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Fix formatting of examples & recipes (#835)
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‎examples/finished/atsp.py

Lines changed: 113 additions & 115 deletions
Original file line numberDiff line numberDiff line change
@@ -1,5 +1,5 @@
11
##@file atsp.py
2-
#@brief solve the asymmetric traveling salesman problem
2+
# @brief solve the asymmetric traveling salesman problem
33

44
"""
55
@@ -11,9 +11,10 @@
1111
1212
Copyright (c) by Joao Pedro PEDROSO and Mikio KUBO, 2012
1313
"""
14-
from pyscipopt import Model, quicksum, multidict
14+
from pyscipopt import Model, quicksum
1515

16-
def mtz(n,c):
16+
17+
def mtz(n, c):
1718
"""mtz: Miller-Tucker-Zemlin's model for the (asymmetric) traveling salesman problem
1819
(potential formulation)
1920
Parameters:
@@ -24,30 +25,29 @@ def mtz(n,c):
2425

2526
model = Model("atsp - mtz")
2627

27-
x,u = {},{}
28-
for i in range(1,n+1):
29-
u[i] = model.addVar(lb=0, ub=n-1, vtype="C", name="u(%s)"%i)
30-
for j in range(1,n+1):
28+
x, u = {}, {}
29+
for i in range(1, n + 1):
30+
u[i] = model.addVar(lb=0, ub=n - 1, vtype="C", name="u(%s)" % i)
31+
for j in range(1, n + 1):
3132
if i != j:
32-
x[i,j] = model.addVar(vtype="B", name="x(%s,%s)"%(i,j))
33+
x[i, j] = model.addVar(vtype="B", name="x(%s,%s)" % (i, j))
3334

34-
for i in range(1,n+1):
35-
model.addCons(quicksum(x[i,j] for j in range(1,n+1) if j != i) == 1, "Out(%s)"%i)
36-
model.addCons(quicksum(x[j,i] for j in range(1,n+1) if j != i) == 1, "In(%s)"%i)
35+
for i in range(1, n + 1):
36+
model.addCons(quicksum(x[i, j] for j in range(1, n + 1) if j != i) == 1, "Out(%s)" % i)
37+
model.addCons(quicksum(x[j, i] for j in range(1, n + 1) if j != i) == 1, "In(%s)" % i)
3738

38-
for i in range(1,n+1):
39-
for j in range(2,n+1):
39+
for i in range(1, n + 1):
40+
for j in range(2, n + 1):
4041
if i != j:
41-
model.addCons(u[i] - u[j] + (n-1)*x[i,j] <= n-2, "MTZ(%s,%s)"%(i,j))
42+
model.addCons(u[i] - u[j] + (n - 1) * x[i, j] <= n - 2, "MTZ(%s,%s)" % (i, j))
4243

43-
model.setObjective(quicksum(c[i,j]*x[i,j] for (i,j) in x), "minimize")
44-
45-
model.data = x,u
46-
return model
44+
model.setObjective(quicksum(c[i, j] * x[i, j] for (i, j) in x), "minimize")
4745

46+
model.data = x, u
47+
return model
4848

4949

50-
def mtz_strong(n,c):
50+
def mtz_strong(n, c):
5151
"""mtz_strong: Miller-Tucker-Zemlin's model for the (asymmetric) traveling salesman problem
5252
(potential formulation, adding stronger constraints)
5353
Parameters:
@@ -57,34 +57,34 @@ def mtz_strong(n,c):
5757
"""
5858

5959
model = Model("atsp - mtz-strong")
60-
61-
x,u = {},{}
62-
for i in range(1,n+1):
63-
u[i] = model.addVar(lb=0, ub=n-1, vtype="C", name="u(%s)"%i)
64-
for j in range(1,n+1):
60+
61+
x, u = {}, {}
62+
for i in range(1, n + 1):
63+
u[i] = model.addVar(lb=0, ub=n - 1, vtype="C", name="u(%s)" % i)
64+
for j in range(1, n + 1):
6565
if i != j:
66-
x[i,j] = model.addVar(vtype="B", name="x(%s,%s)"%(i,j))
66+
x[i, j] = model.addVar(vtype="B", name="x(%s,%s)" % (i, j))
6767

