MIP Solver and Solution Audit

Core principle

A valid optimization submission has one final solution, one set of recomputed metrics, and one truthful solver report. The solver objective, written output, metrics file, and explanation must all refer to the same final solution.

Feasible does not mean optimal. A time-limited MIP solve may return a useful incumbent without proving optimality. Report that distinction clearly.

Solver discovery

For Python optimization tasks, test installed solver packages before concluding that no solver is available. Prefer a callable installed solver over writing a model for an unavailable package or falling back to a heuristic-only method.

PySCIPOpt is a good first check for binary and mixed-integer models:

try:
    from pyscipopt import Model, quicksum
    SCIP_AVAILABLE = True
except Exception as exc:
    SCIP_AVAILABLE = False
    SCIP_IMPORT_ERROR = exc

If PySCIPOpt imports successfully, use it unless the task or environment clearly provides a better solver. Do not skip it because other packages or command-line binaries are unavailable.

If the task requires an integer program or optimization solver, do not submit a pure greedy search, local search, swap heuristic, or advisory script as the main method unless the task explicitly allows that substitution.

Minimal PySCIPOpt pattern

from pyscipopt import Model, quicksum

model = Model("mip_model")
model.setParam("limits/time", 600.0)

# create binary/integer variables
# add hard constraints
# build named objective components
model.setObjective(objective_expr, "minimize")

model.optimize()
status = str(model.getStatus()).lower()

if model.getNSols() == 0:
    raise RuntimeError(f"No feasible solution found; solver status={status}")

sol = model.getBestSol()
incumbent_objective = float(model.getObjVal())

try:
    best_bound = float(model.getDualbound())
except Exception:
    best_bound = None

try:
    mip_gap = float(model.getGap())
except Exception:
    mip_gap = None

Use model.getSolVal(sol, var) or model.getVal(var) to read values. Do not call unsupported variable methods such as .