The irregular satellites within the Jupiter system hold high scientific value due to their potential to contain clues about the early evolution of the solar system. This paper proposes a method for designing trajectories capable of flying by multiple irregular satellites. The method is based on beam search, using the virtual trajectory between layers to determine potential flyby targets, and considers both cases with and without Galilean moon gravity assist throughout the entire process, resulting in mission trajectories that meet certain constraints.In the final part, the idea of introducing diversity into the algorithm was used to expand the solution space. Simulation results demonstrate that by increasing the diversity of branches in beam search, the number of flybys of irregular satellites can be significantly augmented. Furthermore, incorporating gravity assist from Galilean moons into the mission design for initial orbits with shorter periods has also been shown to be effective in increasing the number of irregular satellite flybys.