Abstract: This paper presents a multiobjective optimization design method for transonic cascades with mixed variables and constraints.On the basis of the computation method of two-dimensional Euler equations coupled with boundary equations for transonic viscous flow,the cascade aerodynamic losses and work potential are considered as the two objective functions,and a united objective function is formulated using dimensionless minimum-deviation method,by which the two-objective optimization problem is divided into two single-objective optimization problems.Then,the efficient optimal solution is obtained with the optimization algorithm of flexible tolerance method.