Computational offloading can improve the energy efficiency of mobile devices, by executing some tasks of a mobile application in the cloud. In this paper, a new algorithm called 'Dynamic Programming with Randomization' (DPR) is presented. The DPR algorithm iteratively improves an offloading decision vector, by generating random bit strings with a biased probability of generating 0s, which represent a decision to offload a task. If fragments of these bit strings improve the decision vector, they are incorporated into the decision vector (which is similar to genetic optimization). The DPR algorithm also uses a hamming distance termination criterion, with a preference to offload tasks, to find a nearly-optimal offloading solution quickly. The DPR algorithm will offload as many tasks as possible to the cloud server when the network transmission bandwidth is high, thereby improving the total execution time of all tasks and minimizing the energy consumption of the mobile device. The DPR algorithm can find excellent quality solutions with low computational overhead, by using biased randomization. Furthermore, the DPR algorithm can scale to handle larger offloading problems without loosing computational efficiency or solution quality, as the computational time grows linearly (with a slope less than unity) with the problem size. Performance evaluation shows that the proposed DPR algorithm can minimize energy requirements while meeting an application's execution time constraints, and it is able to find a nearly-optimal offloading decision vector in a few iterations.