A two phase removing algorithm for minimum independent dominating set problem

The minimum independent dominating set (MIDS) problem is a famous combinatorial optimization problem and is widely used in real-world domains. In this paper, we design a novel local search algorithm with tabu method and two phase removing strategies including double-checked removing strategy and random diversity removing strategy to solve the MIDS problem. The first removing strategy checks and then removes the second-level neighbourhood of the just removal vertex to break the limitation of the independence property. When the quality of candidate solution has not been improved after some steps, the second removing strategy dynamically and greedily removes lots of vertices so that the current candidate solution can escape from suboptimal search space, and then we introduce the random walk into the repair process. Experiments are carried out on two classical benchmarks named DIMACS and BHOSLIB, and the results show that the proposed algorithm significantly outperforms the previous state-of-the-art MIDS heuristic algorithms.