Heuristics for minimizing the maximum within-clusters distance

Fioruci, José Augusto; Toledo, Franklina Maria Bragion de; Nascimento, Mariá C. V.

doi:10.1590/s0101-74382012005000023

Cited by 7 publications

(4 citation statements)

References 18 publications

(8 reference statements)

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“…Third, we always warm-start the branch-and-price procedure by computing lower and upper bounds for the problem, as follows: An upper bound can be obtained by executing the constructive heuristic introduced in Section 5. Moreover, we have implemented an iterated local search method to improve this solution that uses the LS presented in Fioruci et al (2012), with a perturbation based on the random selection of diameter nodes (two nodes that have maximum intra-cluster distance) and the reassignment of those nodes to randomly selected clusters. The value achieved by the ILS is then used as a cut-off value for the branch-and-price algorithm.…”

Section: Acceleration Techniquesmentioning

confidence: 99%

A sampling-based exact algorithm for the solution of the minimax diameter clustering problem

Aloise

Contardo²

2018

J Glob Optim

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We consider the problem of clustering a set of points so as to minimize the maximum intra-cluster dissimilarity, which is strongly NP-hard. Exact algorithms for this problem can handle datasets containing up to a few thousand observations, largely insufficient for the nowadays needs. The most popular heuristic for this problem, the complete-linkage hierarchical algorithm, provides feasible solutions that are usually far from optimal. We introduce a sampling-based exact algorithm aimed at solving large-sized datasets. The algorithm alternates between the solution of an exact procedure on a small sample of points, and a heuristic procedure to prove the optimality of the current solution. Our computational experience shows that our algorithm is capable of solving to optimality problems containing more than 500,000 observations within moderate time limits, this is two orders of magnitude larger than the limits of previous exact methods. Keywords clustering • diameter • large-scale optimization 1 IntroductionClustering is one of the most essential tasks in data mining and machine learning (Anderberg 1973;Kaufman and Rousseeuw 1990). It involves the reading and treatment of unlabeled observations so as to identify hidden and non-obvious patterns that could otherwise not be found by simple inspection

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Section: Acceleration Techniquesmentioning

confidence: 99%

A sampling-based exact algorithm for the solution of the minimax diameter clustering problem

Aloise

Contardo²

2018

J Glob Optim

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“…A history perspective is given in Section 2. A mixed-integer programming model will be presented in Section 3. In Section 4 we analyze the intrinsic complexity of the problem and some theoretical results useful to construct exact solutions for simple but important cases.…”

Section: Optimal Design Of An Ip/mpls Over Dwdm Networkmentioning

confidence: 99%

“…The Greedy Randomized Adaptive Search Procedure (GRASP), is a metaheuristic successfully applied to construct good quality solutions for several combinatorial optimization problems of diverse areas, which range from clustering ( [3,17]) to network design problems ( [16]). …”

Section: Grasp Implementationmentioning

confidence: 99%

Optimal design of an IP/MPLS over DWDM network

2014

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ABSTRACT. Different approaches for deploying resilient optical networks of low cost constitute a traditional group of NP-Hard problems that have been widely studied. Most of them are based on the construction of low cost networks that fulfill connectivity constraints. However, recent trends to virtualize optical networks over the legacy fiber infrastructure, modified the nature of network design problems and turned inappropriate many of these models and algorithms. In this paper we study a design problem arising from the deployment of an IP/MPLS network over an existing DWDM infrastructure. Besides cost and resiliency, this problem integrates traffic and capacity constraints. We present: an integer programming formulation for the problem, theoretical results, and describe how several metaheuristics were applied in order to find good quality solutions, for a real application case of a telecommunications company.

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“…Heuristic techniques are widely used to solve many TSP variants Dong, Guo & Tickle [9], Escario, Jimenez & Giron-Sierra [10], and Nagata & Soler [35]. There are also heuristic procedures based on different approaches Fioruci, Toledo & Nascimento [13], Subramanian & Battarra [40], Létocart, Plateau & Plateau [26], Martínez, Alvarez-Valdes & Parreño [32], and Vidal, Battarra, Subramanian & Erdogan [41] to solve different variants of combinatorial optimization problems.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Heuristic Algorithm for the Clustered Traveling Salesman Problem

Mestria

2016

Pesqui. Oper.

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This paper proposes a hybrid heuristic algorithm, based on the metaheuristics Greedy Randomized Adaptive Search Procedure, Iterated Local Search and Variable Neighborhood Descent, to solve the Clustered Traveling Salesman Problem (CTSP). Hybrid Heuristic algorithm uses several variable neighborhood structures combining the intensification (using local search operators) and diversification (constructive heuristic and perturbation routine). In the CTSP, the vertices are partitioned into clusters and all vertices of each cluster have to be visited contiguously. The CTSP is N P-hard since it includes the well-known Traveling Salesman Problem (TSP) as a special case. Our hybrid heuristic is compared with three heuristics from the literature and an exact method. Computational experiments are reported for different classes of instances. Experimental results show that the proposed hybrid heuristic obtains competitive results within reasonable computational time.

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Heuristics for minimizing the maximum within-clusters distance

Cited by 7 publications

References 18 publications

A sampling-based exact algorithm for the solution of the minimax diameter clustering problem

A sampling-based exact algorithm for the solution of the minimax diameter clustering problem

Optimal design of an IP/MPLS over DWDM network

A Hybrid Heuristic Algorithm for the Clustered Traveling Salesman Problem

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