Path Planning under Time-Dependent Uncertainty

TL;DR

This paper introduces a new path-planning algorithm for graphs with uncertain, probabilistically dependent, time-varying edge costs, ensuring optimal routes under stochastic conditions and demonstrating effectiveness in stochastic bus network models.

Contribution

It develops a generalized dynamic-programming approach based on stochastic dominance for uncertain, dependent edge costs, extending traditional shortest path algorithms.

Findings

The algorithm produces optimal paths under time-dependent uncertainty.

Empirical results show improved performance over existing methods.

Application to stochastic bus networks validates practical effectiveness.

Abstract

Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential probabilistic dependencies among the costs. Although these dependencies violate the standard dynamic-programming decomposition, we identify a weaker stochastic consistency condition that justifies a generalized dynamic-programming approach based on stochastic dominance. We present a revised path-planning algorithm and prove that it produces optimal paths under time-dependent uncertain costs. We test the algorithm by applying it to a model of stochastic bus networks, and present empirical performance results comparing it to some alternatives. Finally, we consider extensions of these concepts to a more general class of problems of heuristic search under uncertainty.