Equilibrium in multi-criteria supply and demand networks with capacity constraints

Truong, Thi Thanh Phuong

doi:10.1007/s00186-014-0487-4

Cited by 7 publications

(3 citation statements)

References 26 publications

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“…Recently, Phuong and Luc [13] established the equivalent relationship between strong vector equilibrium flows and the solutions of variational inequality problems in terms of a kind of increasing functions. Moreover, they presented a modified projection method to handle multi-criteria traffic network equilibrium problems.…”

Section: Literature Reviewsmentioning

confidence: 99%

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%

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

2023

Axioms

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“…Regarding theoretical analysis for multi-criteria traffic equilibrium models, we refer the reader to Yang and Goh [9]; Li et al [10], Luc et al [11], Raith and Ehrgott [12] for further contributions. Recently, Phuong and Luc [13] established the equivalent relationship between strong vector equilibrium flows and the solutions of variational inequality problems in terms of a kind of increasing functions. Moreover, they presented a method to handle 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

Phuong

2016

J Optim Theory Appl

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Equilibrium in multi-criteria supply and demand networks with capacity constraints

Cited by 7 publications

References 26 publications

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

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

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

Equilibrium in Multi-criteria Transportation Networks

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