The explosion of wireless network services forces us to seek new technologies and resource allocation schemes. Three joint resource allocation frameworks for device-to-device (D2D) communication in non-orthogonal multiple access (NOMA) assisted multi-cell systems are proposed. D2D can reduce the access pressure of base station (BS) equipment, and NOMA can multiplex network spectrum resources, and the integration of them can further improve the performance of multi-cell networks. We investigate the joint user association, resource block (RB) assignment, and power allocation problem in multi-cell systems with the aim of maximizing the sum rate of D2Ds. To solve this mixed-integer non-linear programming (MINLP) problem, we propose three differential evolution (DE) algorithms. First, we invoke the coevolution DE-based resource allocation (CDRA) framework which encodes the RB assignment and power allocation into the same individual for evolution. Second, we invoke the iteration-combining DE-based resource allocation (IDRA) framework, which adopts two-steps DE algorithm to solve optimal power allocation and RB assignment scheme iteratively. Last, we invoke the power-repairing DE-based resource allocation (PDRA) framework, which combines a similar joint RB assignment and power allocation as CDRA, where power repair is added after each iteration. Simulation results demonstrate that: \romannumeral1) the integration of D2D and NOMA techniques is capable of enhancing the achievable sum rate of D2Ds; \romannumeral2) the proposed three proposed frameworks for multi-cell NOMA networks can effectively optimize the objective function. However, comparing with CDRA and IDRA, PDRA performs better in terms of convergence speed and maximum D2D rate.