Distributionally robust stochastic shortest path problem

Cheng, Jianqiang; Lisser, Abdel; Letournel, Marc

doi:10.1016/j.endm.2013.05.132

Cited by 11 publications

(4 citation statements)

References 12 publications

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“…A stochastic network where arc costs are deterministic while the delay on each arc is a random variable was modeled by Cheng et al . , and a semi‐definite programming relaxation approach was developed to find the shortest path. Lin addressed the problem of finding the quickest path in a stochastic network where the travel time on each arc is probabilistic.…”

Section: Related Literaturementioning

confidence: 99%

Finding time‐robust fuel‐efficient paths for a call‐taxi in a stochastic city road network

Godwin

Sajeev

George

2016

J of Advced Transportation

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Summary Intra‐city commuting is being revolutionized by call‐taxi services in many developing countries such as India. A customer requests a taxi via phone, and it arrives at the right time and at the right location for the pick‐up. This mode of intra‐city travel has become one of the most reliable and convenient modes of transportation for customers traveling for business and non‐business purposes. The increased number of vehicles on city roads and raising fuel costs has prompted a new type of transportation logistics problem of finding a fuel‐efficient and quickest path for a call‐taxi through a city road network, where the travel times are stochastic. The stochastic travel time of the road network is induced by obstacles such as the traffic signals and intersections. The delay and additional fuel consumption at each of these obstacles are calculated that are later imputed to the total travel time and fuel consumption of a path. A Monte‐Carlo simulation‐based approach is proposed to identify unique fuel‐efficient paths between two locations in a city road network where each obstacle has a delay distribution. A multi‐criteria score is then assigned to each unique path based on the probability that the path is fuel efficient, the average travel time of the path and the coefficient of variation of the travel times of the path. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Related Literaturementioning

confidence: 99%

Finding time‐robust fuel‐efficient paths for a call‐taxi in a stochastic city road network

Godwin

Sajeev

George

2016

J of Advced Transportation

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“…However, in a short period of time, its distribution is similar to the determined distribution, but it is not exactly the same, that is, the moment of the probability distribution is also uncertain. The distributed robust optimization under moment uncertainty (DRO-MU) method recently studied in the field of mathematics [31] can consider the similar but different characteristics of long-term fitting of random variables [32].…”

Section: Introductionmentioning

confidence: 99%

A Distributionally Robust Chance-Constrained Unit Commitment with N-1 Security and Renewable Generation

Sha¹,

Wang²,

Wang³

2021

Energies

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With the increasing penetration of renewable energy generation, one of the major challenges is the problem of how to express the stochastic process of wind power and photovoltaic output as the exact probability density and distribution, in order to improve the security and accuracy of unit commitment results, a distributed robust security-constrained optimization model based on moment uncertainty is proposed, in which the uncertainty of wind and photovoltaic power is captured by two uncertain sets of first- and second-order moments, respectively. The two sets contain the probability distribution of the forecast error of the wind and photovoltaic power, and in the model, the energy storage is considered. In order to solve the model effectively, firstly, based on the traditional chance-constrained second-order cone transformation, according to the first- and second-order moments polyhedron expression of the distribution set, a cutting plane method is proposed to solve the distributed robust chance constraints. Secondly, the modified IEEE-RTS 24 bus system is selected to establish a simulation example, an improved generalized Benders decomposition algorithm is developed to solve the model to optimality. The results show that the unit commitment results with different emphasis on economy and security can be obtained by setting different conservative coefficients and confidence levels and, then, provide a reasonable decision-making basis for dispatching operation.

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“…An alternative approach is to apply the distributionally robust (DR) optimization technique to the shortest path problem (Cheng et al, 2013;Shahabi et al, 2015;Yang & Zhou, 2017;Zhang et al, 2018), leading to a distributionally robust shortest path (DRSP) model. The DRSP model assumes that the true distribution belongs to an ambiguity set of distributions, over which an optimal path is to be found in some worst-case sense, e.g., the one minimizes the worst-case α-reliable mean-excess travel time (METT) (Zhang et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

“…The moment-based ambiguity set which consists of distributions with specified moment constraints is adopted for the DR optimization problem (Delage & Ye, 2010). Specifically, the DRSP model in Cheng et al (2013); Zhang et al (2018) assumes that the ambiguity set contains distributions with the exactly known first and second moments. Observe that this may lead to poor decisions if mismatch moments are used for the ambiguity set.…”

Section: Introductionmentioning

confidence: 99%

Wasserstein distributionally robust shortest path problem

Wang

You

Song

et al. 2020

European Journal of Operational Research

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This paper proposes a data-driven distributionally robust shortest path (DRSP) model where the distribution of the travel time in the transportation network can only be partially observed through a finite number of samples. Specifically, we aim to find an optimal path to minimize the worst-case α-reliable mean-excess travel time (METT) over a Wasserstein ball, which is centered at the empirical distribution of the sample dataset and the ball radius quantifies the level of its confidence. In sharp contrast to the existing DRSP models, our model is equivalently reformulated as a tractable mixed 0-1 convex problem, e.g., 0-1 linear program or 0-1 second-order cone program. Moreover, we also explicitly derive the distribution achieving the worst-case METT by simply perturbing each sample. Experiments demonstrate the advantages of our DRSP model in terms of the out-of-sample performance and computational complexity. Finally, our DRSP model is easily extended to solve the DR bi-criteria shortest path problem and the minimum cost flow problem.

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Distributionally robust stochastic shortest path problem

Cited by 11 publications

References 12 publications

Finding time‐robust fuel‐efficient paths for a call‐taxi in a stochastic city road network

Finding time‐robust fuel‐efficient paths for a call‐taxi in a stochastic city road network

A Distributionally Robust Chance-Constrained Unit Commitment with N-1 Security and Renewable Generation

Wasserstein distributionally robust shortest path problem

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