Time-Dependent, Label-Constrained Shortest Path Problems with Applications

Abstract

In this paper, we consider a variant of shortest path problems where, in addition to congestion related time-dependent link travel times on a given transportation network, we also have specific labels for each arc denoting particular modes of travel. The problem then involves finding a time-dependent shortest path from an origin node to a destination node that also conforms with some admissible string of labels. This problem arises in theRoute Planner Moduleof Transportation Analysis Simulation System (TRANSIMS), which is developed by theLos Alamos National Laboratoryand is part of a multitrackTravel Model Improvement Programsponsored by the U.S. Department of Transportation (DOT) and the Environmental Protection Agency (EPA). We propose an effective algorithm for this problem by adapting efficient existing partitioned shortest path algorithmic schemes to handle time dependency along with the label constraints. We also develop several heuristics to curtail the search based on various route restrictions, indicators of progress, and projected travel times to complete the trip. The proposed methodology is applied to solve some real multimodal test problems related to the Portland, Oregon, transportation system. Computational results for both the exact method and the heuristic curtailing schemes are provided.

State-based accelerations and bidirectional search for bi-objective multi-modal shortest paths

“…As a regular language can be represented by a non-deterministic finite state automaton (NFA), Barett et al [2] proved that the problem is polynomial in the number of states of the automaton. In [1,8,22,26,25], practical implementation issues of this method have been discussed. Barett et al [1] proposed A * and bidirectional accelerations while Delling et al [8] and Pajor [22] proposed, in addition, core-based and access node-based speed-up techniques and also considered time-dependent networks.…”

“…With these techniques, they obtain a CPU time of 2.3 milliseconds on average for computing the O − D shortest path on a large intercontinental network with 50 700 647 nodes, 125 939 503 edges and a 3 state-automaton. Considering deterministic finite-state automaton (DFA) as input, Sherali et al [25] extended the problem to time-dependence and propose a strongly polynomial algorithm for FIFO graphs. Sherali and Jeenanunta [26] further extended the problem to approach-dependent travel times and propose a label-setting algorithm which consistently outperforms a label correcting algorithm designed for the same problem.…”

Efficient Computation of Shortest Paths in Time-Dependent Multi-Modal Networks

“…Another application on multi-modal time-dependent transportation networks can be 62 found in [Sherali et al 2003], [Sherali et al 2006] introduces turn penalties.…”

A Review of Dynamic Traffic Assignment Computer Packages

“…Sherali et al (2003) developed an effective method for implicitly working with the composite graphs rather than constructing the full composite graphs a priori. This model is based on the partitioned shortest-path algorithmic developed by Glover et al (1985) and its dynamic programming (DP) interpretation developed by Sherali (1991).…”

“…This model is based on the partitioned shortest-path algorithmic developed by Glover et al (1985) and its dynamic programming (DP) interpretation developed by Sherali (1991). Furthermore, to reduce the search effort, Sherali et al (2003) proposed several heuristic curtailing schemes by focusing the search to systematically proceed toward the destination from the origin while avoiding the searching of paths that are beyond a defined boundary. They developed an Ellipsoidal Region Technique (ERT) that examines only those paths within the union of some three defined ellipsoidal regions that envelope the origin and destination, including any freeway sections and related entrance and exit ramps.…”