Equilibrium in Multi-criteria Transportation Networks

Phuong, Truong Thi

doi:10.1007/s10957-016-0876-3

Cited by 10 publications

(5 citation statements)

References 27 publications

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“…Moreover, they presented a modified projection method to handle multi-criteria traffic network equilibrium problems. Subsequently, Luc and Phuong [14] introduced two optimization problems to show that the optimal solutions are exactly the equilibrium of the traffic network and then put forward a modified Frank-Wolfe gradient algorithm for multi-criteria traffic network equilibrium problems. However, this method may lead to the non-differentiability of the objective functions of the two optimization problems.…”

Section: Literature Reviewsmentioning

confidence: 99%

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Robust Multi-Criteria Traffic Network Equilibrium Problems with Path Capacity Constraints

2023

Axioms

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With the progress of society and the diversification of transportation modes, people are faced with more and more complicated travel choices, and thus, multi-criteria route choosing optimization problems have drawn increased attention in recent years. A number of multi-criteria traffic network equilibrium problems have been proposed, but most of them do not involve data uncertainty nor computational methods. This paper focuses on the methods for solving robust multi-criteria traffic network equilibrium problems with path capacity constraints. The concepts of the robust vector equilibrium and the robust vector equilibrium with respect to the worst case are introduced, respectively. For the robust vector equilibrium, an equivalent min–max optimization problem is constructed. A direct search algorithm, in which the step size without derivatives and redundant parameters, is proposed for solving this min–max problem. In addition, we construct a smoothing optimization problem based on a variant version of ReLU activation function to compute the robust weak vector equilibrium flows with respect to the worst case and then find robust vector equilibrium flows with respect to the worst case by using the heaviside step function. Finally, extensive numerical examples are given to illustrate the excellence of our algorithms compared with existing algorithms. It is shown that the proposed min–max algorithm may take less time to find the robust vector equilibrium flows and the smoothing method can more effectively generate a subset of the robust vector equilibrium with respect to the worst case.

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Section: Literature Reviewsmentioning

confidence: 99%

“…After that, Phuong [15] proposed a smoothing method to solve multi-criteria network equilibrium problems. Although this method solves the defects existing in [14], it does not take into account the data uncertainty.…”

Section: Literature Reviewsmentioning

confidence: 99%

Robust Multi-Criteria Traffic Network Equilibrium Problems with Path Capacity Constraints

2023

Axioms

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“…The multi-criteria traffic network equilibrium model is used to evaluate the traffic flow pattern and the travel costs, and it has played an important role in the traffic network programming and the traffic control. The topic has received increasing interest from many researchers, e.g., see [37,38,46,52]. Recently, Cao et al [6] and Wei et al [51] discuss existence and optimality conditions for multi-criteria traffic network equilibrium problems with uncertain demands.…”

Section: Applications To Uncertain Multi-criteria Traffic Network Equilibrium Problemsmentioning

confidence: 99%

Image Space Analysis for Set Optimization Problems with Applications

Zhou

Zhu

2021

J Optim Theory Appl

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In this paper, we consider a set optimization problem with a partial order relation, which is defined by Minkowski difference. By using the image space analysis, we establish the relationships among the set optimization problem, a vector optimization problem and a set-valued optimization with vector criterion related to the image of the set optimization problem. In addition, two nonlinear regular weak separation functions are proposed for the set optimization problem. Based on the two nonlinear regular weak separation functions, saddle point sufficient optimality conditions, gap functions and error bounds for the set optimization problem, are obtained. Finally, we explore some applications of the obtained results to investigate robust multi-objective optimization problems and verify the validity of the results in shortest path problems with data uncertainty and multi-criteria traffic network equilibrium problems with interval-valued cost functions.

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“…Moreover, they presented a method to handle multi-criteria network equilibrium problems. Subsequently, Luc and Phuong [14] put forward a modified Frank-Wolfe gradient algorithm for multi-criteria network equilibrium problems. After that, Phuong [15] proposed a smoothing method to solve multi-criteria network equilibrium problems.…”

Section: Introductionmentioning

confidence: 99%

“…After that, Phuong [15] proposed a smoothing method to solve multi-criteria network equilibrium problems. Numerical methods proposed in Phuong and Luc [13], Luc and Phuong [14] and Phuong [15], can be seen as a first step for the computation of multi-criteria network equilibrium problems.…”

Section: Introductionmentioning

confidence: 99%

Robust Multi-Criteria Traffic Network Equilibrium Problems with Path Capacity Constraints

Xu¹,

Ma²

2023

Preprint

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This paper focuses on robust multi-criteria traffic network equilibrium problems with path capacity constraints. The concepts of robust vector equilibrium and robust vector equilibrium with respect to worst case are introduced, respectively. To generate a subset of robust vector equilibrium, an equivalent min-max optimization problem is constructed. In addition, a direct search algorithm, in which the step size without derivatives and redundant parameters, for solving this min-max problem is proposed. To find a subset of robust vector equilibrium with respect to worst case, an equivalent smoothing optimization problem based on a variant version of ReLU activation function is established. Numerical experiments are also presented to expound the advantages of the algorithms.

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Equilibrium in Multi-criteria Transportation Networks

Cited by 10 publications

References 27 publications

Robust Multi-Criteria Traffic Network Equilibrium Problems with Path Capacity Constraints

Robust Multi-Criteria Traffic Network Equilibrium Problems with Path Capacity Constraints

Image Space Analysis for Set Optimization Problems with Applications

Robust Multi-Criteria Traffic Network Equilibrium Problems with Path Capacity Constraints

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