Abstract-The computational grid provides a promising platform for the deployment of various high-performance computing applications. In computational grid, an efficient scheduling of task onto the processors that minimizes the entire execution time is vital for achieving a high performance.Solving this problem is very hard and many attempts have been made to solve the problem. Using classical algorithms, With regard to the complexity of this problem, is not the good way; so the indefinite method acts better than classical method. Evolutionary algorithms are the best choice for solving this hard problem. In this paper, contrary to prior ways, the new string representation has been used, communication costs has not been ignored and presents as a major factor for reaching to optimum solution