Maximizing the Probability of Arriving on Time: A Practical Q-Learning Method

The stochastic shortest path problem is of crucial importance for the development of sustainable transportation systems. Existing methods based on the probability tail model seek for the path that maximizes the probability of arriving at the destination before a deadline. However, they suffer from low accuracy and/or high computational cost. We design a novel Q-learning method where the converged Q-values have the practical meaning as the actual probabilities of arriving on time so as to improve accuracy. By further adopting dynamic neural networks to learn the value function, our method can scale well to large road networks with arbitrary deadlines. Experimental results on real road networks demonstrate the significant advantages of our method over other counterparts

A Framework for Data-Driven Explainability in Mathematical Optimization

Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the perception of optimization software as a black box. Although well understood by scientists, this lacks easy accessibility for practitioners. Hence, we advocate for introducing the explainability of a solution as another evaluation criterion, next to its objective value, which enables us to find trade-off solutions between these two criteria. Explainability is attained by comparing against (not necessarily optimal) solutions that were implemented in similar situations in the past. Thus, solutions are preferred that exhibit similar features. Although we prove that already in simple cases the explainable model is NP-hard, we characterize relevant polynomially solvable cases such as the explainable shortest-path problem. Our numerical experiments on both artificial as well as real-world road networks show the resulting Pareto front. It turns out that the cost of enforcing explainability can be very small

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Tractable Pathfinding for the Stochastic On-Time Arrival Problem

We present a new and more efficient technique for computing the route that maximizes the probability of on-time arrival in stochastic networks, also known as the path-based stochastic on-time arrival (SOTA) problem. Our primary contribution is a pathfinding algorithm that uses the solution to the policy-based SOTA problem---which is of pseudo-polynomial-time complexity in the time budget of the journey---as a search heuristic for the optimal path. In particular, we show that this heuristic can be exceptionally efficient in practice, effectively making it possible to solve the path-based SOTA problem as quickly as the policy-based SOTA problem. Our secondary contribution is the extension of policy-based preprocessing to path-based preprocessing for the SOTA problem. In the process, we also introduce Arc-Potentials, a more efficient generalization of Stochastic Arc-Flags that can be used for both policy- and path-based SOTA. After developing the pathfinding and preprocessing algorithms, we evaluate their performance on two different real-world networks. To the best of our knowledge, these techniques provide the most efficient computation strategy for the path-based SOTA problem for general probability distributions, both with and without preprocessing.Comment: Submission accepted by the International Symposium on Experimental Algorithms 2016 and published by Springer in the Lecture Notes in Computer Science series on June 1, 2016. Includes typographical corrections and modifications to pre-processing made after the initial submission to SODA'15 (July 7, 2014

Effects of Data Resolution and Human Behavior on Large Scale Evacuation Simulations

Traffic Analysis Zones (TAZ) based macroscopic simulation studies are mostly applied in evacuation planning and operation areas. The large size in TAZ and aggregated information of macroscopic simulation underestimate the real evacuation performance. To take advantage of the high resolution demographic data LandScan USA (the zone size is much smaller than TAZ) and agent-based microscopic traffic simulation models, many new problems appeared and novel solutions are needed. A series of studies are conducted using LandScan USA Population Cells (LPC) data for evacuation assignments with different network configurations, travel demand models, and travelers compliance behavior. First, a new Multiple Source Nearest Destination Shortest Path (MSNDSP) problem is defined for generating Origin Destination matrix in evacuation assignments when using LandScan dataset. Second, a new agent-based traffic assignment framework using LandScan and TRANSIMS modules is proposed for evacuation planning and operation study. Impact analysis on traffic analysis area resolutions (TAZ vs LPC), evacuation start times (daytime vs nighttime), and departure time choice models (normal S shape model vs location based model) are studied. Third, based on the proposed framework, multi-scale network configurations (two levels of road networks and two scales of zone sizes) and three routing schemes (shortest network distance, highway biased, and shortest straight-line distance routes) are implemented for the evacuation performance comparison studies. Fourth, to study the impact of human behavior under evacuation operations, travelers compliance behavior with compliance levels from total complied to total non-complied are analyzed.Comment: PhD dissertation. UT Knoxville. 130 pages, 37 figures, 8 tables. University of Tennessee, 2013. http://trace.tennessee.edu/utk_graddiss/259