随机用户均衡交通分配问题的蚁群优化算法

研究了出行者对路网熟悉程度的指标与交通流分配均衡性之间的关系, 提出了具有指数形式信息素更新策略的随机用户均衡模型蚁群优化算法, 建立了从Logit模型加载, 到交通需求确认及路径流量、路段流量、路段阻抗、路径阻抗迭代计算的交通分配动态循环流程; 计算了Nguyen-Dupuis路网模型中各路段的流量与阻抗, 并与连续平均算法计算结果进行比较; 通过调节出行者对路网熟悉程度的因子, 分析了蚁群优化算法与连续平均算法的敏感性。研究结果表明: 采用连续平均算法和蚁群优化算法计算的路段流量分布分别为20~280、40~260pcu, 蚁群优化算法的流量分布区间减小了15.4%, 路段流量的最大值减小了7.1%, 因此, 采用蚁群优化算法计算的路段流量较为均衡; 采用蚁群优化算法时, 在Nguyen-Dupuis路网模型中各路段流量的标准差从65pcu降至48pcu, 88%可选路径的阻抗分布在61~64, 且84%的路径阻抗低于采用连续平均算法计算的阻抗, 因此, 采用蚁群优化算法减少了用户出行时间; 当路网熟悉程度分别为0.01、0.1、1、2、7、11时, 采用连续平均算法计算的路段流量标准差分别为75、65、50、47、45、45pcu, 采用蚁群优化算法计算的路段流量标准差分别为48、48、48、47、43、43pcu, 可见, 随着路网熟悉程度的增大, 分配在各路段上的流量范围逐渐减小, 标准差趋于稳定, 信息素更新策略对出行者的路径选择概率影响越明显, 出行者选择阻抗小的路径的概率变大, 因此, 采用蚁群优化算法对路段的流量分配逐渐优于连续平均算法。 

An ant colony optimization algorithm of stochastic user equilibrium traffic assignment problem

The relationship between the indicators of the traveler's familiarity with the road network and the equilibrium of traffic flow assignment was studied. An ant colony optimization algorithm with the pheromone update strategy of exponential form was proposed to solve the stochastic user equilibrium problem. In addition, the dynamic cycle process of traffic assignment was established from the logit model loading to the iterative calculations of traffic demand, path flow, road flow, road impedance and path impedance. The road flows and road impedances of Nguyen-Dupuis road network model were calculated and compared with the result computed by the successive average algorithm. The sensitivities of ant colony optimization algorithm and successive average algorithm were analyzed by adjusting the factors of the traveler's familiaritywith the road network. Analysis result shows that the road flow distributions computed by the successive average algorithm and ant colony optimization algorithm are 20-280 and 40-260 pcu, respectively, and the flow distribution interval computed by the latter decreases by 15.4%, while the maximum road flow decreases by 7.1%. Therefore, the road flow calculated by the ant colony optimization algorithm is more balanced. When using the ant colony optimization algorithm, the standard deviation of each road section flow in Nguyen-Dupuis road network model reduces from 65 to 48 pcu, 88% of the alternative paths' impedances distribute in 61-64, and 84% of the path impedances are lower than the result computed by the successive average algorithm. Therefore, the ant colony optimization algorithm can reduce the user travel time. When the familiarity of the road network is 0.01, 0.1, 1, 2, 7, and 11, respectively, the standard deviation of each road section calculated by the successive average algorithm is 75, 65, 50, 47, 45, and 45 pcu, respectively, and the standard deviation calculated by the ant colony optimization algorithm is 48, 48, 48, 47, 43, and 43 pcu, respectively. With the increase of road network familiarity, the range of the flow assigned to each road gradually decreases, and the standard deviation tends to be stable. The pheromone update strategy has greater influence on the probability of traveler's path selection, and the probability selecting the path with smaller impedance is higher. Therefore, the ant colony optimization algorithm gradually outperforms the successive average algorithm for the flow distribution of each road section.