Benders decomposition for very large scale partial set covering and maximal covering location problems

Cordeau, Jean‐François; Furini, Fabio; Ljubić, Ivana

doi:10.1016/j.ejor.2018.12.021

Cited by 82 publications

(65 citation statements)

References 28 publications

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“…feasible inequality can be found any more. This procedure has been applied to Problem 29 without the sparsity constraint on the u-variables in [17]. The following results for the more general Problem 29 are based on the the idea of Benders' decomposition and extend the results in [17].…”

Section: Proposition 3 the Runtime Of Meiht Ismentioning

confidence: 87%

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Discrete optimization methods for group model selection in compressed sensing

2020

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In this article we study the problem of signal recovery for group models. More precisely for a given set of groups, each containing a small subset of indices, and for given linear sketches of the true signal vector which is known to be group-sparse in the sense that its support is contained in the union of a small number of these groups, we study algorithms which successfully recover the true signal just by the knowledge of its linear sketches. We derive model projection complexity results and algorithms for more general group models than the state-of-the-art. We consider two versions of the classical iterative hard thresholding algorithm (IHT). The classical version iteratively calculates the exact projection of a vector onto the group model, while the approximate version (AM-IHT) uses a head-and a tail-approximation iteratively. We apply both variants to group models and analyse the two cases where the sensing matrix is a Gaussian matrix and a model expander matrix. To solve the exact projection problem on the group model, which is known to be equivalent to the maximum weight coverage problem, we use discrete optimization methods based on dynamic programming and Benders' decomposition. The head-and tail-approximations are derived by a classical greedy-method and LP-rounding, respectively.

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Section: Proposition 3 the Runtime Of Meiht Ismentioning

confidence: 87%

“…3.6. Solving an NP-hard problem this method does not yield a polynomial runtime guarantee but works well in practice as shown in [17]. In Sect.…”

Section: Algorithms With Exact Projection Oraclesmentioning

confidence: 99%

Discrete optimization methods for group model selection in compressed sensing

2020

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“…e SCP model can effectively deal with the strategy of selecting the minimum and optimal locations from candidate nodes and can provide service for the maximum demand in the region [33,34]. e exact method of the SCP is inefficient due to the significant time needed for large problems [35].…”

Section: Logistics Location For Uls Networkmentioning

confidence: 99%

Design of a Support System for Complicated Logistics Location Integrating Big Data

Cheng

Pan

2021

Advances in Civil Engineering

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Logistics location is an important component of logistics planning that affects traffic pressure and vehicle emissions. To date, there has not been an adequate study of the integration of big data into the location for a complicated logistics system. This study developed a decision support system that can address location problems for complicated logistics systems, e.g., a multilevel urban underground logistics system (ULS), using logistics big data. First, information needed in the logistics location, such as the traffic performance index (TPI) and the origin/destination (OD) matrix, was collected and calculated using a big data platform, and this information was digitized and represented based on a geographic information system (GIS) tool. Second, a two-stage location model for a ULS was designed to balance the construction costs and traffic congestion. The first stage is establishing a set-covering model to identify optimum locations for secondary hubs based on the ant colony optimization algorithm, and the second stage is clustering of the secondary hubs to determine locations for primary hubs using the iterative self-organizing data analysis technique algorithm (ISODATA). Finally, the Xianlin district of Nanjing, China, was chosen as a case study to validate the effectiveness of the proposed system. The system can be used to facilitate logistics network planning and to promote the application of big data in logistics.

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“…To solve two variants of MCLP, the first variant can be reformulated as the second one for which they have developed a method to solve it using a case study in Sichuan, China. To solve very large-scale problems of partial SCLP and MCLP up to millions of demand points and obtaining an optimal solution for this huge size of problems, Cordeau et al [46] presented a Benders decomposition method. The good performance of their method is due to the utilization of a Branch-and-Benders-cut algorithm.…”

Section: Literature Reviewmentioning

confidence: 99%

Hybrid Set Covering and Dynamic Modular Covering Location Problem: Application to an Emergency Humanitarian Logistics Problem

Alizadeh

Nishi

2020

Applied Sciences

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This paper presents an extension of the covering location problem as a hybrid covering model that utilizes the set covering and maximal covering location problems. The developed model is a multi-period model that considers strategic and tactical planning decisions. Hybrid covering location problem (HCLP) determines the location of the capacitated facilities by using dynamic set covering location problem as strategic decisions and assigns the constructive units of facilities and allocates the demand points by using dynamic modular capacitated maximal covering location problem as tactical decisions. One of the applications of the proposed model is locating first aid centers in humanitarian logistic services that have been addressed by studying a threat case study in Japan. In addition to validating the developed model, it has been compared to other possible combined problems, and several randomly generated examples have been solved. The results of the case study and model validation tests approve that the main hybrid developed model (HCLP) is capable of providing better coverage percentage compared to conventional covering models and other hybrid variants.

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Benders decomposition for very large scale partial set covering and maximal covering location problems

Cited by 82 publications

References 28 publications

Discrete optimization methods for group model selection in compressed sensing

Discrete optimization methods for group model selection in compressed sensing

Design of a Support System for Complicated Logistics Location Integrating Big Data

Hybrid Set Covering and Dynamic Modular Covering Location Problem: Application to an Emergency Humanitarian Logistics Problem

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