Metaheuristic Approaches for the Blockmodel Problem

Blockmodel problem (BMP) deals with identifying structural similarities or equivalences among entities which, in turn, provide many insights into the structures or patterns of complex networks such as social networks. The objective of this problem is to find a small number of large blocks containing structural similarities or equivalences among entities in a given graph representing a complex network. In this paper, we present an evolutionary approach and a swarm intelligence approach for the BMP. The evolutionary approach consists of a steady-state grouping genetic algorithm (GA), whereas the swarm intelligence approach is based on the artificial bee colony (ABC) algorithm. The BMP is a grouping problem, i.e., a problem whose objective is to find an optimal assignment of entities according to a given fitness function into different groups subject to some constraints. Grouping GAs are especially designed to handle grouping problems as the traditional GA suffers from the problem of redundancy, context insensitivity, and schema disruption while handling grouping problems. Our ABC algorithm is also designed in such a manner that it tries to preserve grouping information as far as possible in order to find high-quality solutions. To our knowledge, this is the first application of the ABC algorithm for a problem with a variable number of groups. Computational results show the effectiveness of our approaches.