The problems of routing and fiber-core assignment in the elastic optical networks (EONs) with multi-cores are investigated. Since the exchange of cores has an effect on the performance of the network, a global constrained optimization model is established which minimizes the blocking ratio. Taking the length and spectral availability of path into account, the candidate path set is selected for each connection request. Based on this, to solve the model effectively, an efficient genetic algorithm with high efficient encoding scheme, tailor-made crossover, mutation and local search operators is designed. The simulation experiments are conducted on different network topographies, and the experimental results show that the proposed algorithm can be used to obtain a small blocking ratio under the same scene.