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<p>We investigate the use of low-precision first-order methods (FOMs) within a fix-and-propagate (FP) framework for solving mixed-integer programming problems (MIPs). We employ GPU-accelerated PDLP, a variant of the Primal-Dual Hybrid Gradient (PDHG) method specialized to LPproblems, to solve the LP-relaxation of our MIPsto low accuracy. This solution is used to motivate fixings within our FPframework. We evaluate the performance of our heuristic on MIPLIB2017, demonstrating that low-accuracy LPsolutions do not lead to a loss in the quality of the FPheuristic solutions. Further, we use our FPframework to produce high-accuracy solutions for large-scale (up to 243 million nonzeros and 8 million decision variables) unit commitment-based dispatch and expansion planning problems created with the modeling framework REMix. For the largest problems, we can generate solutions with a primal-dual gap of under 2% in less than 4 hours, whereas state-of-the-art commercial solvers cannot produce feasible solutions within 2 days of runtime.</p>

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Fix-and-propagate heuristics using low-precision first-order LP solutions for large-scale mixed-integer linear optimization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月6日

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  • Nils-Christian Kempke,
  • Thorsten Koch

摘要

We investigate the use of low-precision first-order methods (FOMs) within a fix-and-propagate (FP) framework for solving mixed-integer programming problems (MIPs). We employ GPU-accelerated PDLP, a variant of the Primal-Dual Hybrid Gradient (PDHG) method specialized to LPproblems, to solve the LP-relaxation of our MIPsto low accuracy. This solution is used to motivate fixings within our FPframework. We evaluate the performance of our heuristic on MIPLIB2017, demonstrating that low-accuracy LPsolutions do not lead to a loss in the quality of the FPheuristic solutions. Further, we use our FPframework to produce high-accuracy solutions for large-scale (up to 243 million nonzeros and 8 million decision variables) unit commitment-based dispatch and expansion planning problems created with the modeling framework REMix. For the largest problems, we can generate solutions with a primal-dual gap of under 2% in less than 4 hours, whereas state-of-the-art commercial solvers cannot produce feasible solutions within 2 days of runtime.