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

TL;DR

This paper introduces NORTH and NORTH+ frameworks for optimizing real-time systems with black-box schedulability constraints, achieving significant speedups and supporting discrete and continuous variables.

Contribution

The paper presents NORTH and NORTH+ algorithms that handle non-convex, non-differentiable schedulability constraints in real-time system optimization, including discrete variables.

Findings

NORTH achieves 100 to 100,000 times speed improvements over existing methods.

NORTH+ outperforms NORTH by 30% in solution quality.

Both methods support black-box schedulability analysis for broad applicability.

Abstract

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, 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 certain types of discrete variables (e.g., priority assignments, categorical 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 achieved $10^2$ to $10^5$ times speed improvements over 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.