A computational evaluation of a general branch-and-price framework for capacitated network location problems

Ceselli, Alberto; Liberatore, Federico; Righini, Giovanni

doi:10.1007/s10479-008-0375-5

Cited by 13 publications

(11 citation statements)

References 42 publications

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“…By generalizing the CPMP, Ceselli et al [33] generated different problems, which they named as the Capacitated Network Location Problems (CNLP). Their first test bed was based on the single source capacitated facility location problem instances of Holmberg et at.…”

Section: Capacitated Network Location Problemmentioning

confidence: 99%

“…Holmberg's instances are easy and they are omitted. In Table 13 there are only the Diaz's instances for which CPLEX cannot find the optimal solutions in 10 s. Also the results of the B&P algorithm are given, which are taken from the paper [33] and which were obtained on the same PC as for the MGAP.…”

Section: Capacitated Network Location Problemmentioning

confidence: 99%

“…There are also instances based on the CPMP in [33], but they are not available and, thus, are not included into the consideration.…”

Section: Capacitated Network Location Problemmentioning

confidence: 99%

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An implementation of exact knapsack separation

2015

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Cutting planes have been used with great success for solving mixed integer programs. In recent decades, many contributions have led to successive improvements in branch-and-cut methods which incorporate cutting planes in branch and bound algorithm. Using advances that have taken place over the years on 0-1 knapsack problem, we investigate an efficient approach for 0-1 programs with knapsack constraints as local structure. Our approach is based on an efficient implementation of knapsack separation problem which consists of the four phases: preprocessing, row generation, controlling numerical errors and sequential lifting. This approach can be used independently to improve formulations with cutting planes generated or incorporated in branch and cut to solve a problem. We show that this approach allows us to efficiently solve large-scale instances of generalized assignment problem, multilevel generalized assignment problem, capacitated p-median problem and capacitated network location problem to optimality.Keywords Knapsack problem · Cutting plane · Exact separation · Generalized assignment problem · Multilevel generalized assignment problem · Capacitated p-median problem · Capacitated network location problem B Igor Vasilyev

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Section: Capacitated Network Location Problemmentioning

confidence: 99%

Section: Capacitated Network Location Problemmentioning

confidence: 99%

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An implementation of exact knapsack separation

2015

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“…The number of median nodes is enforced by the equality (11). Capacity constraints (12) ensure that the total demand of the nodes assigned to the median node i cannot exceed its capacity q i . Variable Upper Bound constraints x ij ≤ y i , ij ∈ A could be added to strengthen the formulation (9)- (14).…”

Section: B Capacitated P-median Problemmentioning

confidence: 99%

New computational results with an exact knapsack separation procedure for structured Binary Integer Programming problems

Boccia

Hanafi

Vasilyev

2013

2013 5th International Conference on Modeling, Simulation and Applied Optimization (ICMSAO)

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In this paper we report new computational results with an approach based on the generation of general cutting planes for several classes of Binary Integer Programming (BIP) Problems such as Generalized Assignment, Multi-Dimensional Knapsack, Capacitated P-median and Capacitated Network Location. These problems are characterized by a formulation including a great number of knapsack constraints, which, in general make these problems very hard to solve. The state of the art on these problems requires to use approaches based on Lagrangean Relaxation or decomposition approaches like DantzigWolfe and Column Generation techniques. In this paper we present an approach based on the generation of general cutting planes of the polytope associated with each knapsack constraints. Computational experience on a wide set of benchamrk instances is carried out.

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“…Lorena and Senne (2004) proposed an approach that integrates the column generation and Lagrangean/surrogate relaxation techniques to solve capacitated p-median problems. More recently, Ceselli et al (2009) proposed a computational framework based on column generation and branch-and-price ap-proaches to solve the capacitated network problems. Due to the computational complexity of real-life CCPs, a large number of heuristic approaches have been developed.…”

Section: Capacitated Clustering Problemmentioning

confidence: 99%

Capacitated clustering problem in computational biology: Combinatorial and statistical approach for sibling reconstruction

Chou

Chaovalitwongse

Berger-Wolf

et al. 2012

Computers & Operations Research

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The capacitated clustering problem (CCP) has been studied in a wide range of applications. In this study, we investigate a challenging CCP in computational biology, namely, sibling reconstruction problem (SRP). The goal of SRP is to establish the sibling relationship (i.e., groups of siblings) of a population from genetic data. The SRP has gained more and more interests from computational biologists over the past decade as it is an important and necessary keystone for studies in genetic and population biology. We propose a large-scale mixed integer formulation of the CCP for SRP, that is based on both combinatorial and statistical genetic concepts. The objective is not only to find the minimum number of sibling groups, but also to maximize the degree of similarity of individuals in the same sibling groups Preprint submitted to Computers and Operations Research April 28, 2011 while each sibling group is subject to genetic constraints derived from the Mendel's laws. We develop a new randomized greedy optimization algorithm to effectively and efficiently solve this SRP. The algorithm consists of two key phases: construction and enhancement. In the construction phase, a greedy approach with randomized perturbation is applied to construct multiple sibling groups iteratively. In the enhancement phase, a two-stage local search with a memory function is used to improve the solution quality with respect to the similarity measure. We demonstrate the effectiveness of the proposed algorithm using real biological data sets and compare it with state-of-the-art approaches in the literature. We also test it on larger simulated data sets.The experimental results show that the proposed algorithm provide the best reconstruction solutions.

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A computational evaluation of a general branch-and-price framework for capacitated network location problems

Cited by 13 publications

References 42 publications

An implementation of exact knapsack separation

An implementation of exact knapsack separation

New computational results with an exact knapsack separation procedure for structured Binary Integer Programming problems

Capacitated clustering problem in computational biology: Combinatorial and statistical approach for sibling reconstruction

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