This paper presents a method to obtain the global or quasi-optimum for the discrete and continuous design variables, based on the Modified Generalized Random Tunneling Algorithm (MGRTA). By handling the discrete design variables as penalty function, the augmented objective function is constructed. As a result, all design variables can be treated as the continuous design variables. The augmented objective function becomes non-convex, and has many local minima. That is, finding optimum of discrete design variables is transformed into finding global optimum of this augmented objective function. Then the MGRTA is applied to this augmented objective function, subject to the behavior and side constraints. We also propose the new update scheme of penalty parameter for the penalty function of discrete design variables in this paper. The proposed update scheme of penalty parameter utilizes the information of the penalty function value of discrete design variables. By utilizing the characteristics of MGRTA, some optima are obtained. The validity of the proposed method is examined through typical benchmark problems.