100 lines
3.8 KiB
Python
100 lines
3.8 KiB
Python
import gurobipy as gp
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from gurobipy import GRB, Model, quicksum
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HYPEREDGES = {
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1: ([], ['Xanthine']),
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2: (['Xanthine'], ['p_{0,0}']),
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3: (['Xanthine'], ['p_{0,1}']),
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4: (['Xanthine'], ['p_{0,2}']),
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5: (['p_{0,0}'], ['p_{0,3}']),
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6: (['p_{0,0}'], ['p_{0,4}']),
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7: (['p_{0,1}'], ['p_{0,3}']),
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8: (['p_{0,1}'], ['p_{0,5}']),
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9: (['p_{0,2}'], ['p_{0,4}']),
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10: (['p_{0,2}'], ['p_{0,5}']),
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11: (['p_{0,3}'], ['Caffeine']),
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12: (['p_{0,4}'], ['Caffeine']),
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13: (['p_{0,5}'], ['Caffeine']),
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14: (['Caffeine'], [])
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}
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#Similyrity of Nodes NMR to Measured NMR
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VERTICES = {
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1: ([0, 0], ['Xanthine']),
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2: ([0, 0], ['p_{0,0}']),
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3: ([0, 0], ['p_{0,1}']),
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4: ([1, 0], ['p_{0,2}']),
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5: ([0, 0], ['p_{0,3}']),
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6: ([0, 0], ['p_{0,4}']),
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7: ([0, 1], ['p_{0,5}']),
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8: ([0, 0], ['Caffeine']),
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}
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FIXED_FLOWS = {
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1: 1,
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14: 1,
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}
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def build_model(name, hyperedges, vertices, excluded_support=None):
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model = Model(name)
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x = {e_id: model.addVar(vtype=GRB.INTEGER, lb=0, name=f"x_{e_id}") for e_id in hyperedges}
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b = {e_id: model.addVar(vtype=GRB.BINARY, name=f"b_{e_id}") for e_id in hyperedges}
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vertices = set(v for tails, heads in hyperedges.values() for v in tails + heads)
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for v in vertices:
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inflow = quicksum(x[e_id] for e_id, (_, heads) in hyperedges.items() if v in heads)
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outflow = quicksum(x[e_id] for e_id, (tails, _) in hyperedges.items() if v in tails)
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model.addConstr(inflow == outflow, name=f"flow_conservation_{v}")
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for e_id, value in FIXED_FLOWS.items():
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model.addConstr(x[e_id] == value, name=f"fixed_flow_{e_id}")
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for e_id in hyperedges:
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model.addGenConstrIndicator(b[e_id], 0, x[e_id] == 0, name=f"unused_implies_zero_{e_id}")
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model.addConstr(x[e_id] >= b[e_id], name=f"used_implies_positive_flow_{e_id}")
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if excluded_support:
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model.addConstr(quicksum(b[e_id] for e_id in excluded_support) <= len(excluded_support) - 1, name="different_hyperedges",)
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model.setObjective(quicksum(quicksum(x[v_id]) for v_id in vertices), GRB.MAXIMIZE) #Maximize Similarity of Nodes
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return model, x, b
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def positive_entries(variable_dict, threshold=0.5):
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return {e_id: var.X for e_id, var in variable_dict.items() if var.X > threshold}
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def print_solution(title, flow_solution, binary_solution, hyperedges):
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print(f"\n{title}:")
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for e_id in sorted(flow_solution):
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flow = flow_solution[e_id]
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tails, heads = hyperedges[e_id]
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print(f"Hyperedge {e_id}: Flow = {flow}, Tails = {tails}, Heads = {heads}")
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print("\nBinary Variables:")
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for e_id in sorted(binary_solution):
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print(f"Binary Variable b_{e_id} = {binary_solution[e_id]}")
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print(f"\nTotal flow: {sum(flow_solution.values())}")
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print(f"Number of used hyperedges: {len(binary_solution)}")
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def main():
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model, x, b = build_model("HypergraphFlow", HYPEREDGES, VERTICES)
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model.optimize()
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if model.status != GRB.Status.OPTIMAL:
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print("No optimal solution found for the first model.")
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return
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optimal_solution = positive_entries(x)
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optimal_binary_solution = positive_entries(b)
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print_solution("Optimal Solution", optimal_solution, optimal_binary_solution, HYPEREDGES)
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excluded_support = list(optimal_binary_solution.keys())
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second_model, x2, b2 = build_model("SecondBestHypergraphFlow", HYPEREDGES, excluded_support=excluded_support,)
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second_model.optimize()
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if second_model.status == GRB.Status.OPTIMAL:
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second_solution = positive_entries(x2)
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second_binary_solution = positive_entries(b2)
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print_solution("Second Best Solution", second_solution, second_binary_solution, HYPEREDGES, VERTICES)
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else:
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print("No optimal solution found for the second best model.")
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if __name__ == "__main__":
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main() |