def gcp_fixed_k(V, E, K):
"""gcp_fixed_k -- model for minimizing number of bad edges in coloring a graph
Parameters:
- V: set/list of nodes in the graph
- E: set/list of edges in the graph
- K: number of colors to be used
Returns a model, ready to be solved.
"""
model = Model("gcp - fixed k")
x, z = {}, {}
for i in V:
for k in range(K): # vetex i in color k or not
x[i, k] = model.addVar(vtype="B", name="x(%s,%s)" % (i, k))
for (i, j) in E: # bad edge(same color) or not
z[i, j] = model.addVar(vtype="B", name="z(%s,%s)" % (i, j))
for i in V:
model.addCons(
quicksum(x[i, k] for k in range(K)) == 1, "AssignColor(%s)" % i)
model.addConsSOS1([x[i, k] for k in range(K)])
for (i, j) in E:
for k in range(K):
model.addCons(x[i, k] + x[j, k] <= 1 + z[i, j],
"BadEdge(%s,%s,%s)" % (i, j, k))
model.setObjective(quicksum(z[i, j] for (i, j) in E), "minimize")
model.data = x
return model
def gcp_sos(V, E, K):
"""gcp_sos -- model for minimizing the number of colors in a graph
(use sos type 1 constraints)
Parameters:
- V: set/list of nodes in the graph
- E: set/list of edges in the graph
- K: upper bound to the number of colors
Returns a model, ready to be solved.
"""
model = Model("gcp - sos constraints")
x, y = {}, {}
for k in range(K):
y[k] = model.addVar(vtype="B", name="y(%s)" % k)
for i in V:
x[i, k] = model.addVar(vtype="B", name="x(%s,%s)" % (i, k))
for i in V:
model.addCons(
quicksum(x[i, k] for k in range(K)) == 1, "AssignColor(%s)" % i)
model.addConsSOS1([x[i, k] for k in range(K)])
for (i, j) in E:
for k in range(K):
model.addCons(x[i, k] + x[j, k] <= y[k],
"NotSameColor(%s,%s,%s)" % (i, j, k))
for k in range(K - 1):
model.addCons(y[k] >= y[k + 1], "LowColor(%s)" % k)
model.setObjective(quicksum(y[k] for k in range(K)), "minimize")
model.data = x, y
return model
def gcp_sos(V,E,K):
"""gcp_sos -- model for minimizing the number of colors in a graph
(use sos type 1 constraints)
Parameters:
- V: set/list of nodes in the graph
- E: set/list of edges in the graph
- K: upper bound to the number of colors
Returns a model, ready to be solved.
"""
model = Model("gcp - sos constraints")
x,y = {},{}
for k in range(K):
y[k] = model.addVar(vtype="B", name="y(%s)"%k)
for i in V:
x[i,k] = model.addVar(vtype="B", name="x(%s,%s)"%(i,k))
for i in V:
model.addCons(quicksum(x[i,k] for k in range(K)) == 1, "AssignColor(%s)" % i)
model.addConsSOS1([x[i,k] for k in range(K)])
for (i,j) in E:
for k in range(K):
model.addCons(x[i,k] + x[j,k] <= y[k], "NotSameColor(%s,%s,%s)"%(i,j,k))
for k in range(K-1):
model.addCons(y[k] >= y[k+1], "LowColor(%s)"%k)
model.setObjective(quicksum(y[k] for k in range(K)), "minimize")
model.data = x
return model
def bpp(s, B):
"""bpp: Martello and Toth's model to solve the bin packing problem.
Parameters:
- s: list with item widths
- B: bin capacity
Returns a model, ready to be solved.
"""
n = len(s)
U = len(FFD(s, B)) # upper bound of the number of bins
model = Model("bpp")
# setParam("MIPFocus",1)
x, y = {}, {}
for i in range(n):
for j in range(U):
x[i, j] = model.addVar(vtype="B", name="x(%s,%s)" % (i, j))
for j in range(U):
y[j] = model.addVar(vtype="B", name="y(%s)" % j)
# assignment constraints
for i in range(n):
model.addCons(
quicksum(x[i, j] for j in range(U)) == 1, "Assign(%s)" % i)
# bin capacity constraints
for j in range(U):
model.addCons(
quicksum(s[i] * x[i, j] for i in range(n)) <= B * y[j],
"Capac(%s)" % j)
# tighten assignment constraints
for j in range(U):
for i in range(n):
model.addCons(x[i, j] <= y[j], "Strong(%s,%s)" % (i, j))
# tie breaking constraints
for j in range(U - 1):
model.addCons(y[j] >= y[j + 1], "TieBrk(%s)" % j)
# SOS constraints
for i in range(n):
model.addConsSOS1([x[i, j] for j in range(U)])
model.setObjective(quicksum(y[j] for j in range(U)), "minimize")
model.data = x, y
return model
def bpp(s,B):
"""bpp: Martello and Toth's model to solve the bin packing problem.
Parameters:
- s: list with item widths
- B: bin capacity
Returns a model, ready to be solved.
"""
n = len(s)
U = len(FFD(s,B)) # upper bound of the number of bins
model = Model("bpp")
# setParam("MIPFocus",1)
x,y = {},{}
for i in range(n):
for j in range(U):
x[i,j] = model.addVar(vtype="B", name="x(%s,%s)"%(i,j))
for j in range(U):
y[j] = model.addVar(vtype="B", name="y(%s)"%j)
# assignment constraints
for i in range(n):
model.addCons(quicksum(x[i,j] for j in range(U)) == 1, "Assign(%s)"%i)
# bin capacity constraints
for j in range(U):
model.addCons(quicksum(s[i]*x[i,j] for i in range(n)) <= B*y[j], "Capac(%s)"%j)
# tighten assignment constraints
for j in range(U):
for i in range(n):
model.addCons(x[i,j] <= y[j], "Strong(%s,%s)"%(i,j))
# tie breaking constraints
for j in range(U-1):
model.addCons(y[j] >= y[j+1],"TieBrk(%s)"%j)
# SOS constraints
for i in range(n):
model.addConsSOS1([x[i,j] for j in range(U)])
model.setObjective(quicksum(y[j] for j in range(U)), "minimize")
model.data = x,y
return model
