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In order to design broadband extreme ultraviolet multilayers with many objectives, the multiobjective genetic algorithm and the multiobjective genetics algorithm with reference direction have been improved and combined used. The certain conflicting relations between three primary design objectives have been obtained by analyzing the distribution of nondominated solutions, and the multilayer designs with critical average reflectivities have been found. Basing on the multiobjective genetics algorithm with reference direction, the exact multilayer design has been obtained by guiding the searching in desired region of solution space. Our method can supply the multilayer designs which are the optimal trade-offs among these design objectives, and it has a great potential in designing optical multilayers with more objectives.