A column generation procedure for the side constrained traffic equilibrium problem

Larsson, Torbjörn; Patriksson, Michael; Rydergren, Clas

doi:10.1016/s0191-2615(02)00092-9

Cited by 32 publications

(23 citation statements)

References 16 publications

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“…The instability also worsens the quality of the columns that are generated. It can however be dealt with by using stabilization techniques (e.g., Marsten et al, 1975;du Merle et al, 1999;Larsson et al, 2004). …”

Section: Column Generationmentioning

confidence: 99%

“…Hence, the dual solutions obtained in consecutive iterations tend to vary significantly, which also leads to slow convergence in the primal problem. To improve the stability, the column generation scheme presented in Section 3 is modified to include a boxstep restriction (Marsten et al, 1975) on the individual dual variables, so that each new dual point is kept close to the previous one (see also, e.g., du Merle et al, 1999;Larsson et al, 2004;Westerlund et al, 2006). For the dual problem of the RLPM presented in Section 3.1, we choose to include box constraints only for the dual variables y nt , since the values of the dual variables v u are uniquely determined by the values of y nt due to the structure of the constraints.…”

Section: Master Problem Stabilizationmentioning

confidence: 99%

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Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation

et al. 2015

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We study resource allocation in cellular systems and consider the problem of finding a power efficient scheduling in an uplink single carrier frequency division multiple access system (SC-FDMA). Due to the discrete nature of this problem and its computational difficulty, particularly in a real-time setting, the use of suboptimal algorithms is common practice. We aim at an effective way of gauging the performance of suboptimal algorithms by finding tight bounds on the global optimum.Toward this end, we first provide a basic integer linear programming formulation. Then we propose a significantly stronger column-oriented formulation and a corresponding column generation method, as well as an enhanced column generation scheme. The latter extends the first scheme through the inclusion of a stabilization technique, an approximate column generation principle, and a tailored heuristic that is embedded in the column generation scheme to find high-quality though not necessarily global optimal solutions.The computational evaluation demonstrates that compared with a poor performance by the integer linear programming formulation, the column generation method can produce near-optimal schedules that enable a sharp bounding interval. The enhanced column generation method significantly sharpens the bounding interval. Hence the column generation approach serves well for the purpose of benchmarking results for large-scale instances.

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Section: Column Generationmentioning

confidence: 99%

Section: Master Problem Stabilizationmentioning

confidence: 99%

Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation

et al. 2015

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“…This technique has recently been used, with good results, in [38], where a column generation procedure for the side constrained traffic equilibrium problem is addressed. A modification similar to the boxstep restriction has been used for stabilizing column generation procedures in [15].…”

Section: Stabilized Column Generationmentioning

confidence: 99%

A stabilized column generation scheme for the traveling salesman subtour problem

Westerlund

Göthe‐Lundgren

Larsson

2006

Discrete Applied Mathematics

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Given an undirected graph with edge costs and both revenues and weights on the vertices, the traveling salesman subtour problem is to find a subtour that includes a depot vertex, satisfies a knapsack constraint on the vertex weights, and that minimizes edge costs minus vertex revenues along the subtour.We propose a decomposition scheme for this problem. It is inspired by the classic side-constrained 1-tree formulation of the traveling salesman problem, and uses stabilized column generation for the solution of the linear programming relaxation. Further, this decomposition procedure is combined with the addition of variable upper bound (VUB) constraints, which improves the linear programming bound. Furthermore, we present a heuristic procedure for finding feasible subtours from solutions to the column generation problems. An extensive experimental analysis of the behavior of the computational scheme is presented.

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“…A detailed overview is provided in [5][6][7][8][9]. In the past decade, some efficient algorithms have been proposed to solve the TEPs [10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A semismooth Newton method for traffic equilibrium problem with a general nonadditive route cost

Chen

et al. 2011

Applied Mathematical Modelling

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a b s t r a c tComputing traffic equilibria with a general nonadditive route cost disutility function is considered in this paper. Following the user equilibrium (UE) condition, that is, no driver can unilaterally change route to achieve less travel costs, the traffic equilibrium problem (TEP) can be formulated as a nonlinear complementary problem (NCP). In this paper, we propose a semismooth Newton method with a penalized Fischer-Burmeister (PFB) NCP function to solve the NCP formulation of the TEP, and also, we investigate the properties of the proposed method. Numerical results are provided and compared with the classical TEP with additive route cost functions. The results show the algorithm can achieved substantially better performance than the existing approaches. A sensitivity analysis is also conducted to examine the parameter of the proposed nonadditive route cost function.

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A column generation procedure for the side constrained traffic equilibrium problem

Cited by 32 publications

References 16 publications

Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation

Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation

A stabilized column generation scheme for the traveling salesman subtour problem

A semismooth Newton method for traffic equilibrium problem with a general nonadditive route cost

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