Magnus HedemarkandGitHub
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* feat(constrained-optimization): add formulation and audit methodology * docs(constrained-optimization): register skill and align trigger metadata * docs(constrained-optimization): route templates and define completion * docs(constrained-optimization): cite solver evidence and applicability
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Formulation and solver evidence
Formulation checklist
Write the problem in a unit-consistent form: decision vector and domains; objective(s) with minimize/maximize direction; hard constraints and tolerances; soft constraints and penalty units; data/configuration revision; and a feasibility predicate that can be run independently. Normalize objectives only when the scale and reference points are documented. A penalty coefficient must have an interpretable relationship to the objective and cannot make an unacceptable hard violation “worth it.”
Use a feasible incumbent whenever possible. If no feasible point is known, run a feasibility phase or report that the search has not established feasibility. A candidate with a better raw objective but any hard violation is not a solution to the stated problem.
Method evidence
Use an exact or certifying baseline when the formulation and scale allow it. Report solver status, incumbent objective, bound, gap definition, time/memory limit, and tolerance. A feasible incumbent with a nonzero gap is evidence of a candidate and a bound, not proof of global optimality. A heuristic or metaheuristic should report initialization, seed/repeat policy, budget, best feasible value, violation summary, and comparison against the same checker and budget.
Solver status is evidence, not prose. For example, SciPy’s optimization results expose success and a termination message, while its linear-programming tutorial demonstrates checking constraint residuals independently. OR-Tools CP-SAT distinguishes OPTIMAL, FEASIBLE, INFEASIBLE, MODEL_INVALID, and UNKNOWN; UNKNOWN includes stopping before infeasibility is proven. Preserve that distinction in any adapter. See the source index for direct official references, versions, and transfer limits.
Fair comparison and validation
Freeze the formulation, data, checker, hardware class, wall-clock or evaluation budget, and stopping rule. Compare methods on the same feasible-best definition. For stochastic methods, use paired seeds or a declared repeat design and report the distribution, not only the best run. Validate returned decisions with an independent implementation that recomputes units, bounds, equality/inequality residuals, and objective. Keep raw solver output and checker output together.
An “infeasible” conclusion requires a certificate or a solver status that actually proves infeasibility. A timeout, memory stop, numerical failure, or unknown status means unresolved. Relax constraints only as a named scenario and rerun the full audit; never silently relax them in post-processing.