260 lines
11 KiB
Python
260 lines
11 KiB
Python
import math
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import gurobipy as gp
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from gurobipy import GRB, Model, quicksum
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HYPERGRAPH = {
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0: (['Butadien'], []),
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2: (['p_{0,0}'], []),
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3: (['p_{0,1}'], []),
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4: (['Butadien', 'Butadien'], ['p_{0,0}', 'p_{0,1}']),
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6: (['p_{0,2}'], []),
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7: (['Butadien', 'Butadien'], ['p_{0,2}']),
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10: (['p_{0,0}', 'p_{0,1}'], ['Butadien', 'Butadien']),
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12: (['p_{0,3}'], []),
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13: (['p_{0,0}', 'p_{0,2}'], ['p_{0,3}']),
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17: (['p_{0,4}'], []),
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18: (['p_{0,1}', 'p_{0,1}'], ['Butadien', 'p_{0,4}']),
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19: (['p_{0,5}'], []),
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20: (['p_{0,1}', 'p_{0,2}'], ['Butadien', 'p_{0,5}']),
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23: (['Butadien', 'p_{0,1}'], ['p_{0,0}', 'p_{0,4}']),
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26: (['Butadien', 'p_{0,2}'], ['p_{0,0}', 'p_{0,5}']),
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27: (['p_{0,6}'], []),
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28: (['p_{0,0}', 'p_{0,1}'], ['p_{0,6}']),
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29: (['p_{0,7}'], []),
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30: (['Butadien', 'p_{0,0}'], ['p_{0,7}']),
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31: (['p_{0,8}'], []),
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32: (['Butadien', 'p_{0,1}'], ['p_{0,8}']),
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33: (['Butadien', 'p_{0,1}'], ['p_{0,5}']),
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34: (['p_{0,9}'], []),
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35: (['Butadien', 'p_{0,1}'], ['p_{0,9}']),
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36: (['p_{0,10}'], []),
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37: (['Butadien', 'p_{0,1}'], ['p_{0,10}']),
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38: (['p_{0,3}'], ['p_{0,0}', 'p_{0,2}']),
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41: (['p_{0,11}'], []),
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42: (['p_{0,4}'], ['p_{0,0}', 'p_{0,11}']),
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43: (['p_{0,12}'], []),
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44: (['p_{0,5}'], ['p_{0,12}']),
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63: (['p_{0,13}'], []),
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64: (['p_{0,4}', 'p_{0,6}'], ['p_{0,1}', 'p_{0,13}']),
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65: (['p_{0,2}', 'p_{0,4}'], ['p_{0,1}', 'p_{0,5}']),
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66: (['p_{0,0}', 'p_{0,4}'], ['Butadien', 'p_{0,1}']),
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67: (['Butadien', 'p_{0,4}'], ['p_{0,1}', 'p_{0,1}']),
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77: (['p_{0,5}', 'p_{0,6}'], ['p_{0,2}', 'p_{0,13}']),
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79: (['p_{0,0}', 'p_{0,5}'], ['Butadien', 'p_{0,2}']),
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80: (['Butadien', 'p_{0,5}'], ['p_{0,1}', 'p_{0,2}']),
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83: (['p_{0,1}', 'p_{0,5}'], ['p_{0,2}', 'p_{0,4}']),
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96: (['Butadien', 'p_{0,6}'], ['p_{0,0}', 'p_{0,13}']),
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97: (['p_{0,1}', 'p_{0,6}'], ['Butadien', 'p_{0,13}']),
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99: (['p_{0,14}'], []),
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100: (['p_{0,0}', 'p_{0,6}'], ['p_{0,14}']),
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101: (['p_{0,15}'], []),
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102: (['p_{0,0}', 'p_{0,7}'], ['p_{0,15}']),
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121: (['p_{0,0}', 'p_{0,4}'], ['p_{0,13}']),
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122: (['p_{0,16}'], []),
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123: (['p_{0,0}', 'p_{0,4}'], ['p_{0,16}']),
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124: (['p_{0,17}'], []),
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125: (['Butadien', 'p_{0,7}'], ['p_{0,17}']),
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127: (['p_{0,12}'], ['p_{0,5}']),
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130: (['p_{0,14}'], ['p_{0,0}', 'p_{0,6}']),
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132: (['p_{0,15}'], ['p_{0,0}', 'p_{0,7}']),
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135: (['p_{0,0}', 'p_{0,11}'], ['p_{0,4}']),
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153: (['Butadien', 'p_{0,13}'], ['p_{0,1}', 'p_{0,6}']),
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155: (['p_{0,0}', 'p_{0,13}'], ['Butadien', 'p_{0,6}']),
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157: (['p_{0,1}', 'p_{0,13}'], ['p_{0,4}', 'p_{0,6}']),
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158: (['p_{0,2}', 'p_{0,13}'], ['p_{0,5}', 'p_{0,6}']),
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210: (['p_{0,18}'], []),
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211: (['Butadien', 'p_{0,11}'], ['p_{0,18}']),
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213: ([], ['Butadien']),
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}
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HYPERGRAPH2 = {
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2: (['p_{0,0}'], []),
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3: (['p_{0,1}'], []),
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4: (['Butadien', 'Butadien'], ['p_{0,0}', 'p_{0,1}']),
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6: (['p_{0,2}'], []),
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7: (['Butadien', 'Butadien'], ['p_{0,2}']),
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17: (['p_{0,4}'], []),
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23: (['Butadien', 'p_{0,1}'], ['p_{0,0}', 'p_{0,4}']),
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41: (['p_{0,11}'], []),
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42: (['p_{0,4}'], ['p_{0,0}', 'p_{0,11}']),
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213: ([], ['Butadien']),
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}
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HYPERGRAPH3 = {
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0: (['Butadien'], []),
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213: ([], ['Butadien']),
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4: (['Butadien', 'Butadien'], ['p_{0,0}', 'Butadien']),
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2: (['p_{0,0}'], []),
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}
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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}']
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#Vergleich mit dem NMR von Ethylen und Hexatrien
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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]
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#Vergleich mit dem NMR von Ethylen und Octrien
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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]
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#Vergleich mit dem NMR von Ethylen und Benzol
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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]
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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']
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NMRMAX = [max(n1,n2,n3) for n1,n2,n3 in zip(NMR1,NMR2,NMR3)]
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#Implement Edgelikelihood before Model
