A greedy randomized adaptive search procedure (GRASP) for minimum weakly connected dominating set problem

The minimum weakly connected dominating set problem (MWCDSP), a variant of the classical minimum dominating set problem, aims to find a minimum weakly connected dominating set on a given connected and undirected graph. To address this problem, a 0–1 integer linear programming (ILP) model and a framework of greedy randomized adaptive search procedure (GRASP) for MWCDSP are proposed. Specially, two novel local search procedures are introduced to improve the initial candidate solution in GRASP based on two greedy functions and tabu strategy. First, two greedy functions Dscore and Nscore are proposed to define the dominating score and neighbor score of each vertex respectively. Second, a tabu strategy is introduced to avoid the cycling problems. Third, a new local search procedure for searching a (k-1)-size solution after obtaining a k-size solution based on the Dscore function and tabu strategy is proposed, which is further improved by integrating Nscore into the selection process of moving vertices in an improved local search algorithm. Experimental results on four kinds of graph instances show that our GRASPs outperforms the famous CPLEX, the self-stabilizing algorithm MWCDS and the memetic algorithm MA. Specially, the GRASP with improved local search procedure outperforms all of the competitors.