What the study found
The study found that low-precision linear programming (LP) solutions can be used in a fix-and-propagate heuristic for mixed-integer programming (MIP) without lowering the quality of the heuristic's solutions. The authors also report that this approach produced high-accuracy solutions for very large planning problems.
Why the authors say this matters
The authors suggest this matters because it shows that low-accuracy LP solutions from first-order methods can still be useful inside a fix-and-propagate framework. They also indicate that the approach can help solve large-scale optimization problems more effectively than the commercial solvers they compared against.
What the researchers tested
The researchers tested a fix-and-propagate (FP) heuristic for mixed-integer programming problems, using GPU-accelerated PDLP, a first-order method for linear programming relaxations, to solve the LP relaxation to low accuracy. They evaluated the heuristic on MIPLIB2017 and on unit commitment-based dispatch and expansion planning problems built with the REMix modeling framework.
What worked and what didn't
On MIPLIB2017, low-accuracy LP solutions did not reduce the quality of the fix-and-propagate heuristic solutions. For the largest REMix problems, the framework produced solutions with a primal-dual gap of under 2% in less than 4 hours, while state-of-the-art commercial solvers could not produce feasible solutions within 2 days. The abstract does not describe any case where the approach failed on the tested problems.
What to keep in mind
The summary only reports results for the tested benchmark set and REMix-generated planning problems, so the abstract does not establish how the approach performs beyond those settings. It also does not provide detailed information about parameter choices, problem instances, or possible limitations of the heuristic beyond the reported comparisons.
Key points
- Low-precision LP solutions were used to guide fix-and-propagate heuristics for mixed-integer programming.
- On MIPLIB2017, low-accuracy LP inputs did not reduce heuristic solution quality.
- The method produced solutions with under 2% primal-dual gap for the largest REMix problems in less than 4 hours.
- State-of-the-art commercial solvers did not produce feasible solutions within 2 days on those largest problems.
- The tested large problems reached up to 243 million nonzeros and 8 million decision variables.
Disclosure
- Research title:
- Low-precision LP solutions supported fix-and-propagate heuristics
- Authors:
- Nils-Christian Kempke, Thorsten Koch
- Institutions:
- Technische Universität Berlin, Technische Universität Berlin, Zuse Institute Berlin, Zuse Institute Berlin
- Publication date:
- 2026-07-06
- OpenAlex record:
- View
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