Recently, HPR-LP, a GPU linear programming solver jointly developed by Professor Zhao Xinyuan’s team at the School of Mathematics, Statistics and Mechanics of our university and the team led by Professor Sun Defeng at the Research Center for Intelligent Operations Research of The Hong Kong Polytechnic University, achieved a significant breakthrough. In the latest results of the internationally recognized Hans Mittelmann LPfeas public benchmark, HPR-LP ranked first on both the main benchmark comprising 65 instances and the Addendum comprising 13 ultra-large-scale instances. Notably, in the more challenging ultra-large-scale benchmark, HPR-LP was the only solver to successfully solve all 13 instances, outperforming several widely used commercial and open-source solvers, including those developed by NVIDIA and Google.

On the main benchmark comprising 65 instances, HPR-LP successfully solved 63 instances, achieving a scaled overall runtime metric of 1.00, ranking first among the tested solvers and outperforming well-known linear programming solvers including COPT, MOSEK, HiGHS, KNITRO, Google PDLP, and NVIDIA cuOpt. A smaller value of this metric indicates a shorter overall runtime as measured according to the benchmark’s evaluation methodology.

Figure 1 LPfeas: Participating Solvers and Summary Results on the Main Benchmark

Solving ultra-large-scale linear programming problems requires processing massive sparse matrices and large volumes of data generated during the iterative process, placing extremely high demands on GPU memory, data access, and computational efficiency. In this ultra-large-scale instance test, HPR-LP successfully solved all 13 instances under the specified test conditions, making it the only solver in the benchmark to solve all instances. In particular, the qap-tho-150 instance contains approximately 250 million variables, 6.71 million constraints, and more than 1 billion nonzero entries in the constraint matrix. HPR-LP solved this instance in just 463 seconds, demonstrating its outstanding performance in solving ultra-large-scale sparse linear programming problems.

Figure 2 Participating Solvers and Results for Extra-Large-Scale Test Problems

These advances build on the two teams’ long-standing collaboration and continued research efforts in large-scale optimization algorithms and high-performance solvers. To address the computational challenges of ultra-large-scale sparse linear programming, the teams integrated the HPR optimization algorithm with massively parallel GPU computing and jointly optimized key components, including model preprocessing, GPU-based sparse computation, and iterative updates. These efforts effectively improved the computational efficiency and stability of the solver in handling large-scale problems.

Linear programming is a fundamental model in operations research and scientific computing, with wide-ranging applications in production planning, supply chain management, energy systems, transportation scheduling, and other important areas. As real-world decision-making problems continue to grow in scale and complexity, increasingly stringent demands are being placed on the computational efficiency and capability of high-performance linear programming solvers to handle large-scale problems.

The two teams are also actively working to migrate and adapt HPR-LP to domestically developed computing platforms, including adapting it for domestic AI chips such as Huawei Ascend. They are exploring the development of an independently controllable high-performance optimization solver ecosystem with the aim of further expanding the use of domestic computing platforms in large-scale scientific computing and optimization.

Note: Rankings are based on the scaled metric reported in the benchmark, and runtimes are as listed in the benchmark; all solvers were run under the hardware, tolerance, and time limits specified by the benchmark. COPTG in the original figure refers to the GPU version of COPT. The benchmark results were updated on September 16, 2026.

Benchmark: LPfeas Benchmark
Run log: COPT run log for the qap-tho-150 instance
Related paper: HPR-LP: An implementation of an HPR method for solving linear programming