285 lines
12 KiB
Python
285 lines
12 KiB
Python
import math
|
|
import gurobipy as gp
|
|
from gurobipy import GRB, Model, quicksum
|
|
|
|
HYPERGRAPH = {
|
|
0: (['Butadien'], []),
|
|
2: (['p_{0,0}'], []),
|
|
3: (['p_{0,1}'], []),
|
|
4: (['Butadien', 'Butadien'], ['p_{0,0}', 'p_{0,1}']),
|
|
6: (['p_{0,2}'], []),
|
|
7: (['Butadien', 'Butadien'], ['p_{0,2}']),
|
|
10: (['p_{0,0}', 'p_{0,1}'], ['Butadien', 'Butadien']),
|
|
12: (['p_{0,3}'], []),
|
|
13: (['p_{0,0}', 'p_{0,2}'], ['p_{0,3}']),
|
|
17: (['p_{0,4}'], []),
|
|
18: (['p_{0,1}', 'p_{0,1}'], ['Butadien', 'p_{0,4}']),
|
|
19: (['p_{0,5}'], []),
|
|
20: (['p_{0,1}', 'p_{0,2}'], ['Butadien', 'p_{0,5}']),
|
|
23: (['Butadien', 'p_{0,1}'], ['p_{0,0}', 'p_{0,4}']),
|
|
26: (['Butadien', 'p_{0,2}'], ['p_{0,0}', 'p_{0,5}']),
|
|
27: (['p_{0,6}'], []),
|
|
28: (['p_{0,0}', 'p_{0,1}'], ['p_{0,6}']),
|
|
29: (['p_{0,7}'], []),
|
|
30: (['Butadien', 'p_{0,0}'], ['p_{0,7}']),
|
|
31: (['p_{0,8}'], []),
|
|
32: (['Butadien', 'p_{0,1}'], ['p_{0,8}']),
|
|
33: (['Butadien', 'p_{0,1}'], ['p_{0,5}']),
|
|
34: (['p_{0,9}'], []),
|
|
35: (['Butadien', 'p_{0,1}'], ['p_{0,9}']),
|
|
36: (['p_{0,10}'], []),
|
|
37: (['Butadien', 'p_{0,1}'], ['p_{0,10}']),
|
|
38: (['p_{0,3}'], ['p_{0,0}', 'p_{0,2}']),
|
|
41: (['p_{0,11}'], []),
|
|
42: (['p_{0,4}'], ['p_{0,0}', 'p_{0,11}']),
|
|
43: (['p_{0,12}'], []),
|
|
44: (['p_{0,5}'], ['p_{0,12}']),
|
|
63: (['p_{0,13}'], []),
|
|
64: (['p_{0,4}', 'p_{0,6}'], ['p_{0,1}', 'p_{0,13}']),
|
|
65: (['p_{0,2}', 'p_{0,4}'], ['p_{0,1}', 'p_{0,5}']),
|
|
66: (['p_{0,0}', 'p_{0,4}'], ['Butadien', 'p_{0,1}']),
|
|
67: (['Butadien', 'p_{0,4}'], ['p_{0,1}', 'p_{0,1}']),
|
|
77: (['p_{0,5}', 'p_{0,6}'], ['p_{0,2}', 'p_{0,13}']),
|
|
79: (['p_{0,0}', 'p_{0,5}'], ['Butadien', 'p_{0,2}']),
|
|
80: (['Butadien', 'p_{0,5}'], ['p_{0,1}', 'p_{0,2}']),
|
|
83: (['p_{0,1}', 'p_{0,5}'], ['p_{0,2}', 'p_{0,4}']),
|
|
96: (['Butadien', 'p_{0,6}'], ['p_{0,0}', 'p_{0,13}']),
|
|
97: (['p_{0,1}', 'p_{0,6}'], ['Butadien', 'p_{0,13}']),
|
|
99: (['p_{0,14}'], []),
|
|
100: (['p_{0,0}', 'p_{0,6}'], ['p_{0,14}']),
|
|
101: (['p_{0,15}'], []),
|
|
102: (['p_{0,0}', 'p_{0,7}'], ['p_{0,15}']),
|
|
121: (['p_{0,0}', 'p_{0,4}'], ['p_{0,13}']),
|
|
122: (['p_{0,16}'], []),
|
|
123: (['p_{0,0}', 'p_{0,4}'], ['p_{0,16}']),
|
|
124: (['p_{0,17}'], []),
|
|
125: (['Butadien', 'p_{0,7}'], ['p_{0,17}']),
|
|
127: (['p_{0,12}'], ['p_{0,5}']),
|
|
130: (['p_{0,14}'], ['p_{0,0}', 'p_{0,6}']),
