This paper proposes a method for solving mixed-integer nonlinear programming problems to achieve or approach the optimal solution by using modified genetic algorithms. The representation scheme covers both integer and real variables for solving mixed-integer nonlinear programming, nonlinear programming, and nonlinear integer programming. The repairing strategy, a secant method incorporated with a bisection method, plays an important role in converting infeasible chromosomes to feasible chromosomes at the constraint boundary. To prevent premature convergence, the appropriate diversity of the structures in the population must be controlled. A cross-generational probabilistic survival selection method (CPSS) is modified for real number representation corresponding to the representation scheme. The efficiency of the proposed method was validated with several numerical test problems and showed good agreement.