CHAP: A Hybrid GPU-CPU Heuristic for MIP

TL;DR

CHAP is a hybrid GPU-CPU heuristic framework for mixed-integer programming that coordinates multiple heuristics to improve solution quality within limited time, outperforming some existing solvers on benchmark instances.

Contribution

The paper introduces a novel GPU-CPU hybrid primal heuristic framework that integrates multiple heuristics via a shared solution pool for enhanced MIP solving.

Findings

CHAP finds solutions to 47 out of 50 benchmark instances within five minutes.

It outperforms Gurobi in default mode on the benchmark.

It surpasses NVIDIA cuOpt in heuristics-only mode on the benchmark.

Abstract

We present CHAP (Coordinating Heuristics Across Platforms) a GPU-CPU-hybrid primal heuristic framework for mixed-integer programming. CHAP adopts a portfolio approach where it coordinates a set of primal heuristics, including Local Search, Fix-and-Propagate, and Feasibility Pump, via a shared solution pool. The solution pool is used to exchange feasible incumbent solutions, LP solutions, along with promising infeasible solution candidates, enabling a more comprehensive exploration of the solution space. On the GPU side, we implement a native tabu search featuring a novel best-shift algorithm built on sort, scan, and reduce primitives, along with specialized kernel designs. We additionally leverage cuPDLPx as an approximate LP solver. On the CPU side, we employ various Fix-and-Propagate strategies, guided by information from the solution pool, complemented by a CPU-based tabu search and a Feasibility Pump. All components operate collaboratively, iteratively repairing and improving candidate solutions maintained in the pool. We evaluate our framework on the 50-instances benchmark from the 2026 Land-Doig MIP Competition under competition constraints, including a five-minute time limit. In these settings, CHAP finds solutions to 47 instances outperforming both Gurobi (44) in default mode and NVIDIA cuOpt (43) in heuristics-only mode. The results demonstrate that coordinated cross-platform portfolios offer a promising direction for the integration of GPU heuristics into modern high-performance MIP solvers. The code will be made available on GitHub.