A data-driven method for stochastic shortest path problem

This paper aims at solving a stochastic shortest path problem. The objective is to determine an optimal path which maximizes the probability of arriving on time given a time constraint (i.e., a deadline). To solve this problem, we propose a data-driven approach. We first reformulate the original finding optimal path problem as a cardinality minimization problem. Then, we apply an L₁ norm minimization technique to solve the cardinality problem. The problem is transformed into a mix integer linear programming problem, which can be solved using standard solvers. This proposed approach has three advantages over the traditional methods: (1) the proposed approach can handle various or even unknown travel time distributions, while traditional stochastic routing algorithms can only work on specified distributions; (2) the proposed approach does not rely on the assumption that the travel time on different road segments is independent from each other; (3) unlike other existing approaches which require that the deadline must be larger than a certain value, the proposed approach can support more flexible deadline definition. Then we test our approach respectively on artificial and real-world road networks, the experimental results show that the proposed approach can achieve a comparatively high accuracy when the sampling size of travel time is large enough. Moreover, under some reasonable assumptions, the accuracy could be 100%.