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Fix formatting of examples & recipes (#835)
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@mmghannam
mmghannam authored Apr 2, 2024
1 parent e8ec238 commit cc24fc8
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228 changes: 113 additions & 115 deletions examples/finished/atsp.py
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Original file line number Diff line number Diff line change
@@ -1,5 +1,5 @@
##@file atsp.py
#@brief solve the asymmetric traveling salesman problem
# @brief solve the asymmetric traveling salesman problem

"""
Expand All @@ -11,9 +11,10 @@
Copyright (c) by Joao Pedro PEDROSO and Mikio KUBO, 2012
"""
from pyscipopt import Model, quicksum, multidict
from pyscipopt import Model, quicksum

def mtz(n,c):

def mtz(n, c):
"""mtz: Miller-Tucker-Zemlin's model for the (asymmetric) traveling salesman problem
(potential formulation)
Parameters:
Expand All @@ -24,30 +25,29 @@ def mtz(n,c):

model = Model("atsp - mtz")

x,u = {},{}
for i in range(1,n+1):
u[i] = model.addVar(lb=0, ub=n-1, vtype="C", name="u(%s)"%i)
for j in range(1,n+1):
x, u = {}, {}
for i in range(1, n + 1):
u[i] = model.addVar(lb=0, ub=n - 1, vtype="C", name="u(%s)" % i)
for j in range(1, n + 1):
if i != j:
x[i,j] = model.addVar(vtype="B", name="x(%s,%s)"%(i,j))
x[i, j] = model.addVar(vtype="B", name="x(%s,%s)" % (i, j))

for i in range(1,n+1):
model.addCons(quicksum(x[i,j] for j in range(1,n+1) if j != i) == 1, "Out(%s)"%i)
model.addCons(quicksum(x[j,i] for j in range(1,n+1) if j != i) == 1, "In(%s)"%i)
for i in range(1, n + 1):
model.addCons(quicksum(x[i, j] for j in range(1, n + 1) if j != i) == 1, "Out(%s)" % i)
model.addCons(quicksum(x[j, i] for j in range(1, n + 1) if j != i) == 1, "In(%s)" % i)

for i in range(1,n+1):
for j in range(2,n+1):
for i in range(1, n + 1):
for j in range(2, n + 1):
if i != j:
model.addCons(u[i] - u[j] + (n-1)*x[i,j] <= n-2, "MTZ(%s,%s)"%(i,j))
model.addCons(u[i] - u[j] + (n - 1) * x[i, j] <= n - 2, "MTZ(%s,%s)" % (i, j))

model.setObjective(quicksum(c[i,j]*x[i,j] for (i,j) in x), "minimize")

model.data = x,u
return model
model.setObjective(quicksum(c[i, j] * x[i, j] for (i, j) in x), "minimize")

model.data = x, u
return model


def mtz_strong(n,c):
def mtz_strong(n, c):
"""mtz_strong: Miller-Tucker-Zemlin's model for the (asymmetric) traveling salesman problem
(potential formulation, adding stronger constraints)
Parameters:
Expand All @@ -57,34 +57,34 @@ def mtz_strong(n,c):
"""

model = Model("atsp - mtz-strong")
x,u = {},{}
for i in range(1,n+1):
u[i] = model.addVar(lb=0, ub=n-1, vtype="C", name="u(%s)"%i)
for j in range(1,n+1):

x, u = {}, {}
for i in range(1, n + 1):
u[i] = model.addVar(lb=0, ub=n - 1, vtype="C", name="u(%s)" % i)
for j in range(1, n + 1):
if i != j:
x[i,j] = model.addVar(vtype="B", name="x(%s,%s)"%(i,j))
x[i, j] = model.addVar(vtype="B", name="x(%s,%s)" % (i, j))

for i in range(1,n+1):
model.addCons(quicksum(x[i,j] for j in range(1,n+1) if j != i) == 1, "Out(%s)"%i)
model.addCons(quicksum(x[j,i] for j in range(1,n+1) if j != i) == 1, "In(%s)"%i)
for i in range(1, n + 1):
model.addCons(quicksum(x[i, j] for j in range(1, n + 1) if j != i) == 1, "Out(%s)" % i)
model.addCons(quicksum(x[j, i] for j in range(1, n + 1) if j != i) == 1, "In(%s)" % i)

