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19
Finding the k shortest hyperpaths
"... The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. Ho ..."
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Cited by 17 (4 self)
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The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. However, the K shortest hyperpaths problem has not yet been investigated. In this paper we present procedures for finding the K shortest hyperpaths in a directed hypergraph. This is done by extending existing algorithms for K shortest loopless paths. Computational experiments on the proposed procedures are performed, and applications in transportation, planning and combinatorial optimization are discussed.
Stochastic shortest paths via quasiconvex maximization
 PROCEEDINGS OF EUROPEAN SYMPOSIUM OF ALGORITHMS
, 2006
"... We consider the problem of finding shortest paths in a graph with independent randomly distributed edge lengths. Our goal is to maximize the probability that the path length does not exceed a given threshold value (deadline). We give a surprising exact n Θ(log n) algorithm for the case of normally ..."
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Cited by 16 (7 self)
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We consider the problem of finding shortest paths in a graph with independent randomly distributed edge lengths. Our goal is to maximize the probability that the path length does not exceed a given threshold value (deadline). We give a surprising exact n Θ(log n) algorithm for the case of normally distributed edge lengths, which is based on quasiconvex maximization. We then prove average and smoothed polynomial bounds for this algorithm, which also translate to average and smoothed bounds for the parametric shortest path problem, and extend to a more general nonconvex optimization setting. We also consider a number other edge length distributions, giving a range of exact and approximation schemes.
Optimal route planning under uncertainty
 In Proc. of International Conference on Automated Planning and Scheduling
, 2006
"... We present new complexity results and efficient algorithms for optimal route planning in the presence of uncertainty. We employ a decision theoretic framework for defining the optimal route: for a given source S and destination T in the graph, we seek an STpath of lowest expected cost where the edg ..."
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Cited by 13 (6 self)
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We present new complexity results and efficient algorithms for optimal route planning in the presence of uncertainty. We employ a decision theoretic framework for defining the optimal route: for a given source S and destination T in the graph, we seek an STpath of lowest expected cost where the edge travel trimes are eandom variable and the cost is a nonlinear function of total travel time. Although this is a natural model for routeplanning on realworld road networks, results are sparse due to the analytic difficulty of finding closed form expressions for the exptected cost (Fan, Kalaba and Moore), as well as the computational/combinatorial difficulty of efficiently finding an optimal path which minimizes the exptected cost. We identify a family of appropriate cost models and travel time distributions that are closed under convolution and physically valid. We obtain hardness results for routing problems with a given start time and cost functions with a global minimum, in a variety of deterministic and stochastic settings. In general the global cost is not separable into edge costs, precluding classic shortestpath approaches. However, using partial minimization techniques, we exhibit an efficient solution via dynamic programming with low polynomial complexity.
Optimal Vehicle Routing with RealTime Traffic Information
 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
, 2002
"... This paper examines the value of realtime traffic information to optimal vehicle routing in a nonstationary stochastic network. We present a systematic approach to aid in the implementation of transportation systems integrated with real time information technology. We develop decisionmaking procedu ..."
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Cited by 11 (1 self)
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This paper examines the value of realtime traffic information to optimal vehicle routing in a nonstationary stochastic network. We present a systematic approach to aid in the implementation of transportation systems integrated with real time information technology. We develop decisionmaking procedures for determining the optimal driver attendance time, optimal departure times, and optimal routing policies under stochastically changing traffic flows based on a Markov decision process formulation. With a numerical study carried out on an urban road network in Southeast Michigan, we demonstrate significant advantages when using this information in terms of total costs savings and vehicle usage reduction while satisfying or improving service levels for justintime delivery.
A polynomialtime algorithm to find shortest paths with recourse
 Networks
, 2003
"... The Shortest Path with Recourse Problem involves finding the shortest expectedlength paths in a directed network each of whose arcs have stochastic traversal lengths (or delays) that become known only upon arrival at the tail of that arc. The traveler starts at a given source node, and makes routin ..."
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Cited by 8 (0 self)
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The Shortest Path with Recourse Problem involves finding the shortest expectedlength paths in a directed network each of whose arcs have stochastic traversal lengths (or delays) that become known only upon arrival at the tail of that arc. The traveler starts at a given source node, and makes routing decisions at each node in such a way that the expected distance to a given sink node is minimized. We develop an extension of Dijkstra’s algorithm to solve the version of the problem where arclengths are nonnegative and reset after each arc traversal. All known noreset versions of the problem are NPhard. We make a partial extension to the case where negative arclengths are present.
Shortest paths in stochastic networks with correlated link costs
 Computers and Mathematics With Applications
, 2005
"... Abstract. The objective is to minimize expected travel time from any origin to a specific destination in a congestible network with correlated link costs. Each link is assumed to be in one of two possible conditions. Conditional probability density functions for link travel times are assumed known f ..."
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Cited by 6 (0 self)
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Abstract. The objective is to minimize expected travel time from any origin to a specific destination in a congestible network with correlated link costs. Each link is assumed to be in one of two possible conditions. Conditional probability density functions for link travel times are assumed known for each condition. Conditions over the traversed links are taken into account for determining the optimal routing strategy for the remaining trip. This problem is treated as a multistage adaptive feedback control process. Each stage is described by the physical state (the location of the current decision point) and the information state (the service level of the previously traversed links). Proof of existence and uniqueness of the solution to the basic dynamic programming equations and a solution procedure are provided. Key Words. Shortest path, stochastic networks, dynamic programming, adaptive feedback control, correlated link costs.
