Clustering Qualitative Data Based on Binary Equivalence Relations: Neighborhood Search Heuristics for the Clique Partitioning Problem

Abstract

equivalence relation, clique partitioning, clustering, heuristics, tabu search, simulated annealing, neighborhood search,

A Tabu-Search Heuristic for Deterministic Two-Mode Blockmodeling of Binary Network Matrices

“…Tabu-search results from previous applications, as well as some experimentation, were used to guide our selection of the ψ 0 and η 0 parameters. De Amorim et al (1992) used modest parameter settings of ψ 0 = 5 and η 0 = N/2 in their tabu-search application for clique partitioning; however, Brusco and Köhn (2009) found that more aggressive parameter settings of ψ 0 = N/2 and η 0 = 6N yielded substantially better performance for larger, more difficult problems. Our parameter experiments yielded similar findings for two-mode blockmodeling.…”

“…For all test problems, the matrix elements were independently generated based on a uniform distribution with equal probability for a value of 0 or 1. The random generation of matrix elements has also been used in other clustering contexts because of its ability to produce difficult test problems that can differentiate the performance of competitive methods (Charon & Hudry, 2006;Brusco & Köhn, 2009). …”

“…One such extension is the integration of the tabu-search procedure within the framework of variable neighborhood search (see, for example, Brusco & Köhn, 2009). A second, and potentially important, advancement centers on the development of improved procedures for generating initial blockmodeling solutions.…”

“…For example, metaheuristics such as variable neighborhood search (Mladenović & Hansen, 1997) and genetic algorithms (Goldberg, 1989) have been shown to outperform multistart implementations of the K-means algorithm (Steinhaus, 1956) for within-cluster sum-of-squares partitioning (see Brusco & Steinley, 2007b). Similarly, simulated annealing (Aarts & Korst, 1989) and tabu search (Glover & Laguna, 1993) have proven superior to multiple restarts of relocation heuristics for the clique partitioning problem (see Brusco & Köhn, 2009;De Amorim, Barthélemy, & Ribeiro, 1992).…”

A variable neighborhood search method for a two-mode blockmodeling problem in social network analysis

“…Our paper further explores this possibility by developing and testing an adaptation of the variable neighborhood search (VNS; algorithm for deterministic two-mode blockmodeling. In part, this exploration is motivated by the fact that there is compelling evidence that VNS often outperforms TS in a number of contexts that require the clustering of objects, including the p-median problem , minimum sum of squares partitioning (Brusco & Steinley, 2007), and clique partitioning (Brusco & Köhn, 2009).…”