An online transfer learning based multifactorial evolutionary algorithm for solving the clustered Steiner tree problem

Abstract

The rapid increase in the number and computing power of devices interacting through the network over the past few years has led to a growing trend of decentralized clustering network architecture. The Clustered Steiner Tree Problem (CluSteiner) is a recently introduced NP-Hard problem and is assessed to be the core of efficient multicast routing in such networks. However, research on this problem in terms of theory and algorithmic design is still in its infancy as current solving approaches are limited in the literature. Lately, the Multifactorial Evolutionary Algorithm (MFEA) has been applied to solve several clustering-structure network design problems for the reason that these problems rarely exist independently and are often deployed concurrently in practice. To effectively transfer knowledge between problems while solving them simultaneously, this paper proposes an approach based on the novel data-driven MFEA-II to deal with the CluSteiner problem. In the proposal, an efficient encoding and a two-level decoding mechanism are introduced, combined with a module capable of online learning the amount of knowledge transferred between tasks that help the algorithm to explore potential regions of the search space. Experiments are undertaken on various test instances to evaluate the efficacy of the proposed algorithm. The empirical results indicate that our proposal can perform well on both metric and non-metric graphs with the statistical tests used to verify its efficiency over other baseline algorithms regarding the solution quality and convergence trend.