Joint Optimization of Continuous Variables and Priority Assignments for Real-Time Systems with Black-Box Schedulability Constraints

In real-time systems optimization, designers often face a challenging problem posed by the non-convex and non-continuous schedulability conditions, which may even lack an analytical form to understand their properties. To tackle this challenging problem, we treat the schedulability analysis as a black box that only returns true/false results. We propose a general and scalable framework to optimize real-time systems with continuous variables, named Numerical Optimizer with Real-Time Highlight (NORTH). NORTH is built upon the gradient-based active-set methods from the numerical optimization literature but with new methods to manage active constraints for the non-differentiable schedulability constraints. In addition, we also generalize NORTH to NORTH+ to collaboratively optimize priority assignments, a common type of discrete variables, with continuous variables based on numerical optimization algorithms. We demonstrate the algorithm performance with two example applications: energy minimization based on dynamic voltage and frequency scaling (DVFS), and optimization of control system performance. In these experiments, NORTH are 10 2 to 10 5 times faster than state-of-the-art methods while maintaining similar or better solution quality. NORTH+ outperforms NORTH by 30% with similar algorithm scalability. Both NORTH and NORTH+ support black-box schedulability analysis, ensuring broad applicability.