A note on branch-and-cut-and-price

Feillet, Dominique; Gendreau, Michel; Medaglia, Andrés L.; Walteros, Jose L.

doi:10.1016/j.orl.2010.06.002

Cited by 18 publications

(17 citation statements)

References 9 publications

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“…Our paper establishes the validity of the column-and-row generation algorithm in a form that encompasses all special cases of the literature, completing the presentations of [8,9,10,11,14,15,17,23]. We identify what explains the faster convergence: the recombination of previously generated subproblem solutions.…”

Section: Introductionmentioning

confidence: 60%

“…Such column-and-row generation procedure is a technique previously described in the literature in application specific contexts: for bin packing in [23]; for multi-commodity flow in [15] and in [14] where the method is extended to the context of a Lagrangian Decomposition -the resulting methodology is named "Lagrangian pricing"; for the resourceconstrained minimum-weight arborescence problem in [9]; for split delivery vehicle routing in [7,8]; or for network design problems in [8,10]. The convincing computational results of these papers indicate the interest of the method.…”

Section: Introductionmentioning

confidence: 99%

“…Compared to [11], our generic presentation, relying on the definition of an extended formulation, assumes slightly less restrictive assumptions and extends to approximate extended formulation. In [8], Gendreau et al present a branch-and-price-and-cut algorithm where columns and cuts are generated simultaneously; their presentation considers approximate extended formulation but with a weaker termination condition. In [17], Muter et al consider what they call a "simultaneous column-and-row generation" approach, but it takes the meaning of a nested decomposition, different from the method reviewed here: the subproblem has itself a decomposable structure.…”

Section: Introductionmentioning

confidence: 99%

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Column Generation for Extended Formulations

Sadykov

Vanderbeck

2011

Electronic Notes in Discrete Mathematics

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Working in an extended variable space allows one to develop tighter reformulations for mixed integer programs. However, the size of the extended formulation grows rapidly too large for a direct treatment by a MIP-solver. Then, one can work with inner approximations defined and improved by generating dynamically variables and constraints. When the extended formulation stems from subproblems' reformulations, one can implement column generation for the extended formulation using a Dantzig-Wolfe decomposition paradigm. Pricing subproblem solutions are expressed in the variables of the extended formulation and added to the current restricted version of the extended formulation along with the subproblem constraints that are active for the subproblem solutions. This so-called "column-and-row generation" procedure is revisited here in a unifying presentation that generalizes the column generation algorithm and extends to the case of working with an approximate extended formulation. The interest of the approach is evaluated numerically on machine scheduling, bin packing, generalized assignment, and multi-echelon lot-sizing problems. We compare a direct handling of the extended formulation, a standard column generation approach, and the "column-and-row generation" procedure, highlighting a key benefit of the latter: lifting pricing problem solutions in the space of the extended formulation permits their recombination into new subproblem solutions and results in faster convergence.

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Section: Introductionmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Column Generation for Extended Formulations

Sadykov

Vanderbeck

2011

Electronic Notes in Discrete Mathematics

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“…We note D the dual of M P and D k the dual of RM P k . When the addition of columns to a restricted master problem also implies the addition of cuts, it raises new difficulties that invalidate the standard column generation procedure (see Feillet et al (2010)). Indeed, the usual optimality criterion used in column generation relies on the fact that when no column of negative reduced cost exists, the current dual solution (obtained from the solution of the restricted master problem) is feasible for the dual of the master problem.…”

Section: About Simultaneous Cut and Column Generationmentioning

confidence: 99%

A Heuristic Branch-Cut-and-Price Algorithm for the ROADEF/EURO Challenge on Inventory Routing

Absi¹,

Cattaruzza

Feillet

et al. 2020

Transportation Science

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This paper is part of the special section devoted to the ROADEF/EURO challenge on Inventory Routing. We propose an extended formulation that we address with a heuristic branch-price-and-cut method. Among the difficulties, that we had to face, are : a fractional objective function, the simultaneous generation of constraints and columns, and a complex pricing problem. We evaluate our approach on the benchmark instances proposed for the challenge.

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“…The author also proposes asymmetrical services where stations may be skipped in some direction. Feillet et al [36] propose a branch-and-cut-and-price method to efficiently construct multiple lines using express services where some intermediate stops can be skipped. Deadheading is not allowed in such type of services.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Integrated approach to network design and frequency setting problem in railway rapid transit systems

López-Ramos

Codina

Marı́n

et al. 2017

Computers & Operations Research

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© <2017>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This work presents an optimization-based approach to simultaneously solve the Network Design and the Frequency Setting phases on the context of railway rapid transit networks. The Network Design phase allows expanding existing networks as well as building new ones from scratch, considering infrastructure costs. In the Frequency Setting phase, local and/or express services are established considering transportation resources capacities and operation costs. Integrated approaches to these phases improve the transit planning process. Nevertheless, this integration is challenging both at modeling and computational effort to obtain solutions. In this work, a Lexicographic Goal Programming problem modeling this integration is introduced, together with a solving strategy. A solution to the problem is obtained by first applying a Corridor Generation Algorithm and then a Line Splitting Algorithm to deal with multiple line construction. Two case studies are used for validation, including the Seville and Santiago de Chile rapid transit networks. Detailed solution reports are shown and discussed. Conclusions and future research directions are given.Peer ReviewedPostprint (author's final draft

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A note on branch-and-cut-and-price

Cited by 18 publications

References 9 publications

Column Generation for Extended Formulations

Column Generation for Extended Formulations

A Heuristic Branch-Cut-and-Price Algorithm for the ROADEF/EURO Challenge on Inventory Routing

Integrated approach to network design and frequency setting problem in railway rapid transit systems

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