for i in range(1,n+1):
for j in range(2,n+1):
for i in range(1, n + 1):
for j in range(2, n + 1):
if i != j:
model.addCons(u[i] - u[j] + (n-1)*x[i,j] + (n-3)*x[j,i] <= n-2, "LiftedMTZ(%s,%s)"%(i,j))
model.addCons(u[i] - u[j] + (n - 1) * x[i, j] + (n - 3) * x[j, i] <= n - 2, "LiftedMTZ(%s,%s)" % (i, j))

for i in range(2, n + 1):
model.addCons(-x[1, i] - u[i] + (n - 3) * x[i, 1] <= -2, name="LiftedLB(%s)" % i)
model.addCons(-x[i, 1] + u[i] + (n - 3) * x[1, i] <= n - 2, name="LiftedUB(%s)" % i)

for i in range(2,n+1):
model.addCons(-x[1,i] - u[i] + (n-3)*x[i,1] <= -2, name="LiftedLB(%s)"%i)
model.addCons(-x[i,1] + u[i] + (n-3)*x[1,i] <= n-2, name="LiftedUB(%s)"%i)
model.setObjective(quicksum(c[i, j] * x[i, j] for (i, j) in x), "minimize")

model.setObjective(quicksum(c[i,j]*x[i,j] for (i,j) in x), "minimize")

model.data = x,u
model.data = x, u
return model


def scf(n,c):
def scf(n, c):
"""scf: single-commodity flow formulation for the (asymmetric) traveling salesman problem
Parameters:
- n: number of nodes
Expand All @@ -93,40 +93,39 @@ def scf(n,c):
"""
model = Model("atsp - scf")

x,f = {},{}
for i in range(1,n+1):
for j in range(1,n+1):
x, f = {}, {}
for i in range(1, n + 1):
for j in range(1, n + 1):
if i != j:
x[i,j] = model.addVar(vtype="B", name="x(%s,%s)"%(i,j))
if i==1:
f[i,j] = model.addVar(lb=0, ub=n-1, vtype="C", name="f(%s,%s)"%(i,j))
x[i, j] = model.addVar(vtype="B", name="x(%s,%s)" % (i, j))
if i == 1:
f[i, j] = model.addVar(lb=0, ub=n - 1, vtype="C", name="f(%s,%s)" % (i, j))
else:
f[i,j] = model.addVar(lb=0, ub=n-2, vtype="C", name="f(%s,%s)"%(i,j))
f[i, j] = model.addVar(lb=0, ub=n - 2, vtype="C", name="f(%s,%s)" % (i, j))

for i in range(1,n+1):
model.addCons(quicksum(x[i,j] for j in range(1,n+1) if j != i) == 1, "Out(%s)"%i)
model.addCons(quicksum(x[j,i] for j in range(1,n+1) if j != i) == 1, "In(%s)"%i)
for i in range(1, n + 1):
model.addCons(quicksum(x[i, j] for j in range(1, n + 1) if j != i) == 1, "Out(%s)" % i)
model.addCons(quicksum(x[j, i] for j in range(1, n + 1) if j != i) == 1, "In(%s)" % i)

model.addCons(quicksum(f[1,j] for j in range(2,n+1)) == n-1, "FlowOut")
model.addCons(quicksum(f[1, j] for j in range(2, n + 1)) == n - 1, "FlowOut")

for i in range(2,n+1):
model.addCons(quicksum(f[j,i] for j in range(1,n+1) if j != i) - \
quicksum(f[i,j] for j in range(1,n+1) if j != i) == 1, "FlowCons(%s)"%i)
for i in range(2, n + 1):
model.addCons(quicksum(f[j, i] for j in range(1, n + 1) if j != i) - \
quicksum(f[i, j] for j in range(1, n + 1) if j != i) == 1, "FlowCons(%s)" % i)

for j in range(2,n+1):
model.addCons(f[1,j] <= (n-1)*x[1,j], "FlowUB(%s,%s)"%(1,j))
for i in range(2,n+1):
for j in range(2, n + 1):
model.addCons(f[1, j] <= (n - 1) * x[1, j], "FlowUB(%s,%s)" % (1, j))
for i in range(2, n + 1):
if i != j:
model.addCons(f[i,j] <= (n-2)*x[i,j], "FlowUB(%s,%s)"%(i,j))
model.addCons(f[i, j] <= (n - 2) * x[i, j], "FlowUB(%s,%s)" % (i, j))

