The Study of the Target Set Selection Problem under Deterministic Linear Threshold Model Using Evolutionary Algorithms

In this paper we study the Target Set Selection problem (TSS) – the well-known combinatorial problem associated with collective behaviour in networks. For a given network graph and the information diffusion model that specifies a dynamic process of how vertices activate each other, TSS aims to identify a set of initially active vertices of minimum cardinality such that they manage to activate all the other network vertices. This problem is computationally hard but has numerous applications in practice, thus the development of computational algorithms for TSS is a relevant topic. A surprising fact is that the spectrum of algorithms for TSS presented so far in the literature is quite limited. The main novelty of our study consists in the hybrid approach which combines evolutionary and greedy algorithms for TSS. In more detail, we view TSS as a pseudo-Boolean optimization problem and solve it using simple evolutionary algorithms (in fact several variants of (1+1)-EA). In order to identify a good initial approximate solution we employ a greedy algorithm. In the experiments we apply the developed algorithms to TSS in the context of Deterministic Linear Threshold Model (DLTM) and demonstrate that the presented approach shows good effectiveness when solving TSS on networks with dozens thousands of vertices on personal computer.