This investigation focuses on the routing, core allocation and spectrum assignment problems in elastic optical network with multi-cores. To minimize the maximum index of used frequency slots, a global constraint optimization model with crosstalk rate of adjacent cores meeting certain threshold requirement is proposed. In order to solve the model efficiently, a global optimization genetic algorithm is proposed. The groomed connection requests are sorted, and the designed genetic algorithm is used to obtain the optimal schemes of routing and core allocation for all the connection requests. To evaluate the efficiency of the proposed algorithm, different simulations are conducted. The simulation results show that the proposed algorithm can reduce the maximum index of used frequency slot and improve spectrum efficiency.