Efficient elementary and restricted non-elementary route pricing

Martinelli, Rafael; Pecin, Diego; Poggi, Marcus

doi:10.1016/j.ejor.2014.05.005

Cited by 61 publications

(45 citation statements)

References 17 publications

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“…Even if Ω only contains elementary routes, the bounds given by (9)(10)(11) are not good enough to be the basis of efficient exact algorithms (gaps between 1% and 4% are typical in the instances from the literature). The formulation must be reinforced with additional cuts.…”

Section: Cutsmentioning

confidence: 98%

“…On the other hand, the pricing subproblem would become strongly NP-hard. While carefully designed labeling algorithms are now capable of pricing elementary routes on most instances from the literature with up to 199 customers [10], this is still too costly. A more recent alternative for imposing partial elementarity, used in this work, are the ng-routes [2].…”

Section: Formulationsmentioning

confidence: 99%

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Improved Branch-Cut-and-Price for Capacitated Vehicle Routing

Pecin

Pessoa

Poggi

et al. 2014

Integer Programming and Combinatorial Optimization

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Abstract. The best performing exact algorithms for the Capacitated Vehicle Routing Problem are based on the combination of cut and column generation. Some authors could obtain reduced duality gaps by also using a restricted number of cuts over the Master LP variables, stopping separation before the pricing becomes prohibitively hard. This work introduces a technique for greatly decreasing the impact on the pricing of the Subset Row Cuts, thus allowing much more such cuts to be added. The newly proposed Branch-Cut-and-Price algorithm also incorporates and combines for the first time (often in an improved way) several elements found in previous works, like route enumeration and strong branching. All the instances used for benchmarking exact algorithms, with up to 199 customers, were solved to optimality. Moreover, some larger instances with up to 360 customers, only considered before by heuristic methods, were solved too.

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Section: Cutsmentioning

confidence: 98%

Section: Formulationsmentioning

confidence: 99%

Improved Branch-Cut-and-Price for Capacitated Vehicle Routing

Pecin

Pessoa

Poggi

et al. 2014

Integer Programming and Combinatorial Optimization

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“…In order to handle n g -sets with large cardinality, Martinelli, Pecin, and Poggi [30] proposed an adaptation of the DSSR concept. The labeling algorithm starts with the n gsets relaxed into singletons.…”

Section: Ng-routesmentioning

confidence: 99%

Chapter 3: New Exact Algorithms for the Capacitated Vehicle Routing Problem

Poggi¹,

Uchôa²

2014

Vehicle Routing

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Since the seminal work by Desrosiers, Soumis, and Desrochers [15], column generation has been the dominant approach for building exact algorithms for the Vehicle Routing Problem with Time Windows (VRPTW). This technique performed very well on tightly constrained instances (those with narrow time windows). As the Capacitated Vehicle Routing Problem (CVRP) can be regarded as the particular case of VRPTW where time windows are arbitrarily large, column generation was viewed as a non-promising approach for the problem. In fact, in the early 2000's, the best performing algorithms for the CVRP were Branch-and-Cut algorithms that separated quite complex families of cuts identified by polyhedral investigation (see Naddef and Rinaldi [31] and Chapter 2). In spite of their sophistication, some instances from the literature with only 50 customers could not be solved to optimality. At that moment, the Branch-and-Cut-and-Price algorithm (BCP) by Fukasawa et al. [19] showed that the combination of cut and column generation could be much more effective than each of those techniques taken alone. Since then, the most performing exact algorithms proposed for the CVRP are based on that combination.According to the classification proposed in Poggi de Aragão and Uchoa [36], the BCP algorithm in Fukasawa et al. [19] only uses robust cuts. A cut is said to be robust when the value of the dual variable associated with it can be translated into costs in the pricing subproblem. Therefore, the structure and the size of that subproblem remain unaltered, regardless of the number of robust cuts added. On the other hand, non-robust cuts are those that change the structure and/or the size of the pricing subproblem; each additional cut makes it harder.

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“…This technique iteratively grows the size of the neighborhoods on which cycles are forbidden. This idea was later extended by Martinelli et al [15] leading to a speed up of the solution of the ESPPRC.…”

Section: I1 Literature Reviewmentioning

confidence: 96%

“…The first one is the Decremental State Space Relaxation (DSSR), introduced by Righini and Salani in [23] for the pricing with elementary routes and further adapted to the ng-route relaxation by Martinelli et al [15]. The second one is called the completion bounds and finally the last one is a heuristic pricing.…”

mentioning

confidence: 99%

Strong Lower Bounds for the CVRP via Column and Cut

MARTINS¹

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Efficient elementary and restricted non-elementary route pricing

Cited by 61 publications

References 17 publications

Improved Branch-Cut-and-Price for Capacitated Vehicle Routing

Improved Branch-Cut-and-Price for Capacitated Vehicle Routing

Chapter 3: New Exact Algorithms for the Capacitated Vehicle Routing Problem

Strong Lower Bounds for the CVRP via Column and Cut

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