Restricted simplicial decomposition: Computation and extensions

Hearn, Donald W.; Lawphongpanich, Siriphong; Ventura, José A.

doi:10.1007/bfb0121181

Cited by 124 publications

(93 citation statements)

References 21 publications

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“…Comprehensive descriptions of the SD method can be found in [22] and [19] for variational inequalitiesasymmetric traffic assignment-and nonlinear optimization-symmetric traffic assignment-problems, respectively.…”

Section: Algorithm 41 a Generic Sd Algorithm For (3)mentioning

confidence: 99%

Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem

2007

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The purpose of the traffic assignment problem is to obtain a traffic flow pattern given a set of origindestination travel demands and flow dependent link performance functions of a road network. In the general case, the traffic assignment problem can be formulated as a variational inequality, and several algorithms have been devised for its efficient solution. In this work we propose a new approach that combines two existing procedures: the master problem of a simplicial decomposition algorithm is solved through the analytic center cutting plane method. Four variants are considered for solving the master problem. The third and fourth ones, which heuristically compute an appropriate initial point, provided the best results. The computational experience reported in the solution of real large-scale diagonal and difficult asymmetric problems-including a subset of the transportation networks of Madrid and Barcelona-show the effectiveness of the approach.

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Section: Algorithm 41 a Generic Sd Algorithm For (3)mentioning

confidence: 99%

Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem

2007

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“…Thus, the above path-ow formulation is not suitable for a generic complementarity code. Nevertheless, there are path-generation schemes 24,33] that utilize this formulation and generate the paths only if they are needed. The alternative multicommodity formulation to be discussed below completely removes the necessity of enumerating the paths.…”

Section: Mcp Models: User Equilibriummentioning

confidence: 99%

“…0 Zì j (t) uì j ; (i; j) 2 A; t = 0; 1; : : :; T; (27) where the additional supply i (t) is given by (24). The optimal value Q`(X) of the above problem is the rescheduling cost for the plan X, when transition to state`occurs.…”

Section: Stochastic Models In Gamsmentioning

confidence: 99%

“…We then considered the possibility of 2 failures in the network, on arcs (1,2) and arc (21,24). We incorporated capacities of 0.5 only on arcs (15,14) and (22,23) so that when a failure of arc (21,24) occurs, all the ow could not be rerouted through these arcs. The loop statement in Figure 4 is used to compute the steady state solution for each arc failure, required to enforce (28).…”

Section: Stochastic Models In Gamsmentioning

confidence: 99%

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Traffic Modeling and Variational Inequalities Using GAMS

Dirkse

Ferris

1998

Operations Research and Decision Aid Methodologies in Traffic and Transportation Management

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We describe how several tra c assignment and design problems can be formulated within the GAMS modeling language using newly developed modeling and interface tools. The fundamental problem is user equilibrium, where multiple drivers compete noncooperatively for the resources of the tra c network. A description of how these models can be written as complementarity problems, variational inequalities, mathematical programs with equilibrium constraints, or stochastic linear programs is given. At least one general purpose solution technique for each model format is brie y outlined. Some observations relating to particular model solutions are drawn.

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“…If the joint capacity constraints are placed into the objective function with multipliers u, <, 0, the Lagrangian dual of (P) is (LR) max min L(Ui,x) = ex + u^(b^-Ax) (17) u^O x>0…”

mentioning

confidence: 99%