An efficient weighted partial MaxSAT encoding for scheduling in overloaded real-time systems

Scheduling tasks in overloaded real-time systems is a challenging problem that has received a significant amount of attention in recent years. The processor is overloaded with more tasks than its capacity, resulting in missed deadlines and degraded system performance. Therefore, scheduling algorithms play a critical role in ensuring that high-priority tasks are completed on time while minimizing the impact of incomplete lower-priority tasks. This paper proposes an efficient Weighted Partial MaxSAT(WPMS) encoding that returns an optimal solution in which the total weight of incomplete tasks is minimized in a single machine environment. To assess the efficiency of our proposed formulation, a comparative analysis is conducted alongside the state-of-the-art encoding. By examining the solving 75 distinct problems, it becomes evident that the WPMS encoding proposed herein exhibits a considerable advantage in terms of both time and memory efficiency.