弹性需求下带可交易电子路票的交通网络多目标双层规划模型

The multi-objective bi-level programming model for traffic network with tradable credit scheme under elastic demand

交通拥堵和环境污染是阻碍当今城市发展的2大问题。为了缓解城市交通拥堵和机动车尾气排放污染,采用多目标双层规划对弹性需求下的连续均衡城市交通网络进行建模:上层问题中,政府通过增强路段能力和收取电子路票在满足投资、成本约束的条件下使交通网络的综合效益最大化(即经济效益最大化且交通排放最小化);下层问题中,出行者通过选择最佳路径,在满足弹性需求的Wardrop用户均衡(UE)条件下最小化广义出行成本(出行时间和电子路票价值的总和)。据此,构建了弹性需求下带可交易电子路票的交通网络的多目标双层规划模型,对上层目标函数引入决策者的偏好将模型转化为双层单目标规划问题;再以下层规划问题的K-K-T最优性条件代替下层问题,将双层单目标目标规划问题转化为一般非线性规划问题;最后设计了相应的松弛求解算法。数值结果表明,所设计的模型和算法是可行、有效的。

Traffic congestion and environmental pollution are two major problems hindering the development of urban transportation today.In order to alleviate urban traffic congestion and vehicle exhaust pollution, a multi-objective bi-level programming was used to model the continuous equilibrium urban traffic network under elastic demand: In the upper level problem, the government maximizes the comprehensive benefits of the transportation network(i.e. maximizing economic benefits and minimizing traffic emissions) by enhancing the road section capacity and collecting credit scheme under the conditions of meeting the investment and cost constraints;In the lower level problem, by selecting the best path, travelers minimize the generalized travel cost(the sum of travel time and credit scheme value) under the condition of Wardrop user equilibrium(UE) meeting elastic demand. Therefore, the multi-objective bi-level programming model for transportation network with tradable credit scheme under elastic demand was constructed. The preference of decision makers was introduced into the upper objective function, and the model was transformed into a bi-level single objective programming problem. Then the lower level problem was replaced by the corresponding K-K-T optimality conditions, and the bi-level single objective programming problem was transformed into a general nonlinear programming problem. Finally, the corresponding relaxation algorithm was proposed. Numerical results show that the designed model and algorithm are feasible and effective.