Automation and Combination of Linear-Programming Based Stabilization Techniques in Column Generation

Pessoa, Artur Alves; Sadykov, Ruslan; Uchôa, Eduardo; Vanderbeck, François

doi:10.1287/ijoc.2017.0784

Cited by 87 publications

(66 citation statements)

References 34 publications

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“…Pricing problems are solved by a bucket graph based labeling algorithm [58], including a bucket arc elimination procedure based on reduced costs. Automatic dual price smoothing [51] is employed to stabilize the column generation convergence. Path enumeration is performed using an extension of the algorithm from [5,47].…”

Section: Computational Experimentsmentioning

confidence: 99%

A Generic Exact Solver for Vehicle Routing and Related Problems

Pessoa

Sadykov

Uchôa

et al. 2019

Lecture Notes in Computer Science

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Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cutand-Price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best recent VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, and route enumeration; all generalized through the new concept of "packing set". This concept is also used to derive a new branch rule based on accumulated resource consumption and to generalize the Ryan and Foster branch rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best existing specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.

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Section: Computational Experimentsmentioning

confidence: 99%

A Generic Exact Solver for Vehicle Routing and Related Problems

Pessoa

Sadykov

Uchôa

et al. 2019

Lecture Notes in Computer Science

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“…It is well‐known that the convergence of the basic column generation procedure faces several drawbacks, namely dual oscillations, the tailing‐off effect, and primal degeneracy (Vanderbeck, ). To overcome these drawbacks, we adopt the in‐out column generation method that was initially introduced in Ben‐Ameur and Neto () and further studied in Pessoa, Sadykov, Uchoa, and Vanderbeck ()). Yin, Chen, Qin, and Wang () applied it to solve the two‐agent scheduling problem.…”

Section: Branch‐and‐price Algorithmmentioning

confidence: 99%

“…The computational experiments conducted by Ben‐Ameur and Neto () and Yin, Chen, Qin, and Wang () show that a small decrease in α (eg, α = 0.99 instead of α = 1) can completely change the performances of the column generation algorithm. For more details on the convergence property, we refer the reader to Ben‐Ameur and Neto (), and Pessoa et al ().…”

Section: Branch‐and‐price Algorithmmentioning

confidence: 99%

An exact branch‐and‐price algorithm for multitasking scheduling on unrelated parallel machines

Xiong

Zhou

Yin

et al. 2019

Naval Research Logistics

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We consider the multitasking scheduling problem on unrelated parallel machines to minimize the total weighted completion time. In this problem, each machine processes a set of jobs, while the processing of a selected job on a machine may be interrupted by other available jobs scheduled on the same machine but unfinished. To solve this problem, we propose an exact branch‐and‐price algorithm, where the master problem at each search node is solved by a novel column generation scheme, called in‐out column generation, to maintain the stability of the dual variables. We use a greedy heuristic to obtain a set of initial columns to start the in‐out column generation, and a hybrid strategy combining a genetic algorithm and an exact dynamic programming algorithm to solve the pricing subproblems approximately and exactly, respectively. Using randomly generated data, we conduct numerical studies to evaluate the performance of the proposed solution approach. We also examine the effects of multitasking on the scheduling outcomes, with which the decision maker can justify making investments to adopt or avoid multitasking.

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“…To improve the convergence of the column generation procedure on which the diving heuristic relies, we use the automatic dual price smoothing stabilization proposed in Pessoa et al [20].…”

Section: Diving Heuristicsmentioning

confidence: 99%

Pattern-based diving heuristics for a two-dimensional guillotine cutting-stock problem with leftovers

Clautiaux

Sadykov

Vanderbeck

et al. 2019

EURO Journal on Computational Optimization

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To cite this version:François Clautiaux, Ruslan Sadykov, François Vanderbeck, Quentin Viaud. Pattern based diving heuristics for a two-dimensional guillotine cutting-stock problem with leftovers. AbstractWe consider a variant of two-dimensional guillotine cutting-stock problem that arises when different bills of order (or batches) are considered consecutively. The raw material leftover of the last cutting pattern is not counted as waste as it can be reused for cutting the next batch. The objective is thus to maximize the length of the leftover. We propose a diving heuristic based on a Dantzig-Wolfe reformulation solved by column generation in which the pricing problem is solved using dynamic programming (DP). This DP generates so-called nonproper columns, i.e. cutting patterns that cannot participate in a feasible integer solution of the problem. We show how to adapt the standard diving heuristic to this "non-proper" case while keeping its effectiveness. We also introduce the partial enumeration technique, which is designed to reduce the number of nonproper patterns in the solution space of the dynamic program. This technique helps to strengthen the lower bounds obtained by column generation and improve the quality of solutions found by the diving heuristic. Computational results are reported and compared on classical benchmarks from the literature as well as on new instances inspired from industrial data. According to these results, proposed diving algorithms outperform constructive and evolutionary heuristics.The paper is organised as follows. We first give an overview of the literature on related problems in Section 2. Then in Section 3, we recall how it can be modelled by an exponentially large ILP model in which each variable represents a cutting pattern, and how the pricing subproblem can be solved by dynamic programming. Constructive and evolutionary heuristics inspired from the literature for the 2DGCSPL are discussed in Section 4. In Section 5 we present our 2 pattern based diving heuristics for the 2DGCSPL. To obtain better solutions by these diving heuristics, we also propose a partial enumeration technique that is embedded in the dynamic program for solving the pricing subproblem. In Section 6, we report results of computational experiments in which we compare different heuristic algorithms on classical data sets and real-life instances. Conclusions are drawn in Section 7. Literature reviewCutting-stock problems have drawn a large attention because of their significance for the industry, and their theoretical and practical difficulty. When all demands are unitary (d i " 1, @i P I), the problem is also referred in the literature as the bin-packing problem. From a theoretical point of view, one can reformulate a bin-packing problem as a cutting-stock problem, therefore through the rest of this paper, we will use both names.The first study on two-dimensional packing problems appeared in Gilmore and Gomory [13]. Therein, the approach is to formulate the two-dimensional bin-packing problem (2BP) using Line...

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Automation and Combination of Linear-Programming Based Stabilization Techniques in Column Generation

Cited by 87 publications

References 34 publications

A Generic Exact Solver for Vehicle Routing and Related Problems

A Generic Exact Solver for Vehicle Routing and Related Problems

An exact branch‐and‐price algorithm for multitasking scheduling on unrelated parallel machines

Pattern-based diving heuristics for a two-dimensional guillotine cutting-stock problem with leftovers

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