|
|
132: (['p_{0,15}'], ['p_{0,0}', 'p_{0,7}']),
|
|
135: (['p_{0,0}', 'p_{0,11}'], ['p_{0,4}']),
|
|
153: (['Butadien', 'p_{0,13}'], ['p_{0,1}', 'p_{0,6}']),
|
|
155: (['p_{0,0}', 'p_{0,13}'], ['Butadien', 'p_{0,6}']),
|
|
157: (['p_{0,1}', 'p_{0,13}'], ['p_{0,4}', 'p_{0,6}']),
|
|
158: (['p_{0,2}', 'p_{0,13}'], ['p_{0,5}', 'p_{0,6}']),
|
|
210: (['p_{0,18}'], []),
|
|
211: (['Butadien', 'p_{0,11}'], ['p_{0,18}']),
|
|
213: ([], ['Butadien']),
|
|
}
|
|
|
|
HYPERGRAPH2 = {
|
|
2: (['p_{0,0}'], []),
|
|
3: (['p_{0,1}'], []),
|
|
4: (['Butadien', 'Butadien'], ['p_{0,0}', 'p_{0,1}']),
|
|
6: (['p_{0,2}'], []),
|
|
7: (['Butadien', 'Butadien'], ['p_{0,2}']),
|
|
17: (['p_{0,4}'], []),
|
|
23: (['Butadien', 'p_{0,1}'], ['p_{0,0}', 'p_{0,4}']),
|
|
41: (['p_{0,11}'], []),
|
|
42: (['p_{0,4}'], ['p_{0,0}', 'p_{0,11}']),
|
|
213: ([], ['Butadien']),
|
|
}
|
|
|
|
HYPERGRAPH3 = {
|
|
0: (['Butadien'], []),
|
|
213: ([], ['Butadien']),
|
|
4: (['Butadien', 'Butadien'], ['p_{0,0}', 'Butadien']),
|
|
2: (['p_{0,0}'], []),
|
|
}
|
|
|
|
VERTICES = ['Butadien', 'p_{0,0}', 'p_{0,1}', 'p_{0,2}', 'p_{0,3}', 'p_{0,4}', 'p_{0,5}', 'p_{0,6}', 'p_{0,7}', 'p_{0,8}', 'p_{0,9}', 'p_{0,10}', 'p_{0,11}', 'p_{0,12}', 'p_{0,13}', 'p_{0,14}', 'p_{0,15}', 'p_{0,16}', 'p_{0,17}', 'p_{0,18}']
|
|
#Vergleich mit dem NMR von Ethylen und Hexatrien
|
|
NMR1 = [0.32, 0.5, 0.87, 0.0, 0.11, 0.58, 0.06, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.09, 0.0, 0.0, 0.17, 0.0, 0.09]
|
|
#Normalisiert
|
|
NMR1 = [0.11, 0.18, 0.31, 0.0, 0.04, 0.21, 0.02, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03, 0.0, 0.0, 0.06, 0.0, 0.03]
|
|
#Vergleich mit dem NMR von Ethylen und Octrien
|
|
NMR2 = [0.33, 0.43, 0.6, 0.0, 0.13, 0.9, 0.07, 0.01, 0.0, 0.0, 0.01, 0.0, 0.0, 0.01, 0.1, 0.0, 0.0, 0.22, 0.0, 0.13]
|
|
#Normalisiert
|
|
NMR2 = [0.11, 0.15, 0.21, 0.0, 0.04, 0.31, 0.02, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03, 0.0, 0.0, 0.07, 0.0, 0.04]
|
|
#Vergleich mit dem NMR von Ethylen und Benzol
|
|
NMR3 = [0.0, 0.32, 0.0, 0.0, 0.0, 0.0, 0.05, 0.0, 0.0, 0.02, 0.0, 0.29, 0.95, 0.17, 0.0, 0.0, 0.0, 0.0, 0.0, 0.05]
|
|
#Normalisiert
|
|
NMR3 = [0.0, 0.17, 0.0, 0.0, 0.0, 0.0, 0.03, 0.0, 0.0, 0.01, 0.0, 0.16, 0.51, 0.09, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03]
|
|
