Core-periphery structure detection (CPSD) in complex networks is essential to reveal functional nodes in the complicated systems, e.g., influential nodes in a social network and central cells in a biological network. Some progress has been made in solving the CPSD problem with heuristic algorithms. However, CPSD is naturally an NP-hard optimization problem and the core-periphery structures (CPSs) in real networks usually are not clearly distinguishable. The majority of the existing CPSD methods are single-objective methods relying on some assumptions, preference, and/or prior knowledge. They can provide only one trade-off solution that is inevitably biased and lacks of flexibility in terms of resolution. To address this issue, this paper formulates the CPSD problem as a multi-objective optimization problem (MOP), i.e., minimizing the core-node size and maximizing the core-node capacity of the CPSs, simultaneously. Solving the MOP can provide more accurate CPSs and allow one to explore the network structure at different preferred resolutions. A multi-objective memetic algorithm (called MOMA-PCLS) is accordingly proposed to solve the formulated problem. A new plateau-climbing local search (PCLS) method incorporating the information of the heavy-tailed distribution of the node capacity is introduced to fine-tune the individual solutions in MOMA-PCLS. By combining the evolutionary operations and PCLS, MOMA-PCLS manages to improve the search efficiency significantly. Experimental results on both synthetic and real-world data show the superiority of MOMA-PCLS to other state-of-the-art algorithms in detecting CPSs of complex networks.