For the solution of a type of discrete global optimization problems, we provide a unique non-parameter filled function. A relevant solution algorithm that combines the discrete steepest approach with numerical and theoretical characterization of the suggested filled function is created. The suggested approach is a global optimization technique that revises the objective function into a filled function through optimizing a filled function built on earlier found minimum points to find better local minimum points step by step. A global minimum point can be derived through iterating over these programs. The numerical outcomes generated demonstrate the effectiveness of the filled function method. Moreover, we verify that the presented method is promising through the application of the filled function to the assignment problem.