Improved AND/OR Tree Search Algorithm in Analysis of Stochastic and Time-Dependent Shortest Path Problem

Zhi-Ying Xie,Yuan-Tong Jiang,Chih-Cheng Chen,Yuan-Rong He,Qianchuan Zhao

doi:10.1155/2021/9922466

Abstract

Real-time vehicle guidance effectively reduces traffic jams and improves the operational efficiency of urban transportation. The trip time on a route is considered as a random process that changes with time, and the shortest path selection requires a random dynamic model and the solution of a decision-making problem. Thus, the shortest trip time is the criterion to determine the dynamic path selection by a random dynamic programming (DP) model which discretizes the trip times in the continuous segments on the route. In this study, a numerical model of random dynamic programming is established by using a probability tree model and an AND/OR (AO∗) algorithm to select the path of the shortest trip time. The results show that the branches of the probability tree are only accumulated on the “quantity” and do not cause a “qualitative” change. The inefficient accumulation of “quantity” affects the efficiency of the algorithm, so it is important to separate the accumulation of “quantity” from node expansion. The accumulation of “quantity” changes the trip time according to the entering time into a segment, which demands an improved AO∗ algorithm. The new AO∗ algorithm balances between efficiency and the trip time and provides the optimal real-time vehicle guidance on the road.

Highlights

Vehicle-to-everything (V2X) and Internet of ings (IoT) collect a large amount of observation data of traffic from multisource sensors and devices and require big data technology [1,2,3,4]. e collected data may be used to provide the optimal path for vehicles, especially unmanned vehicles
Scientific Programming considers the time to move between them. e path selection is needed from the starting node but from each decision point to reach the target node in the shortest time. e optimal path must be selected to have the shortest trip time to the target node or intersection, and the subsequent selection will be no longer affected by the previous selection process
Is study aims to suggest an AND/OR (AO∗) algorithm to solve an stochastic and time-dependent shortest path (STDSP) problem in finding the optimal path with the shortest trip time between nodes or intersections. e complexity of the shortest path problem in an stochastic time-dependence (STD) network was analyzed by using a probability tree diagram and a first in first out (FIFO) algorithm based on the nonsatisfaction and nonuniqueness of the trip times. en, a model of stochastic dynamic programming for dynamic path selection was applied to the estimation of the minimum trip times

Summary

Introduction

Vehicle-to-everything (V2X) and Internet of ings (IoT) collect a large amount of observation data of traffic from multisource sensors and devices and require big data technology [1,2,3,4]. e collected data may be used to provide the optimal path for vehicles, especially unmanned vehicles. E optimal path must be selected to have the shortest trip time to the target node or intersection, and the subsequent selection will be no longer affected by the previous selection process For this type of decision-making, dynamic programming is regarded to be appropriate. Is study aims to suggest an AND/OR (AO∗) algorithm to solve an STDSP problem in finding the optimal path with the shortest trip time between nodes or intersections. Based on the heuristic function and the two-point discretization of the trip time between segments (between nodes or intersections), an AO∗ algorithm, a heuristic search algorithm was proposed to solve the STDSP problem by using the STD programming model with the consideration of the balances between the efficiency and the optimal trip. The proposed AO∗ algorithm was improved again for suggesting the final algorithm

Theoretical Background

Figure 1

Case Studies and Discussion