Models and algorithms for the traffic assignment problem with link capacity constraints

Nie, Yu; Zhang, H. M.; Lee, Der-Horng

doi:10.1016/s0191-2615(03)00010-9

Cited by 141 publications

(104 citation statements)

References 12 publications

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“…(Note that the mapping Y takes on as values subsets of G, and is in this sense relaxed compared to the column generation mapping of the conceptual scheme, which would take on as values subsets of G ∩ R.) In the context of simplicial decomposition applied to nonlinear network flows, Stefek [87] and Marin [62] have developed methods of that type; see also [47,94,48,54,50,70,64,86,14]. The convergence of this methodology requires a column generation principle which includes a pricing mechanism for the side constraints (cf.…”

Section: Discussionmentioning

confidence: 99%

A generic column generation principle: derivation and convergence analysis

2015

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Given a non-empty, compact and convex set, and an a priori defined condition which each element either satisfies or not, we want to find an element belonging to the former category. This is a fundamental problem of mathematical programming which encompasses nonlinear programs, variational inequalities, and saddle-point problems.We present a conceptual column generation scheme, which alternates between solving a restriction of the original problem and a column generation phase which is used to augment the restricted problems. We establish the general applicability of the conceptual method, as well as to the three problem classes mentioned. We also establish a version of the conceptual method in which the restricted and column generation problems are allowed to be solved approximately, and of a version allowing for the dropping of columns.We show that some solution methods (e.g., Dantzig-Wolfe decomposition and simplicial decomposition) are special instances, and present new convergent column generation methods in nonlinear programming, such as a sequential linear programming (SLP) type method. Along the way, we also relate our quite general scheme in nonlinear programming presented in this paper with several other classic, and more recent, iterative methods in nonlinear optimization.

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Section: Discussionmentioning

confidence: 99%

A generic column generation principle: derivation and convergence analysis

2015

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“…It is proved that the CTAP subject to linear constraints is a strictly convex problem which renders a unique global optimal solution of road flows [49][50][51][52][53][54]. Let us consider w r and b a as Lagrange multipliers for travel demand and capacity constraints, respectively; hence, the KarushKuhn-Tucker (KKT) conditions are established as…”

Section: Karush-kuhn-tucker Conditions and Lagrange Multipliermentioning

confidence: 99%

“…caused by the queue buildup in the oversaturated roads [49][50][51][52][55][56][57][58]. As shown, the beta which represents the value of toll or subsidy is a positive number, whereas the subsidy is supposed to be a negative value.…”

Section: Karush-kuhn-tucker Conditions and Lagrange Multipliermentioning

confidence: 99%

A modern congestion pricing policy for urban traffic: subsidy plus toll

Bagloee

Sarvi

2017

J. Mod. Transport.

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Congestion pricing is seen as an effective policy to address traffic congestion. In such policies where money, people and authorities are involved, the success generally hinges upon two factors: equity (being fair) and acceptability (to both people and authorities). The primary concern is the equity, for which ''tradable credit scheme (TCS)'' has been introduced and extensively studied in the literature. Nevertheless, due to the complexity of the trading schemes, the TCS has yet to find any foot in the real world. To this end, a novel idea of rewarding has substituted the trading component to be known as toll-and-subsidy scheme (TSS). The idea is to charge the drivers on some roads (toll) while rewarding them to use other alternative-and perhaps underutilizedroads (subsidy). The research of the TSS is in its infancy stage. The problem to be tackled in this study is as follows: Given a set of roads constituting a cordon line around the central business district (CBD) or across a screen line, how much toll or subsidy should be assigned to each road? The problem is first transformed into a capacitated traffic assignment problem. We employ a solution method based on augmenting the travel time of roads up to the level at which the traffic volumes do not exceed some target rates. A real dataset from the city of Winnipeg, Canada, is used as a pilot study. We then discuss policy-related applications of the TSS. It is proved in the literature that one can obtain optimal TSSs for various objectives and considerations. To this end, the non-negativity of the toll values is relaxed which results in a valid toll set. Nevertheless, the computational time is found to be of highest significance. Our method differs in the fact that the traffic volumes are bounded from the above and it is quite affordable. The main contribution is first to highlight the concept of subsidy along with traditional thought of merely toll. Second is to interpret the Lagrangian values of the capacity constraints as the values of the toll/subsidy.

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“…When |M j | = 1, the only node in M j is lcn j . Figure 1 illustrates the way to get lcn 11 given that the last common nodes of node 2, ⋯, 10 have been obtained. Assuming that the topological order is consistent with the node number, the last common nodes tree of node 11 is the solid-edge subgraph, and {(i, 11) ∈ A p } is the dashed-edge set { [5,11], [9,11], [10,11]}.…”

Section: Traffic Assignment Model With Capacity Constraintsmentioning

confidence: 99%

An augmented Lagrangian origin‐based algorithm for link‐capacitated traffic assignment problem

Shi

Huang

2014

J of Advced Transportation

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SUMMARYThe origin-based algorithm is embedded into the augmented Lagrangian method for the link-capacitated traffic assignment problem. In order to solve the "nonexistence" problem due to the second partial derivatives of the augmented Lagrangian function at some specific points, the approximate expressions of the second partial derivatives are amended in the origin-based algorithm. The graph of last common nodes is developed on the basis of the restricted single-origin network. A method is proposed for finding n-1 last common nodes of the restricted single-origin network, resulting in computational complexity of O(n 2 ) in finding last common nodes. Numerical analysis on the Sioux Falls network and Chicago Sketch network demonstrated the effectiveness and characteristics of the proposed algorithm.

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Models and algorithms for the traffic assignment problem with link capacity constraints

Cited by 141 publications

References 12 publications

A generic column generation principle: derivation and convergence analysis

A generic column generation principle: derivation and convergence analysis

A modern congestion pricing policy for urban traffic: subsidy plus toll

An augmented Lagrangian origin‐based algorithm for link‐capacitated traffic assignment problem

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