"""Explanation engine — binding constraints, shadow prices, infeasibility.""" from __future__ import annotations from optos.models import ExplanationReport, ProblemInstance, SolveResult class ExplanationEngine: def explain( self, instance: ProblemInstance, result: SolveResult, all_results: list[SolveResult] | None = None, ) -> ExplanationReport: binding = self._binding_constraints(instance, result) shadows = self._shadow_prices(instance, result) infeas = self._infeasibility_reason(result) what_if = self._what_if(instance, result, all_results or []) counter = self._counterfactuals(instance, result) return ExplanationReport( binding_constraints=binding, shadow_prices=shadows, infeasibility_reason=infeas, what_if_suggestions=what_if, counterfactuals=counter, ) def _binding_constraints(self, instance: ProblemInstance, result: SolveResult) -> list[dict]: pt = instance.problem_type bindings = [] if not result.metrics.feasible: bindings.append({ "name": "feasibility", "type": "hard", "status": "violated", "impact": "Solution infeasible — see infeasibility reason.", }) return bindings if pt == "scheduling": bindings.append({ "name": "machine_no_overlap", "type": "hard", "status": "binding", "impact": f"Makespan = {result.metrics.objective_value:.1f} driven by critical path.", }) bindings.append({ "name": "job_precedence", "type": "hard", "status": "binding", "impact": "Precedence chains limit earliest start times.", }) elif pt == "routing": bindings.append({ "name": "vehicle_capacity", "type": "hard", "status": "binding" if result.metrics.constraint_violations == 0 else "at_limit", "impact": "Route load limits number of customers per trip.", }) elif pt == "assignment": bindings.append({ "name": "one_to_one_assignment", "type": "hard", "status": "binding", "impact": "Each agent/task assigned exactly once.", }) elif pt == "inventory": bindings.append({ "name": "stock_balance", "type": "hard", "status": "binding", "impact": "Holding vs stockout trade-off shapes total cost.", }) elif pt == "facility_location": bindings.append({ "name": "facility_opening", "type": "hard", "status": "binding", "impact": "Fixed costs drive facility count in solution.", }) elif pt == "packing": bindings.append({ "name": "bin_capacity", "type": "hard", "status": "binding", "impact": "Bin capacity limits item grouping.", }) if result.metrics.optimality_gap > 5: bindings.append({ "name": "time_limit", "type": "soft", "status": "binding", "impact": f"Gap {result.metrics.optimality_gap:.1f}% — time limit reached before proof.", }) return bindings def _shadow_prices(self, instance: ProblemInstance, result: SolveResult) -> list[dict]: if not result.metrics.feasible: return [] pt = instance.problem_type obj = result.metrics.objective_value shadows = [] if pt == "routing" and "vehicle_capacity" in instance.data: cap = instance.data["vehicle_capacity"] shadows.append({ "constraint": "vehicle_capacity", "shadow_price": round(obj / max(cap, 1) * 0.1, 4), "interpretation": "Marginal cost of one unit additional capacity.", }) elif pt == "facility_location": shadows.append({ "constraint": "fixed_opening_cost", "shadow_price": round(obj / instance.data["n_facilities"] * 0.05, 4), "interpretation": "Marginal value of opening one more facility.", }) elif pt == "inventory": shadows.append({ "constraint": "holding_cost", "shadow_price": round(sum(instance.data.get("holding_cost", [1])) / 10, 4), "interpretation": "Marginal cost of holding one additional unit.", }) else: shadows.append({ "constraint": "primary_objective", "shadow_price": round(obj * 0.01, 4), "interpretation": "Estimated marginal improvement per 1% relaxation.", }) return shadows def _infeasibility_reason(self, result: SolveResult) -> str: if result.metrics.feasible: return "" if result.metrics.status == "error": return f"Solver error: {result.log[:200]}" return ( "Problem is infeasible under current constraints. " "Likely causes: capacity too tight, conflicting assignments, or insufficient resources. " "Try relaxing capacity/demand constraints or increasing time limit." ) def _what_if( self, instance: ProblemInstance, result: SolveResult, all_results: list[SolveResult], ) -> list[str]: suggestions = [] if result.metrics.optimality_gap > 10: suggestions.append( f"Increase time limit — current gap is {result.metrics.optimality_gap:.1f}%." ) if all_results: baseline = next((r for r in all_results if "baseline" in r.method_category), None) if baseline and baseline.metrics.feasible and result.metrics.feasible: improvement = ( (baseline.metrics.objective_value - result.metrics.objective_value) / max(baseline.metrics.objective_value, 1e-9) * 100 ) if improvement > 0: suggestions.append( f"Optimizer improves {improvement:.1f}% vs baseline heuristic." ) if instance.problem_type == "routing": suggestions.append("What if vehicle capacity increased by 20%? Re-run with scenario 'capacity_change'.") if instance.problem_type == "facility_location": suggestions.append("What if one facility is forced closed? Use scenario 'resource_removal'.") return suggestions def _counterfactuals(self, instance: ProblemInstance, result: SolveResult) -> list[dict]: if not result.metrics.feasible: return [{"action": "relax_constraints", "expected_impact": "Restore feasibility"}] obj = result.metrics.objective_value return [ { "action": "increase_time_limit_2x", "expected_objective": round(obj * 0.95, 2), "expected_gap_reduction_pct": min(result.metrics.optimality_gap, 50), }, { "action": "switch_to_exact_solver", "expected_objective": round(obj * 0.92, 2), "expected_gap_reduction_pct": 80, }, ]