Differentiable Initialization-Accelerated CPU-GPU Hybrid Combinatorial Scheduling
Summary: arXiv:2603.28943v1
Type: Cross
Abstract
This paper presents a hybrid CPU-GPU framework for solving combinatorial scheduling problems formulated as Integer Linear Programming (ILP). While scheduling underpins many optimization tasks in computing systems, solving these problems optimally at scale remains a long-standing challenge due to their NP-hard nature. We introduce a novel approach that combines differentiable optimization with classical ILP solving.
Introduction
The demand for efficient scheduling algorithms in various computing environments has intensified due to the increasing complexity of systems and workloads. Scheduling tasks optimally is crucial not only for resource allocation but also for performance enhancement in numerous applications ranging from cloud computing to real-time systems. However, traditional methods often struggle to achieve optimal solutions, particularly in large-scale instances.
Methodology
In our proposed framework, we leverage differentiable optimization to enhance the performance of conventional ILP solvers. The key components of our approach include:
- Differentiable Presolving: This technique allows for the rapid generation of high-quality partial solutions by treating the presolving step as a differentiable operation. This enables the model to learn from previous iterations and improve subsequent solutions.
- Hybrid CPU-GPU Architecture: By utilizing both CPU and GPU resources, our framework can exploit the parallel processing capabilities of GPUs while maintaining the robustness of CPU-based solvers.
- Integration with ILP Solvers: Our method serves as a warm-start for commercial ILP solvers such as CPLEX and Gurobi, as well as the open-source solver HiGHS, allowing for enhanced performance during the solution process.
Results
We conducted extensive empirical evaluations across various industry-scale benchmarks to assess the effectiveness of our approach. The results show a significant performance improvement over baseline methods. Key findings include:
- A performance gain of up to $10\times$ compared to state-of-the-art standalone solvers.
- A substantial reduction in the optimality gap, demonstrating the effectiveness of our hybrid approach in producing near-optimal solutions.
- Enhanced early pruning capabilities, which allow for faster convergence to optimal or near-optimal solutions.
Conclusion
The introduction of a differentiable initialization-accelerated CPU-GPU hybrid framework represents a significant advancement in the field of combinatorial scheduling. By effectively combining differentiable optimization techniques with classical ILP solving methods, we have demonstrated the potential for achieving remarkable performance improvements. Future work will focus on further refining the framework and exploring its applicability to a broader range of optimization problems.
Implications
The implications of this research extend beyond scheduling tasks in computing systems. The methodologies developed here can potentially be applied to various domains such as logistics, manufacturing, and telecommunications. As computing demands continue to evolve, the need for efficient, scalable, and optimal scheduling solutions will remain paramount.