Column Generation based Primal Heuristics

Joncour, Cédric; Michel, Sophie; Sadykov, Ruslan; Sverdlov, Dmitry; Vanderbeck, François

doi:10.1016/j.endm.2010.05.088

Cited by 92 publications

(38 citation statements)

References 12 publications

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“…To increase the efficiency of our BPC, we embedded in it a restricted master heuristic. Restricted master heuristics are the most commonly used primal heuristics with column generation [25]. They consist in solving a restricted master problem (RMP) with integrality constraints on column variables, for example by a branch-and-bound algorithm.…”

Section: Restricted Master Heuristicmentioning

confidence: 99%

A branch-and-price-and-cut approach for sustainable crop rotation planning

Alfandari

Plateau

Schepler

2015

European Journal of Operational Research

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In this paper, we study a multi-periodic production planning problem in agriculture. This problem belongs to the class of crop rotation planning problems, which have received increased attention in the literature in recent years. Crop cultivation and fallow periods must be scheduled on land plots over a given time horizon so as to minimize the total surface area of land used, while satisfying crop demands every period. This problem is proven strongly N P -hard. We propose a 0-1 linear programming compact formulation based on crop-sequence graphs. An extended formulation is then provided with a polynomial-time pricing problem, and a Branch-and-Priceand-Cut (BPC) algorithm is presented with adapted branching rules and cutting planes. The numerical experiments on instances varying the number of crops, periods and plots show the effectiveness of the BPC for the extended formulation compared to solving the compact formulation, even though these two formulations have the same linear relaxation bound.

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Section: Restricted Master Heuristicmentioning

confidence: 99%

A branch-and-price-and-cut approach for sustainable crop rotation planning

Alfandari

Plateau

Schepler

2015

European Journal of Operational Research

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“…A diving heuristic explores one branch of a search tree and is intended to quickly obtain feasible integer solutions in branch-and-bound algorithms [68]. The algorithm starts by solving the root node to optimality.…”

Section: Iterated Diving Heuristicsmentioning

confidence: 99%

Nurse rostering: models and algorithms for theory, practice and integration with other problems

Smet

2016

4OR-Q J Oper Res

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“…We use a generic diving heuristic which is a depth-first heuristic search in the branch-andprice tree that is presented in Joncour et al (2010). Here, the branch-and-price enumeration is not driven by the branching scheme of Section 3.2, but simply by fixing λ B variables.…”

Section: Column Generation Based Primal Heuristicmentioning

confidence: 99%

“…It includes the generic branching scheme of Vanderbeck (2010) and the generic column generation based primal heuristics of Joncour et al (2010). The pricing subproblem is a Knapsack Problem with Conflicts (KPC).…”

Section: Introductionmentioning

confidence: 99%

Bin Packing with Conflicts: A Generic Branch-and-Price Algorithm

Sadykov

Vanderbeck

2013

INFORMS Journal on Computing

129

103

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The bin packing problem with conflicts consists in packing items in a minimum number of bins of limited capacity while avoiding joint assignments of items that are in conflict. Our study demonstrates that a generic implementation of a Branch-and-Price algorithm using specific pricing oracle yields comparatively good performance for this problem. We use our black-box Branch-and-Price solver BaPCod, relying on its generic branching scheme and primal heuristics. We developed a dynamic programming algorithm for pricing when the conflict graph is an interval graph, and a depth-first-search branch-and-bound approach for pricing when the conflict graph has no special structure. The exact method is tested on instances from the literature where the conflict graph is an interval graph, as well as harder instances that we generated with an arbitrarily conflict graph and larger number of items per bin. Our computational experiment report sets new benchmark results for this problem, closing all open instances of the literature in one hour of CPU time.

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Column Generation based Primal Heuristics

Cited by 92 publications

References 12 publications

A branch-and-price-and-cut approach for sustainable crop rotation planning

A branch-and-price-and-cut approach for sustainable crop rotation planning

Nurse rostering: models and algorithms for theory, practice and integration with other problems

Bin Packing with Conflicts: A Generic Branch-and-Price Algorithm

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