To combine the preferences of a decision maker in the evolution process of a vector optimizer in finding an arbitrary fraction of the Pareto front of a multiobjective problem, the light beam search method is proposed to be incorporated into a vector normal boundary intersection method. To adapt different preferences, a new transformed projection mechanism is introduced; to enhance the diversity of the algorithm, a dynamic transitional sub-domain strategy is used. Typical mathematical functions and practical inverse problems are used to testify the effectiveness of the proposed method.