The Whale Optimization Algorithm (WOA) is an innovative metaheuristic inspired by the social hunting behavior of humpback whales. This paper presents a binary version of the WOA applied to the Minimum Dominating Set (MDS) problem, a challenging combinatorial optimization problem known to be NP-hard. However, the WOA suffers from premature convergence, potentially causing the algorithm to become trapped in local optima and fail to reach the global optimum. To address this issue, the paper introduces an enhanced version of WOA called the Local Search Optimization Binary Whale ( Lobw), which incorporates a Local Search technique to improve exploitation ability and prevent the algorithm from getting stuck in local optima. The Lobw algorithm is evaluated on several benchmark datasets, demonstrating its promising performance in terms of solution quality and stability compared to other metaheuristic algorithms. The source code of the  Lobw algorithm and the datasets used in the experiments can be accessed via the following link: https://github.com/elkacem/LOBW-for-MDS.