A hybrid multifactorial evolutionary algorithm and firefly algorithm for the clustered minimum routing cost tree problem

The clustered minimum routing cost tree (CluMRCT) problem is a recent problem with a wide range of real-life applications, especially in designing computer networks with peer-to-peer architecture. Many multifactorial evolutionary algorithms have been proposed to solve multiple CluMRCT problems simultaneously. However, these algorithms only function effectively on complete graphs with small-and-medium sizes. Moreover, the blindness and randomness in the transfer of genetic materials cause a reduction in the exploitation ability and make these algorithms ineffective to solve low-similarity tasks. This paper proposes a hybrid multitasking algorithm named multifactorial firefly algorithm, which integrates the firefly algorithm’s strong exploitation ability to enhance the self-evolution of each task when facing low-similarity tasks while improving inter-task knowledge transfers by delivering higher-quality solutions. Also, the proposed algorithm is equipped with new encoding and decoding to focus more on potential search areas on both complete and sparse graphs. The experiments and Wilcoxon signed-rank tests were conducted on various instances to verify our proposal with several state-of-the-art methods. The results portrayed that the proposed encoding scheme helped multitasking algorithms improve solution quality by 32% on average. Besides, the statistical test values proved the superiority of the proposed hybrid algorithm in terms of solution quality and convergence trend.