An improved master-apprentice evolutionary algorithm for minimum independent dominating set problem

Shiwei Pan, Yiming Ma, Yiyuan Wang, Zhiguo Zhou, Jinchao Ji, Minghao Yin, Shuli Hu

Abstract: The minimum independent dominance set (MIDS) problem is an important version of the dominating set with some other applications. In this work, we present an improved master-apprentice evolutionary algorithm for solving the MIDS problem based on a path-breaking strategy called MAE-PB. The proposed MAE-PB algorithm combines a construction function for the initial solution generation and candidate solution restarting. It is a multiple neighborhood-based local search algorithm that improves the quality of the solution using a path-breaking strategy for solution recombination based on master and apprentice solutions and a perturbation strategy for disturbing the solution when the algorithm cannot improve the solution quality within a certain number of steps. We show the competitiveness of the MAE-PB algorithm by presenting the computational results on classical benchmarks from the literature and a suite of massive graphs from real-world applications. The results show that the MAE-PB algorithm achieves high performance. In particular, for the classical benchmarks, the MAE-PB algorithm obtains the best-known results for seven instances, whereas for several massive graphs, it improves the best-known results for 62 instances. We investigate the proposed key ingredients to determine their impact on the performance of the proposed algorithm.