The efficient scheduling of independent computational tasks in a heterogeneous computing environment is an important problem that occurs in domains such as Grid and Cloud computing. Finding optimal schedules is an NP-hard problem in general, so we have to rely on approximate algorithms to come up schedules that are as near to optimal as possible. In our previous work on this problem, we applied a fast, effective local search to generate reasonably good schedules in a short amount of time and used ant colony optimisation (ACO) to incrementally improve those schedules over a longer time period. In this work, we replace the ACO component with a random disruption algorithm and find that this produces results which are competitive with the current state of the art over a 90 second execution time. We also ran our algorithm for a longer time period on 12 well-known benchmark instances and as a result provide new upper bounds for these instances.