VERTICESSMILES = ['C=CC=C', 'C=C', 'C=CC=CC=C', 'C1CCC(C=C)CC=1', 'C(CCC(C=C)CC=C)=C', 'C=CC=CC=CC=C', 'C1CCC(C=CC=C)CC=1', 'C=CC1C=CCCC1', 'C1CCCCC=1', 'C=CC1CC=CCC1C=C', 'C1CCC(C=C)C(C=C)C=1', 'C(C1CC(C=C)C=CC1)=C', 'C1C=CC=CC=1', 'C(CCC1C=CC=CC1)=C', 'C1C(C=CC=C)CCCC=1', 'C=CC(C=C)CCCC=C', 'C=CCCCCC=C', 'C=CC1C=CC(C=C)CC1', 'C1CC2CCCCC2CC=1', 'C1CC2C=CC=CC2CC=1']
|
|
NMRMAX = [max(n1,n2,n3) for n1,n2,n3 in zip(NMR1,NMR2,NMR3)]
|
|
|
|
#Kombiniert Molekül it Wahrscheinlichkeit für NMR1:
|
|
VERTICE1 = {}
|
|
for vertice, likelihood in zip(VERTICES, NMR1):
|
|
VERTICE1[vertice] = likelihood
|
|
#Kombiniert Molekül it Wahrscheinlichkeit für NMR2:
|
|
VERTICE2 = {}
|
|
for vertice, likelihood in zip(VERTICES, NMR2):
|
|
VERTICE2[vertice] = likelihood
|
|
#Kombiniert Molekül it Wahrscheinlichkeit für NMR3:
|
|
VERTICE3 = {}
|
|
for vertice, likelihood in zip(VERTICES, NMR3):
|
|
VERTICE3[vertice] = likelihood
|
|
|
|
#Kantenwahrscheinlichkeiten für NMR1:
|
|
EDGE1 = {}
|
|
#Kantenwahrscheinlichkeiten für NMR2:
|
|
EDGE2 = {}
|
|
#Kantenwahrscheinlichkeiten für NMR3:
|
|
EDGE3 = {}
|
|
#Maximum der verschiedenen Kantenwahrscheinlichkeiten:
|
|
EDGEMAX = {}
|
|
|
|
modes = ["Product", "Average"]
|
|
mode = modes[0]
|
|
#Ordnet die Kantenwahrscheinlichkeit basierend auf dem Mittel oder Produkt der Wahrscheinlichkeiten der Produkte
|
|
for edge, (heads, tails) in HYPERGRAPH.items():
|
|
if heads != [] and tails != [] and mode == "Product":
|
|
#Produkt klappt nur, wenn normalisierte Likelihoods
|
|
EDGE1[edge] = math.prod(VERTICE1[head] for head in heads)
|
|
EDGE2[edge] = math.prod(VERTICE2[head] for head in heads)
|
|
EDGE2[edge] = math.prod(VERTICE2[head] for head in heads)
|
|
if heads != [] and tails != [] and mode == "Average":
|
|
EDGE1[edge] = quicksum(VERTICE1[head] for head in heads)/len(heads)
|
|
EDGE2[edge] = quicksum(VERTICE2[head] for head in heads)/len(heads)
|
|
EDGE3[edge] = quicksum(VERTICE3[head] for head in heads)/len(heads)
|
|
else:
|
|
EDGE1[edge] = 0.0
|
|
EDGE2[edge] = 0.0
|
|
EDGE3[edge] = 0.0
|
|
EDGEMAX[edge] = max([EDGE1[edge], EDGE2[edge], EDGE2[edge]])
|
|
|
|
|
|
FIXED_FLOWS = {
|
|
#213: 3,
|
|
#2: 3,
|
|
#4: 1,
|
|
#23: 1,
|
|
#41: 1,
|
|
#42: 1,
|
|
}
|
|
|
|
def build_model(name, hyperedges, edgelikelihoodsmax, edgelikelihoods1, edgelikelihoods2, edgelikelihoods3, excluded_support=None):
|
|
model = Model(name)
|
|
|
|
x = {e_id: model.addVar(vtype=GRB.INTEGER, lb = 0, name = f"x_{e_id}") for e_id in hyperedges}
|
|
b = {e_id: model.addVar(vtype=GRB.BINARY, name = f"b_{e_id}") for e_id in hyperedges}
|
|
