Many real-world problems, including the design problem, involve multiple and often conflicting objectives. Evolutionary Algorithm (EA) is an effective method to solve such multiobjective optimization problems. The application of EAs in multiobjective optimization is normally called Evolutionary Multiobjective Optimization (EMO). In the engineering design, the designer usually has some information and knowledge based on his/her experience. This paper describes a new method for multiobjective optimization problems using Genetic Algorithm (GA), which can integrate designer's vague preferences into GA search. In the proposed GA, in order to obtain a group of Pareto-optimal solutions in which the designer is interested, a new strategy based on tournament selection is proposed. Through a simple numerical example, we show the effectiveness of the proposed method.