Every second, a large amount of digital data is transported through infinite types of devices via cellular networks worldwide, and expectations are at a greatly accelerated growth with increasingly large requests. In few years, these networks could thereby reach their maximum capacities in terms of data transmission. To face these challenges, Network Slicing has been presented as a novel virtualized infrastructure for the new generation cellular network system. This technology now not only covers application-level abstraction but also physical and switching layers virtualization, with different radio access and link communication technologies. Hence, each service provider is to be able to deploy its communication services on top of logical networks, named Network Slices, specifically tailored to its technical requirements. The Device-to-Device communication mode is another approach presented as a promising alternative to traditional communication in cellular networks. This technology allows to reuse radio resources and to decrease the end-to-end latency of local communications. Consequently, the optimization of physical resources in cellular networks becomes crucial to better deploy virtual networks. The overall objective of our research is therefore to define and study the concept of device-to-device communication and network slice design in 5G systems, and propose mathematical models and innovative algorithms to solve the underlying optimization problems.