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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.

Background: A central problem of systems biology is the reconstruction of the topology of gene regulatory networks (GRNs) using high throughput genomic data like microarray gene expression data. The main challenge in gene expression data is that the number of genes is high, number of samples is low, and the data are often impregnated with noise. Objective: In this paper, we present a method for Gene Regulatory Network Inference using Rotation Forest (GENIRF). Methods: The rotation forest will exploit the embedded variable ranking mechanism of tree-based ensemble methods and dimension reduction. This feature solves the main challenge in gene expression data. GENIRF decomposes the prediction of a gene regulatory network between p genes into p different regression problems. Each regression problem is constructed with a transformed expression pattern and rotation forest. The expression pattern of the target gene is predicted from the expression patterns of all the remaining genes, using rotation forest. Results: GENIRF does not make any hypotheses regarding the nature of gene regulation, so it can identify combinatorial and non-linear interactions in GRN. Experimental results on the DREAM4 in silico multifactorial challenge simulated data indicate that GENIRF has better accuracy and compares favorably with existing well known algorithms. Furthermore, it is a fast and scalable method. Conclusion: GENIRF shows high performance across this benchmark with different performance metrics and the overall score of GENIRF is slightly better than other method. We have also shown that the dimension reduction of the gene expression data can further improve the performance of GENIRF and other methods. In addition, GENIRF is competitive in terms of computational efficiency, especially with ensemble methods and for big data, our method can be easily parallelized.