Achieving a balance between the exploration and exploitation capabilities of genetic algorithms is a key factor for their success in solving complicated search problems. Incorporating a local search method within a genetic algorithm can enhance the exploitation of local knowledge but it risks decelerating the schema building process. This paper defines some features of a local search method that might improve the balance between exploration and exploitation of genetic algorithms. Based on these features a probabilistic local search method is proposed. The proposed search method has been tested as a secondary method within a staged hybrid genetic algorithm and as a standalone method. The experiments conducted showed that the proposed method can speed up the search without affecting the schema processing of genetic algorithms. The experiments also showed that the proposed algorithm as a standalone algorithm can, in some cases, outperform a pure genetic algorithm.