GPU-Accelerated Primal Heuristics for Mixed Integer Programming

TL;DR

The paper tackles the challenge of quickly obtaining high-quality feasible solutions for MILP under time limits by integrating a suite of GPU-accelerated primal heuristics. The core approach fuses a GPU-based approximate LP solver ($PDLP$), a probing cache, bound propagation, advanced rounding, and GPU-enabled local search (Local-MIP) within an Extended Feasibility Pump framework. Key contributions include a scalable bound-propagation kernel with load-balanced CSR layouts, a cache-driven probing mechanism for warm-starts, bulk rounding guided by cache insights, and a parallel, move-based Local-MIP that leverages distance-2 neighborhoods and advanced GPU scheduling. Experimental results on the MIPLIB2017 presolved set show that the GPU framework significantly outperforms CPU baselines in both the number of feasible solutions and objective quality, with Extended FP variants delivering the best performance. Overall, the work demonstrates that comprehensive GPU acceleration of primal heuristics can meaningfully improve practical MILP solving where time budgets limit full optimality, and it provides an open-source cuOpt repository for reproducibility and further development.

Abstract

We introduce a fusion of GPU accelerated primal heuristics for Mixed Integer Programming. Leveraging GPU acceleration enables exploration of larger search regions and faster iterations. A GPU-accelerated PDLP serves as an approximate LP solver, while a new probing cache facilitates rapid roundings and early infeasibility detection. Several state-of-the-art heuristics, including Feasibility Pump, Feasibility Jump, and Fix-and-Propagate, are further accelerated and enhanced. The combined approach of these GPU-driven algorithms yields significant improvements over existing methods, both in the number of feasible solutions and the quality of objectives by achieving 221 feasible solutions and 22% objective gap in the MIPLIB2017 benchmark on a presolved dataset.