Differentiable Initialization-Accelerated CPU-GPU Hybrid Combinatorial Scheduling

2026-03-30

AI Summary

This work addresses the challenge of solving large-scale combinatorial scheduling problems, which are NP-hard and often lead to slow convergence and large optimality gaps when tackled by traditional integer linear programming (ILP) solvers on industrial instances. The paper introduces the first CPU-GPU hybrid framework that leverages differentiable optimization to warm-start state-of-the-art ILP solvers such as CPLEX, Gurobi, and HiGHS. By rapidly generating high-quality partial solutions through differentiable presolving, the approach provides strong initial feasible solutions that significantly enhance early pruning efficiency within branch-and-bound search. This integration of machine learning with exact optimization yields substantial performance gains: on industrial benchmarks, it achieves up to a 10× speedup over existing baselines while reducing the optimality gap to below 0.1%.

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.

Problem

• combinatorial scheduling
• Integer Linear Programming
• NP-hard
• optimization
• scalability

Innovation

• differentiable optimization
• combinatorial scheduling
• integer linear programming
• warm-start initialization
• CPU-GPU hybrid