model.setObjective(quicksum(c[i,j]*x[i,j] for (i,j) in x), "minimize")
model.setObjective(quicksum(c[i, j] * x[i, j] for (i, j) in x), "minimize")

model.data = x,f
model.data = x, f
return model



def mcf(n,c):
def mcf(n, c):
"""mcf: multi-commodity flow formulation for the (asymmetric) traveling salesman problem
Parameters:
- n: number of nodes
Expand All @@ -135,134 +134,133 @@ def mcf(n,c):
"""
model = Model("mcf")

x,f = {},{}
for i in range(1,n+1):
for j in range(1,n+1):
x, f = {}, {}
for i in range(1, n + 1):
for j in range(1, n + 1):
if i != j:
x[i,j] = model.addVar(vtype="B", name="x(%s,%s)"%(i,j))
x[i, j] = model.addVar(vtype="B", name="x(%s,%s)" % (i, j))
if i != j and j != 1:
for k in range(2,n+1):
for k in range(2, n + 1):
if i != k:
f[i,j,k] = model.addVar(ub=1, vtype="C", name="f(%s,%s,%s)"%(i,j,k))
f[i, j, k] = model.addVar(ub=1, vtype="C", name="f(%s,%s,%s)" % (i, j, k))

for i in range(1,n+1):
model.addCons(quicksum(x[i,j] for j in range(1,n+1) if j != i) == 1, "Out(%s)"%i)
model.addCons(quicksum(x[j,i] for j in range(1,n+1) if j != i) == 1, "In(%s)"%i)
for i in range(1, n + 1):
model.addCons(quicksum(x[i, j] for j in range(1, n + 1) if j != i) == 1, "Out(%s)" % i)
model.addCons(quicksum(x[j, i] for j in range(1, n + 1) if j != i) == 1, "In(%s)" % i)

for k in range(2,n+1):
model.addCons(quicksum(f[1,i,k] for i in range(2,n+1) if (1,i,k) in f) == 1, "FlowOut(%s)"%k)
model.addCons(quicksum(f[i,k,k] for i in range(1,n+1) if (i,k,k) in f) == 1, "FlowIn(%s)"%k)
for k in range(2, n + 1):
model.addCons(quicksum(f[1, i, k] for i in range(2, n + 1) if (1, i, k) in f) == 1, "FlowOut(%s)" % k)
model.addCons(quicksum(f[i, k, k] for i in range(1, n + 1) if (i, k, k) in f) == 1, "FlowIn(%s)" % k)

for i in range(2,n+1):
for i in range(2, n + 1):
if i != k:
model.addCons(quicksum(f[j,i,k] for j in range(1,n+1) if (j,i,k) in f) == \
quicksum(f[i,j,k] for j in range(1,n+1) if (i,j,k) in f),
"FlowCons(%s,%s)"%(i,k))
model.addCons(quicksum(f[j, i, k] for j in range(1, n + 1) if (j, i, k) in f) == \
quicksum(f[i, j, k] for j in range(1, n + 1) if (i, j, k) in f),
"FlowCons(%s,%s)" % (i, k))

for (i,j,k) in f:
model.addCons(f[i,j,k] <= x[i,j], "FlowUB(%s,%s,%s)"%(i,j,k))
for (i, j, k) in f:
model.addCons(f[i, j, k] <= x[i, j], "FlowUB(%s,%s,%s)" % (i, j, k))

model.setObjective(quicksum(c[i,j]*x[i,j] for (i,j) in x), "minimize")
model.setObjective(quicksum(c[i, j] * x[i, j] for (i, j) in x), "minimize")

model.data = x,f
model.data = x, f
return model



def sequence(arcs):
"""sequence: make a list of cities to visit, from set of arcs"""
succ = {}
for (i,j) in arcs:
for (i, j) in arcs:
succ[i] = j
curr = 1 # first node being visited
curr = 1 # first node being visited
sol = [curr]
for i in range(len(arcs)-2):
for i in range(len(arcs) - 2):
curr = succ[curr]
sol.append(curr)
return sol


