A new arXiv preprint reports lower final search gaps with EnCore in tests of mixed-integer linear programming (MILP), a form of constrained optimization with integer decisions. EnCore adds a feasible early solution to a graph-based predictor; in Gurobi comparisons, its versions had lower final gaps in 11 of 12 settings. Average gap reductions were 38.7% for Neural Diving, 56.9% for Predict-and-Search and 36.2% for Apollo-MILP.
The reported gap measures the distance to the study’s in-study best-known solution. That reference is not an independently certified optimum; the comparisons also included a 3,600-second Gurobi reference run.
Using a solver’s early clues
EnCore first monitors feasible-solution improvements and the rate at which the local dual gap decays. It stops collecting information when that decay rate falls below a threshold, while respecting minimum and maximum probing times.
The system then adds early assignments to the MILP graph and predicts whether each early integer assignment will agree with the full-budget reference solution. At inference, it can align and average consistency scores from the last few improving solutions before sending the combined scores downstream.
The benchmark evaluation reported 240 training instances, 60 validation instances and 100 testing instances. Main runs used 1,000 seconds end to end, including early-solution collection, inference and downstream solving.
Reported gains across tests
On Workload Apportionment, an early incumbent—the solver’s current feasible answer—agreed with the final solution on 95.63% of binary variables. In a cumulative Predict-and-Search ablation on Combinatorial Auctions, the reported average objective was 97,906.20 for the baseline, 98,318.22 after adding early-solution features, 98,616.65 after changing the target to consistency and 98,627.99 after adding an early-solution ensemble.
On Combinatorial Auctions, EnCore-Predict-and-Search was the best of the compared methods. It reported a 0.00 gap to the in-study best-known solution and an improvement of 179.15 objective units over the 3,600-second Gurobi incumbent within the 1,000-second end-to-end budget.
The pattern was not universal: the sole reported exception was Apollo-MILP on Set Covering, where the gap increased from 0.19 to 0.20.
A test beyond the training solver
The Gurobi-trained checkpoint was run on SCIP without retraining. For EnCore-Neural Diving, the reported absolute-gap reductions were 53.6% on Combinatorial Auctions, 22.0% on Set Covering, 33.1% on Workload Apportionment and 50.7% on Item Placement.
A separate zero-shot evaluation used 11 MIPLIB IIS instances. Original Neural Diving found feasible solutions on 3 of 11, while EnCore-Neural Diving found feasible solutions on all 11.
The reported mean objectives were lower with EnCore in all three comparisons: 173.45 versus 243.00 for Neural Diving, 171.73 versus 172.00 for Predict-and-Search and 172.82 versus 172.91 for Apollo-MILP. The original Neural Diving mean was calculated only from its 3 feasible instances.
What the results do not establish
The paper’s theory says that conditioning variable-level predictions on an early solution cannot reduce the best population accuracy, and can be strictly better under a stated posterior-crossing condition. A second theorem gives a high-probability accuracy bound for selecting among a finite set of rules under sparse-correction assumptions.
These are computational benchmark evaluations, not randomized trials in real operational deployments. The study’s best-known reference is an in-study benchmark rather than an independently certified optimum, and the paper reports no confidence intervals, conventional power calculation or statistical-significance testing.
The finite-sample theorem is narrower than the deployed system: it applies to finite-rule selection under sparse-correction assumptions, not the full stochastic graph-neural-network function class. Its theoretical accuracy comparison also concerns variable-level 0–1 prediction at a fixed local receptive field, while deployment ranks scores and fixes a downstream-selected subset of variables.
The authors interpret the results as support for a solver-informed approach that refines feasible early solutions and may transfer across solvers and problem families. Further tests would need to examine larger or more heterogeneous distributions and the method’s sensitivity to the collection threshold, probing budget, ensemble size and downstream fixing policy.
A preprint, with code available
The work is an arXiv preprint dated 20 August 2026. Its front matter states that code is available through the EnCore GitHub repository.
Paper data and sources
Original title: Learning Early-to-Final Solution Consistency for MILP Acceleration
Authors: Guanlin Li, Chengrui Gao, Chenguang Wang et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text