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ab849c9 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 | """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,
},
]
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