Towards the Optimal Solution of the Multiprocessor Scheduling Problem with Communication Delays

We consider the Multiprocessor Scheduling Problem with Communication Delays, where the delay is proportional to both the amount of exchanged data between pairs of dependent tasks and the distance between processors in the multiprocessor architecture. Although scheduling problems are usually solved by means of heuristics due to their large sizes, we propose methods to identify optimal solutions of small and medium-scale instances. A set of instances with known optima is a useful benchmarking tool for new heuristic algorithms. We propose two new Mixed-Integer Bilinear Programming formulations, we linearize them in two different ways, and test them with CPLEX 8.1. To decrease the time needed by CPLEX for finding the optimal solution, we use Variable Neighborhood Search heuristic to obtain a good approximation for the initial solution.