question (5)+(1) avec networkx et scipy

separation.py

@@ -0,0 +1,57 @@
+import networkx as nx
+import scipy as sc
+import numpy as np
+
+def initGraph(Adj):
+    G = nx.Graph()
+    
+    for l in range(Adj):
+        for c in range(Adj[l]):
+            G.add_edge(l, c, weight = Adj[l][c])
+    
+    return G
+
+def subG(G, x):
+    nbN = len(G.nodes())
+    subG = nx.Graph()
+    for (d, a) in G.edges():
+        subG.add_edge(d, a, weight = G[d][a]['weight'] * x[min(d, a)*nbN+max(d,a)])
+    
+    return subG
+
+def addSubTour(A_ub, b_ub, G, part):
+    nbN = len(G.nodes())
+    
+    newCstr = [0]*len(G.edges())
+
+    for d in part:
+        for a in range(nbN):
+            if(a not in part):
+                newCstr[min(d, a)*nbN + max(d, a)] = 1
+
+    return A_ub.append(newCstr), b_ub.append(2)
+
+def separation(Adj):
+    G = initGraph(Adj)
+    nbN, nbE = len(Adj), len(Adj)*(len(Adj)-1)/2
+    
+    c = Adj.reshape(nbE)
+    A_eq = np.ones((nbN, nbE))
+    b_eq = np.ones((nbN, 1))
+    
+    A_ub = []
+    b_ub = []
+    res = sc.optimize.linprog(c, A_eq = A_eq, b_eq = b_eq, bounds=((0, 1)))
+    x = res.x
+
+    while(True):
+        sG = subG(G, x)
+        cutV, part = nx.stoer_wagner(sG)
+        if(cutV >= 2):
+            break
+        A_ub, b_ub = addSubTour(A_ub, b_ub, G, part[0])
+        
+        res = sc.optimize.linprog(c, A_eq = A_eq, b_eq = b_eq, A_ub = A_ub, b_ub = b_ub, bounds=((0, 1)))
+        x = res.x
+
+    return x, res.fun