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

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.