With the purpose of designing the extreme ultraviolet polarizer with many objectives, a combined application of multiobjective genetic algorithms is theoretically proposed. Owing to the multiobjective genetic algorithm, the relationships between different designing objectives of extreme ultraviolet polarizer have been obtained by analyzing the distribution of nondominated solutions in the 4D objective space, and the optimized multilayer design can be obtained by guiding the searching in the desired region based on the multiobjective genetic algorithm with reference direction. Comparing with the conventional method of multilayer design, our method has a higher probability of achieving the optimal multilayer design. Our work should be the first research in optimizing the optical multilayer designs in the high-dimensional objective space, and our results demonstrate a potential application of our method in the designs of optical thin films.