68-
for i in range(1,n+1):
69-
model.addCons(quicksum(x[i,j] for j in range(1,n+1) if j != i) == 1, "Out(%s)"%i)
70-
model.addCons(quicksum(x[j,i] for j in range(1,n+1) if j != i) == 1, "In(%s)"%i)
68+
for i in range(1, n + 1):
69+
model.addCons(quicksum(x[i, j] for j in range(1, n + 1) if j != i) == 1, "Out(%s)" % i)
70+
model.addCons(quicksum(x[j, i] for j in range(1, n + 1) if j != i) == 1, "In(%s)" % i)
7171

72-
for i in range(1,n+1):
73-
for j in range(2,n+1):
72+
for i in range(1, n + 1):
73+
for j in range(2, n + 1):
7474
if i != j:
75-
model.addCons(u[i] - u[j] + (n-1)*x[i,j] + (n-3)*x[j,i] <= n-2, "LiftedMTZ(%s,%s)"%(i,j))
75+
model.addCons(u[i] - u[j] + (n - 1) * x[i, j] + (n - 3) * x[j, i] <= n - 2, "LiftedMTZ(%s,%s)" % (i, j))
76+
77+
for i in range(2, n + 1):
78+
model.addCons(-x[1, i] - u[i] + (n - 3) * x[i, 1] <= -2, name="LiftedLB(%s)" % i)
79+
model.addCons(-x[i, 1] + u[i] + (n - 3) * x[1, i] <= n - 2, name="LiftedUB(%s)" % i)
7680

77-
for i in range(2,n+1):
78-
model.addCons(-x[1,i] - u[i] + (n-3)*x[i,1] <= -2, name="LiftedLB(%s)"%i)
79-
model.addCons(-x[i,1] + u[i] + (n-3)*x[1,i] <= n-2, name="LiftedUB(%s)"%i)
81+
model.setObjective(quicksum(c[i, j] * x[i, j] for (i, j) in x), "minimize")
8082

81-
model.setObjective(quicksum(c[i,j]*x[i,j] for (i,j) in x), "minimize")
82-
83-
model.data = x,u
83+
model.data = x, u
8484
return model
8585

8686

87-
def scf(n,c):
87+
def scf(n, c):
8888
"""scf: single-commodity flow formulation for the (asymmetric) traveling salesman problem
8989
Parameters:
9090
- n: number of nodes
@@ -93,40 +93,39 @@ def scf(n,c):
9393
"""
9494
model = Model("atsp - scf")
9595

96-
x,f = {},{}
97-
for i in range(1,n+1):
98-
for j in range(1,n+1):
96+
x, f = {}, {}
97+
for i in range(1, n + 1):
98+
for j in range(1, n + 1):
9999
if i != j:
100-
x[i,j] = model.addVar(vtype="B", name="x(%s,%s)"%(i,j))
101-
if i==1:
102-
f[i,j] = model.addVar(lb=0, ub=n-1, vtype="C", name="f(%s,%s)"%(i,j))
100+
x[i, j] = model.addVar(vtype="B", name="x(%s,%s)" % (i, j))
101+
if i == 1:
102+
f[i, j] = model.addVar(lb=0, ub=n - 1, vtype="C", name="f(%s,%s)" % (i, j))
103103
else:
104-
f[i,j] = model.addVar(lb=0, ub=n-2, vtype="C", name="f(%s,%s)"%(i,j))
104+
f[i, j] = model.addVar(lb=0, ub=n - 2, vtype="C", name="f(%s,%s)" % (i, j))
105105

106-
for i in range(1,n+1):
107-
model.addCons(quicksum(x[i,j] for j in range(1,n+1) if j != i) == 1, "Out(%s)"%i)
108-
model.addCons(quicksum(x[j,i] for j in range(1,n+1) if j != i) == 1, "In(%s)"%i)
106+
for i in range(1, n + 1):
107+
model.addCons(quicksum(x[i, j] for j in range(1, n + 1) if j != i) == 1, "Out(%s)" % i)
108+
model.addCons(quicksum(x[j, i] for j in range(1, n + 1) if j != i) == 1, "In(%s)" % i)
109109

