Add WithMipStart trait and Gurobi MIP start support

[gabriel-gehrke]

This PR adds support for providing a MIP start (partial initial solution) to solvers that can consume one, and wires it into the Gurobi CLI backend by generating a temporary .mst file and passing it to gurobi_cl via InputFile=....

Motivation

Warm-starting MILPs can significantly reduce solve time when a good incumbent or partial assignment is known (e.g., from a previous solve or a heuristic algorithm). This is also requested downstream at the good_lp package (rust-or/good_lp#111).

Changes

• Introduce a new trait WithMipStart<T>
• Implement WithMipStart<GurobiSolver>
  • Writes assignments to a temporary .mst file in Gurobi MIP start format
  • Configures GurobiSolver to pass it through gurobi_cl using InputFile=
• Add tests
  • Verify arguments() contains an InputFile=/tmp/*.mst entry (without relying on an exact filename)

Example Usage

use lp_solvers::solvers::{GurobiSolver, WithMipStart};

let solver = GurobiSolver::new()
    .with_mip_start([("x", 1.0_f32), ("y", 0.0_f32)])
    .expect("valid MIP start");

Notes

• The .mst file is persisted in the system temp directory (similar to how “temporary” solution output paths are handled in the crate right now).
• Follow-up improvements could include
  • cleanup strategy for persisted temp files
  • supporting multiple InputFile= entries, as Gurobi indicates it can do, (e.g., hints .hnt, basis .bas)

[lovasoa]

Happy to merge once ci passes

[gabriel-gehrke]

Ah, I hardcoded /tmp in the test instead of handling it via the environment. I'm on it.

In the meantime, what do you think about switching from a hash map to an iterator based start solution as in good_lp's WithInitialSolution? In the beginning I thought this was overkill (and the hash map way fitting in better with the existing codebase) but now I think especially for large problems the conversion to hash map and back when calling from good_lp is unnecessary.

[lovasoa]

I doubt there are any cases when the performance impact won't be tiny compared to actually solving the problem. But feel free to prove me wrong !

[lovasoa]

Thanks, merged !