programming model and the special discreteness based on the distance toll function, it is difficult for any gradient-based solution method to solve the established model. Genetic algorithm (GA) is one of the non-numerical optimization algorithms. Without considering the mathematical structure of the model, it is more suitable for solving the multi-objective bilevel programming model. Finally, a case is given to verify the rationality and feasibility of the proposed model and algorithm. It is proved that the distance-based optimal congestion toll function is highly nonlinear and can make the network system performance optimal.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：U491

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本文編號(hào)：1824441