Generally, several IoT (Internet of Things) applications employ cloud data centre for processing the data generated by edge devices like smartphones and tablets. Due to the increasing use of the IoT devices, the demand for higher computational and communication capabilities are also increasing.With the advent of Edge Computing and given the fact that computational capabilities are currently untapped, a part of the computational load can be offloaded to the edge nodes. In this paper, a Grefenstette bias based Genetic Algorithm for MultiSite Offloading (GGA-MSO) is proposed. This algorithm decides the schedule of the application that could be offloaded. The proposed algorithm provides a solution which has convergence in lesser time by employing diversification of initial population using the Grefenstette's Bias method. Besides, the container based lightweight virtualization is analyzed for offloading code and data to the nearby devices. The evaluation of the proposed work on random graphs shows that the proposed method starts to converge with significantly lesser iterations than its counterpart with undiversified population. The test bed results on Single Board Computers (SBC) like Raspberry Pi setup indicates that by adapting container virtualization in the edge environment, the performance of the IoT devices is improved and the communication overhead is reduced. © 2019 - IOS Press and the authors.