Randomized heuristics for the Capacitated Clustering Problem

Martı́nez-Gavara, Anna; Landa-Silva, Dario; Campos, Vicente; Martı́, Rafael

doi:10.1016/j.ins.2017.06.041

Cited by 14 publications

(9 citation statements)

References 29 publications

(36 reference statements)

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“…Martinez-Gavara et al [17] developed a GRASP and an iterated greedy metaheuristics to solve the CCP. Besides, a matheuristic is proposed as a post-processing phase.…”

Section: Related Approachesmentioning

confidence: 99%

“…Martinez-Gavara et al [17] presented a hybrid approach for the CCP. First, the algorithm applies a GRASP -Iteration Greedy metaheuristic for the generation of an initial solution.…”

Section: Variable Fixing Heuristic (Vf)mentioning

confidence: 99%

“…Furthermore, we introduce an innovative matheuristic that hybridizes the well-known GRASP algorithm with the SR algorithm. Also, we develop a variable fixing heuristic (VF), which is an extension of the matheuristic presented by [17]. Finally, we propose a hybrid matheuristic based on the SR and VFH algorithms.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid matheuristics for the multi-capacitated clustering problem

2022

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The capacitated clustering problem is a well-known and largely studied combinatorial optimization problem with several industrial applications. Although a great attention has been paid to this problem in the literature, the deeming of the problem with clients of multiple types and clusters with multiple capacities is quite limited. We introduce a novel variant of capacitated clustering problems named multi-capacitated clustering problem (MCCP), a NP-hard optimization problem in which there are several clients that must be grouped into different sets that have different capacities for different types of clients. It is taken into account the distance between each one of these clients and the potential clusters to which they can be allocated, aiming to minimize the sum of such distances. It is presented an integer programming model for this problem, which it is shown to have limited application solving large-sized instances. As solution procedures, we present the following algorithms. We propose a greedy heuristic to generate a feasible solution within a negligible computational effort. We adapt a size-reduction (SR) matheuristic to solve the problem under study. Furthermore, we introduce an innovative matheuristic that hybridizes the well-known GRASP algorithm with the SR algorithm. Also, we develop a variable fixing (VF) heuristic, which is an extension of the matheuristic presented by Martinez-Gavara et al. \cite{martinez2017randomized}. Finally, we propose a hybrid matheuristic based on the SR and VFH algorithms. Computational results over a set of 100 randomly generated test instances point out the quality of the solutions found by the proposed algorithms. Our proposals are among the best heuristics developed for this problem.

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“…Martinez-Gavara et al [17] developed a GRASP and an iterated greedy metaheuristics to solve the CCP. Besides, a matheuristic is proposed as a post-processing phase.…”

Section: Related Approachesmentioning

confidence: 99%

“…Martinez-Gavara et al [17] presented a hybrid approach for the CCP. First, the algorithm applies a GRASP -Iteration Greedy metaheuristic for the generation of an initial solution.…”

Section: Variable Fixing Heuristic (Vf)mentioning

confidence: 99%

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Hybrid matheuristics for the multi-capacitated clustering problem

2022

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“…As previously mentioned, the neighborhood exploited by FLS is defined by a joint use of three basic move operators, which have previously been employed in [7,10,24,29,30]. These operators are briefly described as follows:…”

Section: Neighborhood Structuresmentioning

confidence: 99%

Heuristic search to the capacitated clustering problem

Zhou

Benlic²,

et al. 2019

European Journal of Operational Research

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Given a weighted graph, the capacitated clustering problem (CCP) is to partition a set of nodes into a given number of distinct clusters (or groups) with restricted capacities, while maximizing the sum of edge weights corresponding to two nodes from the same cluster. CCP is an NP-hard problem with many relevant applications. This paper proposes two effective algorithms for CCP: a Tabu Search (denoted as FITS) that alternates between exploration in feasible and infeasible search space regions, and a Memetic Algorithm (MA) that combines FITS with a dedicated cluster-based crossover. Extensive computational results on five sets of 183 benchmark instances from the literature indicate that the proposed FITS competes favorably with the state-of-the-art algorithms. Additionally, an experimental comparison between FITS and MA under an extended time limit demonstrates that further improvements in terms of the solution quality can be achieved with MA in most cases. We also analyze several essential components of the proposed algorithms to understand their importance to the success of these approaches.

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“…Both models are difficult to be solved to optimality due to their NP-hard computational complexity. Particularly for large problems, this has led to the development of metaheuristics to provide near-optimal solutions [25]. In the literature, metaheuristics based on Clustering Search (CS) have been reported as the most competitive methods for the CCCP [24].…”

Section: Introductionmentioning

confidence: 99%

Extended GRASP-Capacitated K-Means Clustering Algorithm to Establish Humanitarian Support Centers in Large Regions at Risk in Mexico

Caballero‐Morales

Barojas-Payán

Sánchez‐Partida

et al. 2018

Journal of Optimization

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Mexico is located within the so-called Fire Belt which makes it susceptible to earthquakes. In fact, two-thirds of the Mexican territory have a significant seismic risk. On the other hand, the country’s location in the tropical zone makes it susceptible to hurricanes which are generated in both the Pacific and Atlantic Oceans. Due to these situations, each year many communities are affected by diverse natural disasters in Mexico and efficient logistic systems are required to provide prompt support. This work is aimed at providing an efficient metaheuristic to determine the most appropriate location for support centers in the State of Veracruz, which is one of the most affected regions in Mexico. The metaheuristic is based on the K-Means Clustering (KMC) algorithm which is extended to integrate (a) the associated capacity restrictions of the support centers, (b) a micro Genetic Algorithm μGA to estimate a search interval for the most suitable number of support centers, (c) variable number of assigned elements to centers in order to add flexibility to the assignation task, and (d) random-based decision model to further improve the final assignments. These extensions on the KMC algorithm led to the GRASP-Capacitated K-Means Clustering (GRASP-CKMC) algorithm which was able to provide very suitable solutions for the establishment of 260 support centers for 3837 communities at risk in Veracruz, Mexico. Validation of the GRASP-CKMC algorithm was performed with well-known test instances and metaheuristics. The validation supported its suitability as alternative to standard metaheuristics such as Capacitated K-Means (CKM), Genetic Algorithms (GA), and Variable Neighborhood Search (VNS).

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Randomized heuristics for the Capacitated Clustering Problem

Cited by 14 publications

References 29 publications

Hybrid matheuristics for the multi-capacitated clustering problem

Hybrid matheuristics for the multi-capacitated clustering problem

Heuristic search to the capacitated clustering problem

Extended GRASP-Capacitated K-Means Clustering Algorithm to Establish Humanitarian Support Centers in Large Regions at Risk in Mexico

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