Solver + primal/dual skill
An LLM uses the dedicated primal and dual skills together with MIP solvers, including Gurobi and COPT, on the same 20 instances. Each skill was given an overall runtime limit of 150 minutes per instance.
Approach
Structure, experiments, and verification
- Find useful structure: identify exploitable patterns, primal heuristics, and dual certificates instead of relying only on generic solver tuning.
- Run targeted experiments: turn structural observations into focused tests with an optimization solver.
- Verify every result: check candidate solutions and bounds against the original model, using independent verification to determine what can be claimed.
Comparison design
Two workflows, 20 instances
Vanilla prompting
An archived LLM + solver workflow on the same 20 minimization instances, run without the dedicated primal/dual skills. It still used computational tools and problem-specific methods; it is not a solver-only control.
Paired results
Primal and dual bounds
This table reports the Solver + primal/dual skill workflow, combining dedicated primal-skill and dual-skill runs. The solver baseline selects the best valid primal and dual bounds across the recorded COPT and Gurobi runs; it is a post-hoc combination, not one solver run.
Instance results
All 20 paired results
Swipe sideways to see every column.