A new kind of multiobjective simulated annealing algorithm is proposed,in which the concept of non-dominate d character is introduced and a new multiobjective acceptance criterion is set u p.The optimization example of a typical mathematical problem with two minimum ob jective functions indicates that all of the solutions contract to the set of the non-dominated points,and the variation trend of the optimal solutions is verif ied to be identical with that obtained using Genetic Algor thms.The ne w developed algorithm is then applied to the multiobjective optimization design of turbine cascades,in which it is coupled with the aerodynamics computation of the cascade flow fields and performance and the calculated loss coefficient and work potential of the cascade are considered as the objective functions,thus set ting up a technique to the engineering optimization design for the cascades.The optimization results,by the view of a group of optimal solutions,show that the a lgorithm is superior to the traditional technique of multiobjective optimization design and can be applied to more than two objective optimization cascade desig n problem or other engineering multiobjective optimization designs.