Core switching on different links in optical networks enables network operators to allocate network resources more flexibly, so as to reduce the network request blocking ratio under limited resources. Facing a differentiated network environment and diversified user demands, network operators need to optimize multiple objectives that are independent and diversionary of each other, and to provide multiple resource allocation schemes whose objective values do not dominate each other. For the static routing, spectrum, and core assignment (RSCA) problem in elastic optical networks with multi-core fiber (MCF-EONs), there is no literature that simultaneously considers core switching and multiobjective optimization algorithms. This paper improves the existing models and algorithms to adapt to the RSCA problem. In this paper, the RSCA problem is formulated as an integer linear programming model to minimize both network request blocking and crosstalk ratios simultaneously by considering core switching and inter-core crosstalk. To solve the model efficiently, we, therefore, design a joint routing and core coding scheme supporting core switching and propose a multiobjective evolutionary algorithm based on decomposition with adaptation and multi-strategy fusion (MOEA/D-AMSF), which integrates the new mechanisms of hybrid initial population generation, adaptive crossover, and double-layer and multi-point mutation in different iteration stages. These new mechanisms accelerate algorithm convergence and enhance solution diversity. Simulation results show that the proposed algorithm can obtain more dominated and diverse solutions compared with the existing multiobjective algorithm without considering core switching.