Stochastic shortest paths with recourse

Andreatta, Giovanni; Romeo, Luciano

doi:10.1002/net.3230180306

Cited by 66 publications

(45 citation statements)

References 14 publications

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“…Most of these path finding algorithms were usually investigated under an ideal traffic condition; that is, the travel times are deterministic. For example, Andreatta and Romeo [1] considered Stochastic Shortest Path (SSP) problems in probabilistic networks. Polychronopoulos and Tsitsiklis [2] considered shortest path problems defined on graphs with random arc costs.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The unreliability (or uncertainty) issue has been considered in some recently developed algorithms (Andreatta and Romeo [1], Polychronopoulos and Tsitsiklis [2], Fu and Rilett [6], and Zhang et al [7]). When scheduling important issues (e.g., attending a conference), a network user considers a shorter travel time, as well as a higher reliability of on-time arrival.…”

Section: Literature Reviewmentioning

confidence: 99%

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The Global Optimal Algorithm of Reliable Path Finding Problem Based on Backtracking Method

Shen

Shao

Zhang

et al. 2017

Mathematical Problems in Engineering

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There is a growing interest in finding a global optimal path in transportation networks particularly when the network suffers from unexpected disturbance. This paper studies the problem of finding a global optimal path to guarantee a given probability of arriving on time in a network with uncertainty, in which the travel time is stochastic instead of deterministic. Traditional path finding methods based on least expected travel time cannot capture the network user's risk-taking behaviors in path finding. To overcome such limitation, the reliable path finding algorithms have been proposed but the convergence of global optimum is seldom addressed in the literature. This paper integrates the -shortest path algorithm into Backtracking method to propose a new path finding algorithm under uncertainty. The global optimum of the proposed method can be guaranteed. Numerical examples are conducted to demonstrate the correctness and efficiency of the proposed algorithm.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

The Global Optimal Algorithm of Reliable Path Finding Problem Based on Backtracking Method

Shen

Shao

Zhang

et al. 2017

Mathematical Problems in Engineering

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“…Fu and Rilett [10] studied a dynamic and stochastic shortest path problem and suggested a heuristic based on k -shortest path algorithm to find the expected shortest path. Another variant is a stochastic shortest path problem with recourse, where network information is revealed throughout the entire time-horizon of problem, and a decision maker needs to recalculate the expected cost for the remaining routes at each decision point based on the information disclosed [32,33]. Kang and Ouyang [34] extended the stochastic traveling purchaser problem in which multiple sellers offer stochastic prices for different commodities, and the purchaser chooses to visit sellers of each commodity while minimizing the total travel and purchase cost.…”

Section: Literature Reviewmentioning

confidence: 99%

Urban Freight Truck Routing under Stochastic Congestion and Emission Considerations

Hwang

Ouyang

2015

Sustainability

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Abstract:Freight trucks are known to be a major source of air pollutants as well as greenhouse gas emissions in U.S. metropolitan areas, and they have significant effects on air quality and global climate change. Emissions from freight trucks during their deliveries should be considered by the trucking service sector when they make routing decisions. This study proposes a model that incorporates total delivery time, various emissions including CO2, VOC, NOX, and PM from freight truck activities, and a penalty for late or early arrival into the total cost objective of a stochastic shortest path problem. We focus on urban transportation networks in which random congestion states on each link follows an independent probability distribution. Our model finds the best truck routing on a given network so as to minimize the expected total cost. This problem is formulated into a mathematical model, and two solution algorithms including a dynamic programming approach and a deterministic shortest path heuristic are proposed. Numerical examples show that the proposed approach performs very well even for the large-size U.S. urban networks.

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“…CTP is a special case of the Stochastic Shortest Paths with Recourse (SPR) problem of Andreatta and Romeo [1], who present a stochastic dynamic programming formulation for SPR and note its intractability. Polychronopoulos and Tsitsiklis [12] also present a stochastic dynamic programming formulation for SPR and then prove the intractability of several variants.…”

Section: Overviewmentioning

confidence: 99%

“…Andreatta and Romeo [1] note that if there is a limit of K = 1 disambiguations allowed, then SPR can be efficiently solved. Indeed, we are willing to assume here a limit K on the number of allowed disambiguations, but solving our random disambiguation problem-even a discrete variant of it-is not currently practical unless K has a very small value.…”

Section: Overviewmentioning

confidence: 99%

Disambiguation Protocols Based on Risk Simulation

Fishkind

Priebe

Giles³

et al. 2007

IEEE Trans. Syst., Man, Cybern. A

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Suppose there is a need to swiftly navigate through a spatial arrangement of possibly forbidden regions, each region marked with the probability that it is indeed forbidden. In close proximity to any of these regions, you have the dynamic capability of disambiguating the region and learning for certain whether or not the region is forbidden-only in the latter case may you proceed through that region. The central issue is how to most effectively exploit this disambiguation capability to minimize the expected length of the traversal.Regions are never entered while they are possibly forbidden and, thus, no risk is ever actually incurred. Nonetheless, for the sole purpose of deciding where to disambiguate, it may be advantageous to simulate risk, temporarily pretending that possibly forbidden regions are riskily traversable, and each potential traversal is weighted with its level of undesirability, which is a function of its traversal length and traversal risk. Introduced in this paper is the simulated risk disambiguation protocol, which has you follow along a shortest traversal-in this undesirability sense-until an ambiguous region is about to be entered; at that location, a disambiguation is performed on this ambiguous region. (The process is then repeated from the current location, until the destination is reached.)We introduce the tangent arc graph as a means of simplifying the implementation of simulated risk disambiguation protocols, and we show how to efficiently implement the simulated risk disambiguation protocols which are based on linear undesirability functions. The effectiveness of these disambiguation protocols is illustrated with examples, including an example involving mine countermeasures path planning.

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Stochastic shortest paths with recourse

Cited by 66 publications

References 14 publications

The Global Optimal Algorithm of Reliable Path Finding Problem Based on Backtracking Method

The Global Optimal Algorithm of Reliable Path Finding Problem Based on Backtracking Method

Urban Freight Truck Routing under Stochastic Congestion and Emission Considerations

Disambiguation Protocols Based on Risk Simulation

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