基于距离的交通拥挤收费模型与算法研究

发布时间：2018-04-30 11:50

本文选题：基于距离拥挤收费 + 路径成本不可加　；参考：《东南大学》2015年硕士论文

【摘要】：目前正在实施的所有拥挤收费都采用的是单一固定的收费方法,比如区域通行证收费策略。这种单一的收费策略忽略了在收费区域内车辆行驶的距离和时间,同时还会引起网络用户的不公平问题。为了改善当前收费系统,本文提出了基于距离拥挤收费模式并对其进行深入的研究。本文首先定义基于距离拥挤收费是收费区域内车辆行驶距离的非线性函数,并保持正的、非递减性质。随后建立了基于距离拥挤收费的用户均衡模型并证明了模型解的存在性和唯一性。由于收费函数的非线性数学表达形式是广义的,因此为了能够确定具体的收费形式,本文利用分段线性逼近方法来重新表达非线性收费函数。同时,基于距离的非线性收费模式还将导致路径成本不可加性,即路径成本不等于使用该路径的各个路段成本之和,因此无法直接使用传统的Frank-Wolfe算法来求解。为了解决这种路径成本不可加性问题,本文采用基于梯度投影的路径算法来求解,并结合k条最短路算法来寻找广义路径成本下的最短路径。考虑基于距离拥挤收费条件下的路径选择行为,为了求得满足决策者目标期望的最优费率,本文建立了基于距离拥挤收费费率优化双层规划模型。上层是多目标优化模型,要求网络效率、网络环境和网络公平性三个目标尽可能达到期望值,决策变量是基于距离收费函数；下层是基于距离收费下的用户均衡模型。由于本文建立的多目标优化模型的各个子目标之间是存在矛盾的,因此本文采用目标规划法来处理多目标问题。由于多目标双层规划模型的复杂性和基于距离收费函数特殊的离散性,任何基于梯度的求解方法很难用来求解建立的模型,遗传算法作为非数值优化算法中的一种,无需考虑模型具体的数学结构,更适合用来求解建立的多目标双层规划模型。最后通过一个案例验证了本文提出的模型和算法的合理性和可行性,证明了基于距离最优拥挤收费函数是高度非线性的并可以使网络系统性能达到最优。
[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.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：U491

【参考文献】