Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Differentiable Initialization-Accelerated CPU-GPU Hybrid Combinatorial Scheduling

Mingju Liu, Jiaqi Yin, Alvaro Velasquez, Cunxi Yu

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.

Differentiable Initialization-Accelerated CPU-GPU Hybrid Combinatorial Scheduling

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 performance gain over baselines, narrowing the optimality gap to . 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.

Paper Structure

This paper contains 23 sections, 8 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Scheduling and Problem statement
  4. SDC and Related Methods
  5. Approach
  6. Warm-start With a Partial Solution Set
  7. Confidence-Based Differentiable Partial Solution Generation
  8. Differentiable SDC formulation
  9. Search Space Vectorization
  10. Differentiable Constraint Encoding
  11. Differentiable Optimization
  12. Constrained Probability Formulation
  13. Differentiable Cost Objectives
  14. Gradient-guided Differentiable Warm-start
  15. Two-Stage Hybrid CPU-GPU Optimization Workflow
  16. ...and 8 more sections

Figures (5)

  • Figure 1: Example of SDC-based scheduling. (Left) A DFG with three scheduling stages, having a latency of $L=3$. (Right) The corresponding dependency constraints and objective functions include minimizing peak resource and inter-stage communication costs.
  • Figure 2: Comparison of warm-start strategies: full solution vs. partial solution. Normalized objective values are obtained at a 900s solving time. Error bars represent the range of objective values obtained when warm-starting different solvers with varying partial solutions.
  • Figure 3: Confidence analysis: Left: Aggregated confidence distributions with the top 30% region shaded. Right: Average confidence for the top 30% assignments across 30 iterations. Rows correspond to RW, EPFL, and mapped EPFL designs.
  • Figure 4: Performance comparison across 24 benchmark instances, sorted by ILP constraint count (small to large). Cold-start/Warm-start results are collected at 3600s/1800s, respectively. Lower objective value indicates better performance.
  • Figure 5: Solver performance vs. partial solution order.