Device-to-device (D2D) communication, which can offload data from base stations by direct transmission between mobile devices, is a promising technology for fifth generation (5G) wireless networks. However, the limited battery capacity of mobile devices is a barrier to fully exploiting the benefits of D2D communication. Meanwhile, high data rate D2D communication is required to support the increasing traffic demand of emerging applications. In this paper, we study relay-assisted D2D communication in millimeter wave (mmWave)-based 5G networks to address these issues. Multiple D2D user pairs are assisted by full-duplex relays that are equipped with directional antennas. To design an efficient relay selection and power allocation scheme, we formulate a multi-objective combinatorial optimization problem, which balances the trade-off between total transmit power and system throughput. The problem is transformed into a weighted bipartite matching problem. We then propose a centralized relay selection and power allocation algorithm and prove that it can achieve a Pareto optimal solution in polynomial time. We further propose a distributed algorithm based on stable matching. Simulation results show that our proposed algorithms substantially reduce the total transmit power and improve the system throughput compared with two existing algorithms in the literature.