For the task-scheduling problem, we propose an augmented neural-network approach, which allows the integration of greedy as well as nongreedy heuristics (AugNN-GNG), to give improved solutions in a small number of iterations. The problem we address is that of minimizing the makespan of n tasks on m identical machines (or processors), where tasks are nonpreemptive and follow a precedence order. The proposed approach exploits the observation that a nongreedy search heuristic often finds better solutions than do its greedy counterparts. We hypothesize that combinations of nongreedy and greedy heuristics when integrated with an augmented neural-network approach can lead to better solutions than can either one alone. We show the formulation of such integration and provide empirical results on over a thousand problems. This approach is found to be very robust in that the results were not very sensitive to the type of greedy heuristic chosen. The new approach is able to find solutions, on average, within 1.8% to 2.8% of the lower bound compared to 2.0% to 8.3% for the greedy-only AugNN approach. This improvement is obtained without any increase in computational complexity. In fact the number of iterations used to find the solution decreased.