enmax = model.addVars(hyperedges, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "edgenmrmax")
|
|
en1 = model.addVars(hyperedges, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "edgenmr1")
|
|
en2 = model.addVars(hyperedges, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "edgenmr2")
|
|
en3 = model.addVars(hyperedges, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "edgenmr3")
|
|
|
|
|
|
for edge, elmax, el1, el2, el3 in zip(hyperedges, edgelikelihoodsmax, edgelikelihoods1, edgelikelihoods2, edgelikelihoods3):
|
|
enmax[edge] = elmax
|
|
en1[edge] = el1
|
|
en2[edge] = el2
|
|
en3[edge] = el3
|
|
|
|
|
|
vertices = set(v for tails, heads in hyperedges.values() for v in tails + heads)
|
|
|
|
#Every item created has to be consumed:
|
|
'''
|
|
for v in vertices:
|
|
count[v] = 0
|
|
count = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, name = "count")
|
|
for mol in vertices:
|
|
for edge, (heads, tails) in hyperedges.items():
|
|
count[mol] += x[edge] * (heads.count(mol) - tails.count(mol))
|
|
model.addConstr(count[mol] == 0)
|
|
'''
|
|
|
|
for v in vertices:
|
|
inflow = quicksum(x[e_id] * heads.count(v) for e_id, (_, heads) in hyperedges.items())
|
|
outflow = quicksum(x[e_id] * tails.count(v) for e_id, (tails, _) in hyperedges.items())
|
|
model.addConstr(inflow == outflow, name = f"flow_conservation_{v}")
|
|
|
|
for e_id, value in FIXED_FLOWS.items():
|
|
model.addConstr(x[e_id] == value, name = f"fixed_flow_{e_id}")
|
|
|
|
for e_id in hyperedges:
|
|
model.addGenConstrIndicator(b[e_id], 0, x[e_id] == 0, name = f"unused_implies_zero_{e_id}")
|
|
model.addConstr(x[e_id] >= b[e_id], name = f"used_implies_positive_flow_{e_id}")
|
|
|
|
reaction_path = {}
|
|
|
|
|
|
if excluded_support:
|
|
model.addConstr(quicksum(b[e_id] for e_id in excluded_support) <= len(excluded_support) - 1, name = "different_hyperedges",)
|
|
|
|
#Multiplizier den node Wert mit infow + outflow
|
|
model.ModelSense = GRB.MAXIMIZE
|
|
|
|
#Multiply edgelikelihood with the edge use boolean
|
|
#Adapt to have
|
|
model.setObjectiveN(
|
|
quicksum(enmax[e_id] * b[e_id] for e_id, (_, _) in hyperedges.items()),
|
|
index = 0,
|
|
priority = 2,
|
|
name = "maximize_nmr_similarity",
|
|
)
|
|
#Minimize the overall flow
|
|
model.setObjectiveN(
|
|
quicksum(-1 * x[e_id] for e_id in hyperedges),
|
|
index=1,
|
|
priority= 1,
|
|
name="minimize_used_hyperedges",
|
|
)
|
|
|
|
#Excluding creation and destruction only three reactions for three nmr
|
|
