Fix-and-propagate heuristics using low-precision first-order LP solutions for large-scale mixed-integer linear optimization
- 1Technical University Berlin, Chair of Software and Algorithms for Discrete Optimization, Straße des 17. Juni 136, 10623, Berlin, Germany
- 2Zuse Institute Berlin, Applied Algorithmic Intelligence Methods, Takustraße 7, 14195, Berlin, Germany
Abstract
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.
Related
- On the nonnegative integer solutions to the equation Fn2+Fm=2a
- Existence of positive Solutions to Hénon equation on integer Lattice graph and Half-Space
- A short proof of a range-relative FPTAS for polynomial integer optimization over bounded polyhedra
- Computing Approximate Solutions of Inconsistent Max-Min Fuzzy Relational Equations by Mixed-Integer Programming
- A Frank-Wolfe-based primal heuristic for quadratic mixed-integer optimization
BibTeX
@article{kempke2026fixandpropagate,
title = {{Fix-and-propagate heuristics using low-precision first-order LP solutions for large-scale mixed-integer linear optimization}},
author = {Nils-Christian Kempke and Thorsten Koch},
journal = {Mathematical Programming Computation},
year = {2026},
month = jul,
doi = {10.1007/s12532-026-00312-7},
url = {https://doi.org/10.1007/s12532-026-00312-7},
note = {CC BY},
}
RIS
TY - JOUR
TI - Fix-and-propagate heuristics using low-precision first-order LP solutions for large-scale mixed-integer linear optimization
AU - Nils-Christian Kempke
AU - Thorsten Koch
PY - 2026
DA - 2026/07/06
JO - Mathematical Programming Computation
DO - 10.1007/s12532-026-00312-7
UR - https://doi.org/10.1007/s12532-026-00312-7
AB - 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.
SN - 1867-2949
SN - 1867-2957
ER -