Evolutionary Multi Objective Optimization Algorithm for Community Detection in Complex Social Networks

TL;DR

This paper introduces two novel three-objective evolutionary algorithms for community detection in social networks, demonstrating improved or comparable results to existing methods on benchmark datasets.

Contribution

It proposes two new multi-objective formulations using NSGA-III for community detection, incorporating novel objective functions and a ranking method for Pareto solutions.

Findings

The proposed algorithms outperform or match state-of-the-art methods.

Adding a third objective does not compromise the quality of solutions.

A new Pareto ranking measure based on hyper-volume and IGD is effective.

Abstract

Most optimization-based community detection approaches formulate the problem in a single or bi-objective framework. In this paper, we propose two variants of a three-objective formulation using a customized non-dominated sorting genetic algorithm III (NSGA-III) to find community structures in a network. In the first variant, named NSGA-III-KRM, we considered Kernel k means, Ratio cut, and Modularity, as the three objectives, whereas the second variant, named NSGA-III-CCM, considers Community score, Community fitness and Modularity, as three objective functions. Experiments are conducted on four benchmark network datasets. Comparison with state-of-the-art approaches along with decomposition-based multi-objective evolutionary algorithm variants (MOEA/D-KRM and MOEA/D-CCM) indicates that the proposed variants yield comparable or better results. This is particularly significant because the addition of the third objective does not worsen the results of the other two objectives. We also propose a simple method to rank the Pareto solutions so obtained by proposing a new measure, namely the ratio of the hyper-volume and inverted generational distance (IGD). The higher the ratio, the better is the Pareto set. This strategy is particularly useful in the absence of empirical attainment function in the multi-objective framework, where the number of objectives is more than two.