if __name__ == "__main__":
n = 5
c = { (1,1):0, (1,2):1989, (1,3):102, (1,4):102, (1,5):103,
(2,1):104, (2,2):0, (2,3):11, (2,4):104, (2,5):108,
(3,1):107, (3,2):108, (3,3):0, (3,4):19, (3,5):102,
(4,1):109, (4,2):102, (4,3):107, (4,4):0, (4,5):15,
(5,1):13, (5,2):103, (5,3):104, (5,4):101, (5,5):0,
c = {(1, 1): 0, (1, 2): 1989, (1, 3): 102, (1, 4): 102, (1, 5): 103,
(2, 1): 104, (2, 2): 0, (2, 3): 11, (2, 4): 104, (2, 5): 108,
(3, 1): 107, (3, 2): 108, (3, 3): 0, (3, 4): 19, (3, 5): 102,
(4, 1): 109, (4, 2): 102, (4, 3): 107, (4, 4): 0, (4, 5): 15,
(5, 1): 13, (5, 2): 103, (5, 3): 104, (5, 4): 101, (5, 5): 0,
}

model = mtz(n,c)
model.hideOutput() # silent mode
model = mtz(n, c)
model.hideOutput() # silent mode
model.optimize()
cost = model.getObjVal()
print()
print("Miller-Tucker-Zemlin's model:")
print("Optimal value:", cost)
#model.printAttr("X")
# model.printAttr("X")
for v in model.getVars():
if model.getVal(v) > 0.001:
print(v.name, "=", model.getVal(v))

x,u = model.data
sol = [i for (p,i) in sorted([(int(model.getVal(u[i])+.5),i) for i in range(1,n+1)])]
x, u = model.data
sol = [i for (p, i) in sorted([(int(model.getVal(u[i]) + .5), i) for i in range(1, n + 1)])]
print(sol)
arcs = [(i,j) for (i,j) in x if model.getVal(x[i,j]) > .5]
arcs = [(i, j) for (i, j) in x if model.getVal(x[i, j]) > .5]
sol = sequence(arcs)
print(sol)
# assert cost == 5

model = mtz_strong(n,c)
model.hideOutput() # silent mode
model = mtz_strong(n, c)
model.hideOutput() # silent mode
model.optimize()
cost = model.getObjVal()
print()
print("Miller-Tucker-Zemlin's model with stronger constraints:")
print("Optimal value:",cost)
#model.printAttr("X")
print("Optimal value:", cost)
# model.printAttr("X")
for v in model.getVars():
if model.getVal(v) > 0.001:
print(v.name, "=", model.getVal(v))

x,u = model.data
sol = [i for (p,i) in sorted([(int(model.getVal(u[i])+.5),i) for i in range(1,n+1)])]
x, u = model.data
sol = [i for (p, i) in sorted([(int(model.getVal(u[i]) + .5), i) for i in range(1, n + 1)])]
print(sol)
arcs = [(i,j) for (i,j) in x if model.getVal(x[i,j]) > .5]
arcs = [(i, j) for (i, j) in x if model.getVal(x[i, j]) > .5]
sol = sequence(arcs)
print(sol)
# assert cost == 5

model = scf(n,c)
model.hideOutput() # silent mode
model = scf(n, c)
model.hideOutput() # silent mode
model.optimize()
cost = model.getObjVal()
print()
print("Single-commodity flow formulation:")
print("Optimal value:",cost)
#model.printAttr("X")
print("Optimal value:", cost)
# model.printAttr("X")
for v in model.getVars():
if model.getVal(v) > 0.001:
print(v.name, "=", model.getVal(v))

x,f = model.data
arcs = [(i,j) for (i,j) in x if model.getVal(x[i,j]) > .5]
x, f = model.data
arcs = [(i, j) for (i, j) in x if model.getVal(x[i, j]) > .5]
sol = sequence(arcs)
print(sol)
# assert cost == 5

model = mcf(n,c)
model.hideOutput() # silent mode
model = mcf(n, c)
model.hideOutput() # silent mode
model.optimize()
cost = model.getObjVal()
print()
print("Multi-commodity flow formulation:")
print("Optimal value:",cost)
#model.printAttr("X")
print("Optimal value:", cost)
# model.printAttr("X")
for v in model.getVars():
if model.getVal(v)>0.001:
if model.getVal(v) > 0.001:
print(v.name, "=", model.getVal(v))

x,f = model.data
arcs = [(i,j) for (i,j) in x if model.getVal(x[i,j]) > .5]
x, f = model.data
arcs = [(i, j) for (i, j) in x if model.getVal(x[i, j]) > .5]
sol = sequence(arcs)
print(sol)
# assert cost == 5
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