Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics

Liu, Zhiyuan; Wang, Shuaian; Zhou, Bojian; Cheng, Qixiu

doi:10.1016/j.trc.2017.03.011

Cited by 81 publications

(64 citation statements)

References 57 publications

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“…This assumption enables the link additive property resulting in a link‐based approach to pricing system modeling and optimization. If nonlinearity is assumed, a path‐based approach should be pursued (Liu et al., ). Let

l_{r}^{o d} false(h false)

and

t_{r}^{o d} false(h false)

be the distance traveled and the time spent within the PZ for path

r \in R^{o d}

during the h th tolling interval, respectively:

l_{r}^{o d} (h) = \sum_{a \in A_{normalp}} l_{a} δ_{a, r}^{o d}

t_{r}^{o d} (h) = \sum_{a \in A_{normalp}} t_{a} (h) δ_{a, r}^{o d}

where

r \in R^{o d}, false(o, d false) \in W, h \in false(1, 2, \dots, m false)

.…”

Section: Problem Formulationmentioning

confidence: 99%

Surrogate‐based toll optimization in a large‐scale heterogeneously congested network

Waller

Saberi

2019

Computer aided Civil Eng

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Toll optimization in a large‐scale dynamic traffic network is typically characterized by an expensive‐to‐evaluate objective function. In this paper, we propose two toll‐level problems (TLPs) integrated with a large‐scale simulation‐based dynamic traffic assignment model of Melbourne, Australia. The first TLP aims to control the pricing zone (PZ) through a time‐varying joint distance and delay toll such that the network fundamental diagram (NFD) of the PZ does not enter the congested regime. The second TLP is built upon the first TLP by further considering the minimization of the heterogeneity of congestion distribution in the PZ. To solve the two TLPs, a computationally efficient surrogate‐based optimization method, that is, regressing kriging with expected improvement sampling, is applied to approximate the simulation input–output mapping, which can balance well between local exploitation and global exploration. Results show that the two optimal TLP solutions reduce the average travel time in the PZ (entire network) by 29.5% (1.4%) and 21.6% (2.5%), respectively. Reducing the heterogeneity of congestion distribution achieves higher network flows in the PZ and a lower average travel time or a larger total travel time saving in the entire network.

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l_{r}^{o d} false(h false)

and

t_{r}^{o d} false(h false)

be the distance traveled and the time spent within the PZ for path

r \in R^{o d}

during the h th tolling interval, respectively:

l_{r}^{o d} (h) = \sum_{a \in A_{normalp}} l_{a} δ_{a, r}^{o d}

t_{r}^{o d} (h) = \sum_{a \in A_{normalp}} t_{a} (h) δ_{a, r}^{o d}

where

r \in R^{o d}, false(o, d false) \in W, h \in false(1, 2, \dots, m false)

.…”

Section: Problem Formulationmentioning

confidence: 99%

Surrogate‐based toll optimization in a large‐scale heterogeneously congested network

Waller

Saberi

2019

Computer aided Civil Eng

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“…e logit-based SUE problem can be equivalently formulated as a mathematical programming problem with a unique solution. is feature facilitates its usage in both theoretical and practical studies [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Improving Truncated Newton Method for the Logit‐Based Stochastic User Equilibrium Problem

Zhou

2019

Mathematical Problems in Engineering

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is study proposes an improved truncated Newton (ITN) method for the logit-based stochastic user equilibrium problem. e ITN method incorporates a preprocessing procedure to the traditional truncated Newton method so that a good initial point is generated, on the basis of which a useful principle is developed for the choice of the basic variables. We discuss the rationale of both improvements from a theoretical point of view and demonstrate that they can enhance the computational efficiency in the early and late iteration stages, respectively, when solving the logit-based stochastic user equilibrium problem. e ITN method is compared with other related methods in the literature. Numerical results show that the ITN method performs favorably over these methods.

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“…In existing works of traffic prediction, common methods can be classified into three categories, namely, traditional time series models, analytical models, and machine learning models. Thanks to the development in data collection tools, the abundance of data nowadays can facilitate a variety of studies, including traffic safety (Gu, Abdel‐Aty, Xiang, Cai, & Yuan, ; Guo, Liu, Wu, & Chen, ; Liu, Wu, Zhou, Bao, & Yang, ), traffic management (Hashemi & Abdelghany, ; Li, Zhang, Wang, & Ran, ; Liu, Jia, Xie, & Liu, ; Liu, Wang, Zhou, & Cheng, ), energy consumption (Pan, Chen, Qiao, Ukkusuri, & Tang, ), and flow prediction (Liu, Liu, & Jia, ). Notably, the emerging deep learning methods significantly extend the possibility of more creative research, such as infrastructure monitoring (Nabian & Meidani, ; Rafiei & Adeli, , ; Xue & Li, ) and material property examination (Rafiei, Khushefati, Demirboga, & Adeli, ).…”

Section: Introductionmentioning

confidence: 99%

A spatio‐temporal ensemble method for large‐scale traffic state prediction

Liu

et al. 2019

Computer aided Civil Eng

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How to effectively ensemble multiple models while leveraging the spatio‐temporal information is a challenging but practical problem. However, there is no existing ensemble method explicitly designed for spatio‐temporal data. In this paper, a fully convolutional model based on semantic segmentation technology is proposed, termed as spatio‐temporal ensemble net. The proposed method is suitable for grid‐based spatio‐temporal prediction in dense urban areas. Experiments demonstrate that through spatio‐temporal ensemble net, multiple traffic state prediction base models can be combined to improve the prediction accuracy.

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Robust optimization of distance-based tolls in a network considering stochastic day to day dynamics

Cited by 81 publications

References 57 publications

Surrogate‐based toll optimization in a large‐scale heterogeneously congested network

Surrogate‐based toll optimization in a large‐scale heterogeneously congested network

Improving Truncated Newton Method for the Logit‐Based Stochastic User Equilibrium Problem

A spatio‐temporal ensemble method for large‐scale traffic state prediction

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