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

Aloise, Daniel; Contardo, Claudio

doi:10.1007/s10898-018-0634-1

Cited by 15 publications

(11 citation statements)

References 19 publications

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“…We have observed that, in a large number of iterations, the optimal value of problem pDP(D, p) does not decrease from one iteration to the next. This type of dual degeneracy is often observed in decremental relaxation schemes (Aloise andContardo 2018, Contardo et al 2019). Therefore, before resorting to executing the exact solver described in the previous section, our heuristic scheme checks if it is possible to select p points out of the p + 1 points identified from the previous iteration-which includes p − 1 optimal clusters that remain untouched plus the one that has been split into two-as described in Section 3.4.…”

Section: Procedures Solvepdp(d # P)mentioning

confidence: 81%

“…2, pp. 134-144, © 2020 observed and reported for other relaxation-based methods for minimax and maximin combinatorial optimization problems (Aloise andContardo 2018, Contardo et al 2019); it seems to be related to the dual degeneracy occurring when a larger number of clusters can be rearranged from one iteration to the next to find solutions of the same cost. This type of degeneracy occurs at a much smaller scale when the target number of points p is small.…”

Section: Computational Experiencementioning

confidence: 85%

“…134-144, © 2020 MMDCP, given n points, a dissimilarity matrix D, and an integer k ≥ 2, the objective is to group the observations into k clusters such as to minimize the maximum intracluster dissimilarity. Aloise and Contardo (2018) introduced a sampling mechanism to solve the MMDCP as a series of smaller MMDCPs in a dynamic fashion, allowing the solution to proven optimality of problems containing up to 600,000 observations.…”

Section: Literature Reviewmentioning

confidence: 99%

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Decremental Clustering for the Solution of p-Dispersion Problems to Proven Optimality

Contardo

2020

INFORMS Journal on Optimization

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Given n points, a symmetric dissimilarity matrix D of dimensions n × n, and an integer p ? 2, the p-dispersion problem (pDP) consists of selecting a subset of exactly p points in such a way that the minimum dissimilarity between any pair of selected points is maximum. The pDP is [Formula: see text] when p is an input of the problem. We propose a decremental clustering method to reduce the problem to the solution of a series of smaller pDPs until reaching proven optimality. A k-means algorithm is used to construct and refine the clusterings along the algorithm’s execution. The proposed method can handle problems orders of magnitude larger than the limits of the state-of-the-art solver for the pDP for small values of p.

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Section: Procedures Solvepdp(d # P)mentioning

confidence: 81%

Section: Computational Experiencementioning

confidence: 85%

Section: Literature Reviewmentioning

confidence: 99%

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Decremental Clustering for the Solution of p-Dispersion Problems to Proven Optimality

Contardo

2020

INFORMS Journal on Optimization

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“…-The subject of the paper [4] by Sonia Cafieri and Claudia D'Ambrosio consists of using feasibility pump heuristics for the problem of aircraft conflict avoidance arising in air traffic management; -M. Fernanda P. Costa, Ana Maria A.C. Rocha and Edite M.G.P. Fernandes investigate in [5] the use of a filter methodology in the DIRECT method to assure convergence in nonconvex constrained global optimization problems; -The paper [6] by Angelo Lucia, Peter A. DiMaggio and Diego Alonso-Martinez considers a new approach to metabolic network analysis using a Nash Equilibrium formulation; -Immanuel M. Bomze, Vaithilingam Jeyakumar and Guoyin Li in their paper [7] guarantee exact copositive and Lagrangian relaxations to extended trust region problems with one or two balls; -The paper [8] by Jan Kronqvist, Andreas Lundel and Tapio Westerlund discusses reformulations for utilizing separability when solving convex mixed-integer nonlinear programming problems; -Two feasibility heuristics based on the integrality gap minimization for binary mixedinteger nonlinear programming are discussed in the paper [9] by Wendel Melo, Marcia Fampa and Fernanda Raupp; -A sampling-based exact algorithm for the solution of the minimax diameter clustering problem is proposed in the paper [10] by Daniel Aloise and Claudio Contardo; -J. J. Moreno, Gloria Ortega, Ernestas Filatovas, J. A. Martínez and E. M. Garzón in their paper [11] discuss the improvement of the performance and energy of non-dominated sorting for evolutionary multiobjective optimization on GPU/CPU platforms.…”

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confidence: 99%

Preface to the Special Issue “GOW’16”

2018

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This special issue of the Journal of Global Optimization consists of papers presented at the XIII Global Optimization Workshop (GOW'16), which took place on September 4th-8th, 2016, at the University of Minho, in Braga, Portugal. This workshop attracted 54 participants from 14 countries and the scientific program contained one invited talk by Professor Panos Pardalos and 47 contributed talks. These global optimization workshops have been held since 1985 and more recently every two years. This special issue mainly focuses on deterministic methods and heuristics for global optimization. Problems with continuous as well as with integer variables are discussed. Some stochastic algorithms are also investigated. The papers were reviewed in the usual process and eleven papers were accepted for publication in this special issue. Below we give a brief presentation of the included papers.

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“…Uma estratégia amplamente utilizada para melhorar a eficiência dos algoritmos de agrupamento é a redução do número de elementos submetidos a esses algoritmos. Essa redução é obtida por meio de técnicas, tal como, amostragem (ALOISE; CONTARDO, 2018). Esse tipo de técnica mostrou-se útil para os métodos que realizam várias iterações considerando diferentes inicializações, como o algoritmo PAM.…”

Section: Estratégias De Otimizaçãounclassified

Agrupamento de dados complexos para apoiar consultas por similaridade com tratamento de restrições

Souza¹

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DE SOUZA, J. A. Clustering complex data for processing constrained similarity queries 2 . 2019. 102 p. Tese (Doutorado em Ciências -Due to the technological advances over the last years, both the amount and variety of data available have been increased at a fast pace. Thus, this scenario has influenced the development of effective strategies for the processing, summarizing, as well as to provide fast and automatic understanding of such data. The Access Methods are strategies that have been explored by researchers in the area to aid these purposes. These methods aim to effectively index data to reduce the time required for processing similarity querying. In addition, they have been applied to aid the processing of Data Mining techniques, such as Clustering Detection. Among the access methods, the metric structures are constructed applying only the criterion based on the distance computation between the elements of the dataset, i.e. similarity operations on the intrinsic characteristics of the dataset. Thus, the results do not always correspond to the context desired by users.This work explored the development of algorithms that allow metric access methods to process queries with a higher semantic load, aimed at contributing to the treatment of the quality question on the results of approaches that involve similarity operation (for example, data mining techniques and similarity queries). In this context, three approaches have been developed: the first approach presents the method clusMAM (Unsupervised Clustering using Metric Access Methods), which aims to display a clustering from a dataset with the application of a Metric Access Method from a summarized set. The second approach presents the CCkNN approach to dealing with the problem of multi-class constraints on the search space. Finally, the third proposal presents the method CfQ (Clustering for Querying) by integrating the techniques clusMAM with CCkNN, using the positive points of each strategy applied by the algorithms. In general, the experiments carried out showed that the proposed methods can contribute to an effective way of reducing similarity computations, which is required during a processing of techniques that are based on distance computations.

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

Cited by 15 publications

References 19 publications

Decremental Clustering for the Solution of p-Dispersion Problems to Proven Optimality

Decremental Clustering for the Solution of p-Dispersion Problems to Proven Optimality

Preface to the Special Issue “GOW’16”

Agrupamento de dados complexos para apoiar consultas por similaridade com tratamento de restrições

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