A simple and effective iterated greedy algorithm for structural balance in signed networks

Recently, problems related to structural balance have received widespread attention in the research fields of signed networks, such as signed network partition, community detection and correlation clustering. Structural balance problems aim to find a partition of a signed network such that the frustration index, the sum of positive edges between subsets and negative edges within subsets, is minimized, which is known to be nondeterministic polynomial-time (NP)-complete and remains an open challenge. Many heuristic and meta-heuristic algorithms are developed to minimize the frustration index. However, most extant algorithms require quite a few parameters and are not efficient enough for large signed networks. In this study, we present a simple and effective iterated greedy (IG) algorithm for solving the structural balance problems with the objective of frustration minimization. In the algorithm, a constructive greedy heuristic is proposed to generate and reconstruct solutions to the problem with high efficiency. A two-stage local search procedure is designed to exploit the search space at different levels of granularity. An adaptive destruction method is developed to enhance the exploitation ability of the algorithm in the early stage and maintain the exploration ability later. Additionally, two acceleration methods are proposed to help the algorithm get a better performance in large signed networks. The experimental results indicate that the proposed IG algorithm outperforms other meta-heuristics in the literature especially in terms of the computational time.