This work addresses a route planning problem constrained by a bus road network that includes the schedules of all buses. Given a query with a starting bus stop and a set of Points of Interest (POIs) to visit, our goal is to find an optimal route on the bus network that allows the user to visit all specified POIs from the starting stop with minimal travel time, which includes both bus travel time and waiting time at bus stops. Although this problem resembles a variant of the Traveling Salesman Problem, it cannot be effectively solved using existing solutions due to the complex nature of bus networks, particularly the constantly changing bus travel times and user waiting times. In this paper, we first propose a modified graph structure to represent the bus network, accommodating the varying bus travel times and their arrival schedules at each stop. Initially, we suggest a brute-force exploration algorithm based on the Dijkstra principle to evaluate all potential routes and determine the best one; however, this approach is too costly for large bus networks. To address this, we introduce the EA-Star algorithm, which focuses on computing the shortest route for promising POI visit sequences. The algorithm includes a terminal condition that halts evaluation once the optimal route is identified, avoiding the need to evaluate all possible POI sequences. During the computation of the shortest route for each POI visiting sequence, it employs the A* algorithm on the modified graph structure, narrowing the search space toward the destination and improving search efficiency. Experiments using New York bus network datasets demonstrate the effectiveness of our approach.
翻译:本研究探讨一个受公交道路网络约束的路径规划问题,该网络包含所有公交车的时刻表。给定一个包含起始公交站和一组待访问兴趣点(POIs)的查询,我们的目标是在公交网络上找到一条最优路径,使用户能够从起始站出发访问所有指定的兴趣点,并使得总旅行时间最小,其中包括公交车行驶时间和在公交站的等待时间。尽管该问题类似于旅行商问题的一个变体,但由于公交网络的复杂性,特别是公交车行驶时间和用户等待时间的不断变化,现有解决方案无法有效求解。本文首先提出一种改进的图结构来表示公交网络,以适应变化的公交车行驶时间及其在各站点的到达时刻表。我们最初提出了一种基于Dijkstra原理的暴力探索算法,以评估所有可能的路径并确定最优解;然而,对于大型公交网络,这种方法成本过高。为此,我们引入了EA-Star算法,该算法专注于计算有希望的POI访问序列的最短路径。该算法包含一个终止条件,一旦识别出最优路径即停止评估,从而避免评估所有可能的POI序列。在计算每个POI访问序列的最短路径时,它在改进的图结构上采用A*算法,缩小朝向目的地的搜索空间,从而提高搜索效率。使用纽约公交网络数据集的实验证明了我们方法的有效性。