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. Specifically, we utilize differentiable presolving to rapidly generate high-quality partial solutions, which serve as warm-starts for commercial ILP solvers (CPLEX, Gurobi) and rising open-source solver HiGHS. This method enables significantly improved early pruning compared to state-of-the-art standalone solvers. Empirical results across industry-scale benchmarks demonstrate up to a $10\times$ performance gain over baselines, narrowing the optimality gap to $<0.1\%$. This work represents the first demonstration of utilizing differentiable optimization to initialize exact ILP solvers for combinatorial scheduling, opening new opportunities to integrate machine learning infrastructure with classical exact optimization methods across broader domains.

翻译：本文提出了一种混合CPU-GPU框架，用于解决以整数线性规划形式建模的组合调度问题。尽管调度是计算系统中诸多优化任务的基础，但由于其NP难特性，大规模精确求解此类问题仍是长期性挑战。我们引入了一种结合可微分优化与经典整数线性规划求解的新方法：具体而言，利用可微分预求解快速生成高质量部分解，作为商用整数线性规划求解器（CPLEX、Gurobi）以及新兴开源求解器HiGHS的热启动方案。与当前最先进的独立求解器相比，该方法显著提升了早期剪枝效率。在工业级基准测试上的实验结果表明，与基线方法相比，性能提升最高可达10倍，最优性差距缩小至0.1%以内。该工作是首次证明利用可微分优化初始化精确整数线性规划求解器用于组合调度的可行性，为跨更广泛领域整合机器学习基础设施与经典精确优化方法开辟了新机遇。