DOI: 10.4018/IJAMC.2017100101 International Journal of Applied Metaheuristic Computing Volume 8 • Issue 4 • October-December 2017 Copyright © 2017, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Social Structure Discovery Using Genetic Algorithm Saeed Nasehi Moghaddam, University of Zanjan, Zanjan, Iran Mehdi Ghazanfari, Iran University of Science and Technology, Tehran, Iran Babak Teimourpour, Department of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran ABSTRACT As a way of simplifying, size reducing and making the structure of each social network be comprehensible, blockmodeling consists of two major, essential components: partitioning of actors to equivalent classes, called positions, and clarifying relations between and within positions. While actor partitioning in conventional blockmodeling is performed by several equivalence definitions, generalized blockmodeling, searches, locally, the best partition vector that best satisfies a predetermined structure. The need for known predefined structure and using a local search procedure, makes generalized blockmodeling be restricted. In this paper, the authors formulate blockmodel problem and employ a genetic algorithm for to search for the best partition vector fitting into original relational data in terms of the known indices. In addition, during multiple samples and situations such as dichotomous, signed, ordinal and interval valued, and multiple relations, the quality of results shows better fitness than classic and generalized blockmodeling. KeywoRDS Blockmodeling, Genetic Algorithm, Likelihood Ratio Statistics G2, Multi Objective Optimization, Social Network Analysis (SNA) 1. INTRoDUCTIoN The discovery of social structure in the network of actors with multiple relations is called positional analysis. During positional analysis process, blockmodeling as a way of simplifying, size reducing and making the structure of each social network be comprehensible, consists of two major, essential components: partitioning of actors to positions (or equivalent classes) and clarifying relations between and within positions. Multiple definitions have been proposed by authors for equivalent classes. Pioneer of them is structural equivalence (SE), introduced by Lorrain and White (1971), which implies that two actors belong to the same structural equivalent class iff they have identical ties to / from all other actors. The other definitions are automorphic, isomorphic and regular equivalence. As mentioned by (Wasserman & Faust, 1994), the definition of equivalence by SE has more adherents among researchers for positional analysis of social networks. In order to reveal the social structure of each network, the relations between and within positions must be specified and this can be done by density matrices, image matrices and reduced graphs. In fact at the end of each positional analysis, the social structure of each network can be summarized in the form of image/density matrices or reduced graphs. With the above considerations, each blockmodel has at least: a partition vector indicating the partitioning of actors to positions and a set of image matrices showing the social structure of each network. 1