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FIXED_FLOWS = {
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#213: 3,
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#2: 3,
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#4: 1,
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#23: 1,
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#41: 1,
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#42: 1,
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}
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def build_model(name, hyperedges, vertices, nmrlikelihoodsmax, nmrlikelihoods1, nmrlikelihoods2, nmrlikelihoods3, 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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count = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, name = "count")
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nmax = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "nmrmax")
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n1 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "nmr1")
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n2 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "nmr2")
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n3 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "nmr3")
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enmax = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "edgenmrmax")
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en1 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "edgenmr1")
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en2 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "edgenmr2")
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en3 = model.addVars(vertices, vtype=GRB.CONTINUOUS, lb = 0.0, ub = 1.0, name = "edgenmr3")
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#Assigns every Molecule the likelihood compared to the three different reference spectra
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for v, nmrmax, nmr1, nmr2, nmr3 in zip(vertices, nmrlikelihoodsmax, nmrlikelihoods1, nmrlikelihoods2, nmrlikelihoods3):
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nmax[v] = nmrmax
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n1[v] = nmr1
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n2[v] = nmr2
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n3[v] = nmr3
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count[v] = 0
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#Assigns the edges a likelihood based on the products
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for e, (tails, heads) in hyperedges.items():
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en1[e] = math.prod(n1[head] for head in heads)
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en2[e] = math.prod(n2[head] for head in heads)
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en3[e] = math.prod(n3[head] for head in heads)
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enmax[e] = max([en1[e], en2[e], en3[e]])
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'''
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if heads != [] and tails != []: #Multiplication better?
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enmax[e] = quicksum(nmax[head] for head in heads)/len(heads)
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en1[e] = quicksum(n1[head] for head in heads)/len(heads)
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en2[e] = quicksum(n2[head] for head in heads)/len(heads)
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en3[e] = quicksum(n3[head] for head in heads)/len(heads)
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else:
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enmax[e] = 0.0
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en1[e] = 0.0
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en2[e] = 0.0
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en3[e] = 0.0
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'''
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#print(enmax[123])
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#print(enmax[42])
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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] * heads.count(v) for e_id, (_, heads) in hyperedges.items() if v in heads)
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outflow = quicksum(x[e_id] * tails.count(v) 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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reaction_path = {}
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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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#Multiplizier den node Wert mit infow + outflow
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model.ModelSense = GRB.MAXIMIZE
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#Multiply edgelikelihood with the edge use boolean
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model.setObjectiveN(
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quicksum(enmax[e_id] * b[e_id] for e_id, (_, _) in hyperedges.items()),
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index = 0,
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priority = 2,
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name = "maximize_nmr_similarity",
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)
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#Minimize the overall flow
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model.setObjectiveN(
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quicksum(-1 * x[e_id] for e_id in hyperedges),
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index=1,
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priority= 1,
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name="minimize_used_hyperedges",
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)
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#Excluding creation and destruction only three reactions for three nmr
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model.addConstr(quicksum(b[e_id] for e_id, (heads, tails) in hyperedges.items() if tails != [] and heads != []) == 3)
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#Restrict number of used edges to prevent using all available
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#model.addConstr(quicksum(x[e_id] for e_id in hyperedges) <= 16)
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#2 Butadien create first different molecule and it has to be created first:
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model.addConstr(b[4] + b[7] == 1)
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model.addConstr(b[213] == 1)
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#model.addConstr(b[41] == 1)
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#Every item created has to be consumed:
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for mol in vertices:
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for edge, (heads, tails) in hyperedges.items():
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count[mol] += x[edge] * (heads.count(mol) - tails.count(mol))
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#model.addConstr(count[mol] == 0)
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#No cyclic reaction pairs:
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for e_id1, (heads1, tails1) in hyperedges.items():
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for e_id2, (heads2, tails2) in hyperedges.items():
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if (heads1, tails1) == (tails2, heads2):
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#print(e_id1, e_id2)
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model.addConstr((b[e_id1] + b[e_id2]) <= 1)
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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", HYPERGRAPH, VERTICES, NMRMAX, NMR1, NMR2, NMR3)
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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, HYPERGRAPH)
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excluded_support = list(optimal_binary_solution.keys())
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second_model, x2, b2 = build_model("SecondBestHypergraphFlow", HYPERGRAPH, VERTICES, NMRMAX, NMR1, NMR2, NMR3, 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, HYPERGRAPH)
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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() |