The rapid and convenient provision of the available computing resources is a crucial requirement in modern cloud computing environments. However, if only the execution time is taken into account when the resources are scheduled, it could lead to imbalanced workloads as well as to significant under-utilisation of the involved Virtual Machines (VMs). In the present work a novel task scheduling scheme is introduced, which is based on the proper adaptation of a modern and quite effective evolutionary optimization method, the Gravitational Search Algorithm (GSA). The proposed scheme aims at optimizing the entire scheduling procedure, in terms of both the tasks execution time and the system (VMs) resource utilisation. Moreover, the fitness function was properly selected considering both the above factors in an appropriately weighted function in order to obtain better results for large inputs. Sufficient simulation experiments show the efficiency of the proposed scheme, as well as its excellence over related approaches of the bibliography, with similar objectives.