State Space Reduction for Nonstationary Stochastic Shortest Path Problems with RealTime Traffic Information
 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
, 2005
"... Routing vehicles based on realtime traffic information has been shown to significantly reduce travel time, and hence cost, in highvolume traffic situations. However, taking realtime traffic data and transforming them into optimal route decisions is a computational challenge. We model the dynamic ..."
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Cited by 4 (0 self)
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Routing vehicles based on realtime traffic information has been shown to significantly reduce travel time, and hence cost, in highvolume traffic situations. However, taking realtime traffic data and transforming them into optimal route decisions is a computational challenge. We model the dynamic route determination problem as a Markov decision process (MDP) and present procedures for identifying traffic data having no decisionmaking value. Such identification can be used to reduce the state space of the MDP, improving its computational tractability. This reduction can be achieved by a twostep process. The first is an a priori reduction that may be performed using a stationary, deterministic network with upper and lower bounds on the cost functions before the trip begins. The second part of the process dynamically reduces the state space further on the nonstationary stochastic road network as the trip optimally progresses. We demonstrate the significant computational advantages of the introduced methods based on an actual road network in southeast Michigan.
Optimal Path Problems with SecondOrder Stochastic Dominance Constraints
, 2009
"... This paper studies optimal path problems integrated with the concept of stochastic dominance. These problems arise from applications where travelers need trade off the risk associated with travel time against other costs when making routing decisions. Riskaverse behavior is embedded by constraining ..."
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Cited by 1 (1 self)
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This paper studies optimal path problems integrated with the concept of stochastic dominance. These problems arise from applications where travelers need trade off the risk associated with travel time against other costs when making routing decisions. Riskaverse behavior is embedded by constraining optimal paths with secondorder stochastic dominance (SSD). A general linear operating cost is introduced to combine link and pathbased costs. The latter is employed to address schedule costs pertinent to late or early arrival. An equivalent linear program of the problem is constructed by transforming the SSD constraint into a finite number of linear constraints. Various solution techniques are discussed, including those based on linear programming and dynamic programming. Numerical results are provided using small and mediumsize examples.
MACHINE LEARNING SOLUTIONS FOR TRANSPORTATION NETWORKS
, 2008
"... This dissertation was presented by Tomas Singliar.
This thesis brings a collection of novel models and methods that result from a new look at practical problems
in transportation through the prism of newly available sensor data. There are four main contributions:
First, we design a generative proba ..."
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This dissertation was presented by Tomas Singliar.
This thesis brings a collection of novel models and methods that result from a new look at practical problems
in transportation through the prism of newly available sensor data. There are four main contributions:
First, we design a generative probabilistic graphical model to describe multivariate continuous densities
such as observed traffic patterns. The model implements a multivariate normal distribution with covariance
constrained in a natural way, using a number of parameters that is only linear (as opposed to quadratic) in
the dimensionality of the data. This means that learning these models requires less data. The primary use
for such a model is to support inferences, for instance, of data missing due to sensor malfunctions.
Second, we build a model of traffic flow inspired by macroscopic flow models. Unlike traditional such
models, our model deals with uncertainty of measurement and unobservability of certain important quantities
and incorporates onthefly observations more easily. Because the model does not admit efficient exact
inference, we develop a particle filter. The model delivers better medium and long term predictions than
generalpurpose time series models. Moreover, having a predictive distribution of traffic state enables the
application of powerful decisionmaking machinery to the traffic domain.
Third, two new optimization algorithms for the common task of vehicle routing are designed, using the
tra±c °ow model as their probabilistic underpinning. Their bene¯ts include suitability to highly volatile
environments and the fact that optimization criteria other than the classical minimal expected time are
easily incorporated.
Finally, we present a new method for detecting accidents and other adverse events. Data collected from
highways enables us to bring supervised learning approaches to incident detection. We show that a support
vector machine learner can outperform manually calibrated solutions. A major hurdle to performance of
supervised learners is the quality of data which contains systematic biases varying from site to site. We build
a dynamic Bayesian network framework that learns and rectifies these biases, leading to improved supervised
detector performance with little need for manually tagged data. The realignment method applies generally
to virtually all forms of labeled sequential data.
Highperformance Heuristics for Optimization in Stochastic Traffic Engineering Problems
"... Abstract. We consider a stochastic routing model in which the goal is to find the optimal route that incorporates a measure of risk. The settings such as task planning (where the time to execute tasks is uncertain), etc. The stochasticity is specified in terms of arbitrary edge length distributions ..."
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Abstract. We consider a stochastic routing model in which the goal is to find the optimal route that incorporates a measure of risk. The settings such as task planning (where the time to execute tasks is uncertain), etc. The stochasticity is specified in terms of arbitrary edge length distributions with given mean and variance values in a graph. The objective function is a positive linear combination of the mean and standard deviation of the route. Both the nonconvex objective and exponentially sized feasible set of available routes present a challenging optimization problem for which no efficient algorithms are known. In this paper we evaluate the practical performance of algorithms and heuristic approaches which show very promising results in terms of both running time and solution accuracy. 1