Growing neural gas as a memory mechanism of a heuristic to solve a community detection problem in networks

Iterative heuristics are commonly used to address combinatorial optimization problems. However, to meet both robustness and efficiency with these methods when their iterations are independent, it is necessary to consider a high number of iterations or to include local search-based strategies in them. Both approaches are very time-consuming and, consequently, not efficient for medium and large-scale instances of combinatorial optimization problems. In particular, the community detection problem in networks is well-known due to the instances with hundreds to thousands of vertices. In the literature, the heuristics to detect communities in networks that use a local search are those that achieve the partitions with the best solution values. Nevertheless, they are not suitable to tackle medium to large scale networks. This paper presents an adaptive heuristic, named GNGClus, that uses the neural network Growing Neural Gas to play the role of memory mechanism. The computational experiment with LFR networks indicates that the proposed strategy significantly outperformed the same solution method with no memory mechanism. In addition, GNGClus was very competitive with a version of the heuristic that employs an elite set of solutions to guide the solution search. (C) 2016 The Authors. Published by Elsevier B.V.Instituto de Ciência e Tecnologia, Universidade Federal de São Paulo (UNIFESP) Av. Cesare M. G. Lattes, 1201, Eugênio de Mello, São José dos Campos-SP, CEP: 12247-014, BrasilInstituto de Ciência e Tecnologia, Universidade Federal de São Paulo (UNIFESP) Av. Cesare M. G. Lattes, 1201, Eugênio de Mello, São José dos Campos-SP, CEP: 12247-014, BrasilWeb of Scienc

Heurística da Colônia de Formigas para Detecção de Comunidades

Maximização da modularidade é um modelo utilizado para detecçãode comunidades. Algoritmos exatos podem não resolver o problema damaximização da modularidade em tempo polinomial, o que justifica o uso debusca heurística. Otimização por Colônia de Formigas (OCF) foi a metaheurísticautilizada em redes do mundo real e aleatórias, a fim de testar suaviabilidade. Duas combinações foram responsáveis por gerar as soluções demelhor qualidade em um tempo computacional polinomial, elas foram:ℎ = 0.3, = 0.3, = 5, = 15, ∈ {0.3,0.7}

Efficient modularity density heuristics in graph clustering and their applications

Modularity Density Maximization is a graph clustering problem which avoids the resolution limit degeneracy of the Modularity Maximization problem. This thesis aims at solving larger instances than current Modularity Density heuristics do, and show how close the obtained solutions are to the expected clustering. Three main contributions arise from this objective. The first one is about the theoretical contributions about properties of Modularity Density based prioritizers. The second one is the development of eight Modularity Density Maximization heuristics. Our heuristics are compared with optimal results from the literature, and with GAOD, iMeme-Net, HAIN, BMD- heuristics. Our results are also compared with CNM and Louvain which are heuristics for Modularity Maximization that solve instances with thousands of nodes. The tests were carried out by using graphs from the “Stanford Large Network Dataset Collection”. The experiments have shown that our eight heuristics found solutions for graphs with hundreds of thousands of nodes. Our results have also shown that five of our heuristics surpassed the current state-of-the-art Modularity Density Maximization heuristic solvers for large graphs. A third contribution is the proposal of six column generation methods. These methods use exact and heuristic auxiliary solvers and an initial variable generator. Comparisons among our proposed column generations and state-of-the-art algorithms were also carried out. The results showed that: (i) two of our methods surpassed the state-of-the-art algorithms in terms of time, and (ii) our methods proved the optimal value for larger instances than current approaches can tackle. Our results suggest clear improvements to the state-of-the-art results for the Modularity Density Maximization problem