model.addConstr(quicksum(b[e_id] for e_id, (heads, tails) in hyperedges.items() if tails != [] and heads != []) == 3)
|
|
#Restrict number of used edges to prevent using all available
|
|
#model.addConstr(quicksum(x[e_id] for e_id in hyperedges) <= 16)
|
|
|
|
#2 Butadien create first different molecule and it has to be created first:
|
|
model.addConstr(b[4] + b[7] == 1)
|
|
model.addConstr(b[213] == 1)
|
|
model.addConstr(b[41] == 1)
|
|
|
|
|
|
|
|
#No cyclic reaction pairs:
|
|
for e_id1, (heads1, tails1) in hyperedges.items():
|
|
for e_id2, (heads2, tails2) in hyperedges.items():
|
|
if (heads1, tails1) == (tails2, heads2):
|
|
#print(e_id1, e_id2)
|
|
model.addConstr((b[e_id1] + b[e_id2]) <= 1)
|
|
|
|
return model, x, b
|
|
|
|
|
|
def positive_entries(variable_dict, threshold = 0.5):
|
|
return {e_id: var.X for e_id, var in variable_dict.items() if var.X > threshold}
|
|
|
|
def print_solution(title, flow_solution, binary_solution, hyperedges):
|
|
print(f"\n{title}:")
|
|
for e_id in sorted(flow_solution):
|
|
flow = flow_solution[e_id]
|
|
tails, heads = hyperedges[e_id]
|
|
print(f"Hyperedge {e_id}: Flow = {flow}, Tails = {tails}, Heads = {heads}")
|
|
print("\nBinary Variables:")
|
|
for e_id in sorted(binary_solution):
|
|
print(f"Binary Variable b_{e_id} = {binary_solution[e_id]}")
|
|
|
|
print(f"\nTotal flow: {sum(flow_solution.values())}")
|
|
print(f"Number of used hyperedges: {len(binary_solution)}")
|
|
|
|
def main():
|
|
model, x, b = build_model("HypergraphFlow", HYPERGRAPH, EDGEMAX, EDGE1, EDGE2, EDGE3)
|
|
model.optimize()
|
|
if model.status != GRB.Status.OPTIMAL:
|
|
print("No optimal solution found for the first model.")
|
|
return
|
|
optimal_solution = positive_entries(x)
|
|
optimal_binary_solution = positive_entries(b)
|
|
print_solution("Optimal Solution", optimal_solution, optimal_binary_solution, HYPERGRAPH)
|
|
|
|
excluded_support = list(optimal_binary_solution.keys())
|
|
second_model, x2, b2 = build_model("SecondBestHypergraphFlow", HYPERGRAPH, EDGEMAX, EDGE1, EDGE2, EDGE3, excluded_support=excluded_support,)
|
|
|
|
second_model.optimize()
|
|
if second_model.status == GRB.Status.OPTIMAL:
|
|
second_solution = positive_entries(x2)
|
|
second_binary_solution = positive_entries(b2)
|
|
print_solution("Second Best Solution", second_solution, second_binary_solution, HYPERGRAPH)
|
|
else:
|
|
print("No optimal solution found for the second best model.")
|
|
|
|
if __name__ == "__main__":
|
|
main() |