Path finding under uncertainty

Chen, Anthony; Ji, Zhaowang

doi:10.1002/atr.5670390104

Cited by 132 publications

(87 citation statements)

References 13 publications

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“…However, due to the non-additive property of the effective travel time, conventional shortest path algorithm does not work. To overcome this difficulty, Chen and Ji (2005) proposed a genetic algorithm which is able to find the route with the minimum effective travel time. Their method can be incorporated into the column generation procedure to generate the route set.…”

Section: Detailed Algorithmic Stepsmentioning

confidence: 99%

A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand

2006

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This paper presents a novel reliability-based stochastic user equilibrium traffic assignment model in view of the day-to-day demand fluctuations for multi-class transportation networks. In the model, each class of travelers has a different safety margin for on-time arrival in response to the stochastic travel times raised from demand variations. Travelers' perception errors on travel time are also considered in the model. This model is formulated as an equivalent variational inequality problem, which is solved by the proposed heuristic solution algorithm. Numerical examples are presented to illustrate the applications of the proposed model and the efficiency of solution algorithm. Copyright Springer Science + Business Media, LLC 2006Reliability-based, Multiple user classes, Demand variations, Variational inequality, Traffic assignment problem,

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Section: Detailed Algorithmic Stepsmentioning

confidence: 99%

A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand

2006

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“…Shao et al [9] proposed a heuristic algorithm to search for the highest reliability path. Chen and Ji [10] developed a simulation-based genetic algorithm procedure to solve these path finding models under uncertainties. Ying [11] presented a reliable routing algorithm with real time and historical information.…”

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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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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“…However, in many applications reliability considerations are very important: riskaverse users need reassurance regarding the level of risk, and not just the expected cost of the provided solution. For example, the transportation community has recognized the importance of reliable route plans (e.g., [7,28,25,37,9]), however the solutions offered are typically inefficient or heuristic with unknown approximation guarantee. Similarly, reliability is a key consideration in finance and other continuous optimization settings [34].…”

Section: Introductionmentioning

confidence: 99%

Approximation Algorithms for Reliable Stochastic Combinatorial Optimization

Nikolova

2010

Lecture Notes in Computer Science

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We consider optimization problems that can be formulated as minimizing the cost of a feasible solution w T x over an arbitrary combinatorial feasible set F ⊂ {0, 1} n . For these problems we describe a broad class of corresponding stochastic problems where the cost vector W has independent random components, unknown at the time of solution. A natural and important objective that incorporates risk in this stochastic setting is to look for a feasible solution whose stochastic cost has a small tail or a small convex combination of mean and standard deviation. Our models can be equivalently reformulated as nonconvex programs for which no efficient algorithms are known. In this paper, we make progress on these hard problems.Our results are several efficient general-purpose approximation schemes. They use as a black-box (exact or approximate) the solution to the underlying deterministic problem and thus immediately apply to arbitrary combinatorial problems. For example, from an available δ-approximation algorithm to the linear problem, we construct a δ(1 + ǫ)-approximation algorithm for the stochastic problem, which invokes the linear algorithm only a logarithmic number of times in the problem input (and polynomial in 1 ǫ ), for any desired accuracy level ǫ > 0. The algorithms are based on a geometric analysis of the curvature and approximability of the nonlinear level sets of the objective functions.

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Path finding under uncertainty

Cited by 132 publications

References 13 publications

A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand

A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand

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

Approximation Algorithms for Reliable Stochastic Combinatorial Optimization

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