The global optimization of the moon tour design problem is addressed in this paper. These missions are usually designed using graphical methods or grid search, which require simplifying assumptions, and a skillful mission designer. The grid search methods are computationally intense. Trajectories with a high number of flybys and multiple resonance flybys are usually hard to optimize, especially with small-size/short-period flyby moons. This work proposes a new mutation operator that is incorporated with the Monotonic Basin Hopping in the Evolutionary Mission Trajectory Generator tool; this mutation operator increases the exploration of resonance flybys to improve convergence in moon tour design optimization problems. In this work, the Hidden Genes Genetic Algorithm is used to optimize the undetermined number of moon flybys. A Europa Clipper-like mission is optimized assuming two-body dynamics, and a validation study for the proposed resonance mutation operator is presented. The results include an optimized baseline solution and a new solution with a different sequence of flybys with a different sequence of flybys for the Europa Clipper-like mission, in addition to an optimized moon tour in the Saturnian system.