In this paper, we combine the network-assisted full-duplex (NAFD) technology and distributed radar sensing to implement integrated sensing and communication (ISAC). The ISAC system features both uplink and downlink remote radio units (RRUs) equipped with communication and sensing capabilities. We evaluate the communication and sensing performance of the system using the sum communication rates and the Cramer-Rao lower bound (CRLB), respectively. We compare the performance of the proposed scheme with other ISAC schemes, the result shows that the proposed scheme can provide more stable sensing and better communication performance. Furthermore, we propose two power allocation algorithms to optimize the communication and sensing performance jointly. One algorithm is based on the deep Q-network (DQN) and the other one is based on the non-dominated sorting genetic algorithm II (NSGA-II). The proposed algorithms provide more feasible solutions and achieve better system performance than the equal power allocation algorithm.