A Local Search Algorithm with Reinforcement Learning Based Repair Procedure for Minimum Weight Independent Dominating Set

The minimum weight independent dominating set problem (MWIDS) is a famous NP-hard combinatorial optimization problem. We herein propose a local search algorithm with reinforcement-learning-based repair procedure (LSRR). The proposed algorithm combines local search with repair procedure based on the mind of reinforcement learning. This algorithm iterates through three procedures: the greedy procedure to improve the initial solution, the local search procedure to further improve the solution, and the repair procedure to destroy the initial solution and then reconstruct a new solution. In addition, because of the particularity of the weight functions in all benchmarks, we propose three novel scoring functions. Experiments are performed on two types of graphs including random graphs and random geometric graphs. Experimental results display that LSRR outperforms the previous MWIDS algorithms significantly.