Differentiable Initialization-Accelerated CPU-GPU Hybrid Combinatorial Scheduling

TL;DR

This paper introduces a hybrid CPU-GPU framework that uses differentiable optimization to initialize ILP solvers, significantly improving scheduling performance and solution quality at scale.

Contribution

It presents the first integration of differentiable presolving with exact ILP solvers for combinatorial scheduling, achieving substantial performance gains.

Findings

Up to 10x performance improvement over baselines.

Reduced optimality gap to less than 0.1%.

Effective warm-starts for commercial ILP solvers.

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. 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.