110-
model.addCons(quicksum(f[1,j] for j in range(2,n+1)) == n-1, "FlowOut")
110+
model.addCons(quicksum(f[1, j] for j in range(2, n + 1)) == n - 1, "FlowOut")
111111

112-
for i in range(2,n+1):
113-
model.addCons(quicksum(f[j,i] for j in range(1,n+1) if j != i) - \
114-
quicksum(f[i,j] for j in range(1,n+1) if j != i) == 1, "FlowCons(%s)"%i)
112+
for i in range(2, n + 1):
113+
model.addCons(quicksum(f[j, i] for j in range(1, n + 1) if j != i) - \
114+
quicksum(f[i, j] for j in range(1, n + 1) if j != i) == 1, "FlowCons(%s)" % i)
115115

116-
for j in range(2,n+1):
117-
model.addCons(f[1,j] <= (n-1)*x[1,j], "FlowUB(%s,%s)"%(1,j))
118-
for i in range(2,n+1):
116+
for j in range(2, n + 1):
117+
model.addCons(f[1, j] <= (n - 1) * x[1, j], "FlowUB(%s,%s)" % (1, j))
118+
for i in range(2, n + 1):
119119
if i != j:
120-
model.addCons(f[i,j] <= (n-2)*x[i,j], "FlowUB(%s,%s)"%(i,j))
120+
model.addCons(f[i, j] <= (n - 2) * x[i, j], "FlowUB(%s,%s)" % (i, j))
121121

122-
model.setObjective(quicksum(c[i,j]*x[i,j] for (i,j) in x), "minimize")
122+
model.setObjective(quicksum(c[i, j] * x[i, j] for (i, j) in x), "minimize")
123123

124-
model.data = x,f
124+
model.data = x, f
125125
return model
126126

127127

128-
129-
def mcf(n,c):
128+
def mcf(n, c):
130129
"""mcf: multi-commodity flow formulation for the (asymmetric) traveling salesman problem
131130
Parameters:
132131
- n: number of nodes
@@ -135,134 +134,133 @@ def mcf(n,c):
135134
"""
136135
model = Model("mcf")
137136

138-
x,f = {},{}
139-
for i in range(1,n+1):
140-
for j in range(1,n+1):
137+
x, f = {}, {}
138+
for i in range(1, n + 1):
139+
for j in range(1, n + 1):
141140
if i != j:
142-
x[i,j] = model.addVar(vtype="B", name="x(%s,%s)"%(i,j))
141+
x[i, j] = model.addVar(vtype="B", name="x(%s,%s)" % (i, j))
143142
if i != j and j != 1:
144-
for k in range(2,n+1):
143+
for k in range(2, n + 1):
145144
if i != k:
146-
f[i,j,k] = model.addVar(ub=1, vtype="C", name="f(%s,%s,%s)"%(i,j,k))
145+
f[i, j, k] = model.addVar(ub=1, vtype="C", name="f(%s,%s,%s)" % (i, j, k))
147146

148-
for i in range(1,n+1):
149-
model.addCons(quicksum(x[i,j] for j in range(1,n+1) if j != i) == 1, "Out(%s)"%i)
150-
model.addCons(quicksum(x[j,i] for j in range(1,n+1) if j != i) == 1, "In(%s)"%i)
147+
for i in range(1, n + 1):
148+
model.addCons(quicksum(x[i, j] for j in range(1, n + 1) if j != i) == 1, "Out(%s)" % i)
149+
model.addCons(quicksum(x[j, i] for j in range(1, n + 1) if j != i) == 1, "In(%s)" % i)
151150

152-
for k in range(2,n+1):
153-
model.addCons(quicksum(f[1,i,k] for i in range(2,n+1) if (1,i,k) in f) == 1, "FlowOut(%s)"%k)
154-
model.addCons(quicksum(f[i,k,k] for i in range(1,n+1) if (i,k,k) in f) == 1, "FlowIn(%s)"%k)
151+
for k in range(2, n + 1):
152+
model.addCons(quicksum(f[1, i, k] for i in range(2, n + 1) if (1, i, k) in f) == 1, "FlowOut(%s)" % k)
153+
model.addCons(quicksum(f[i, k, k] for i in range(1, n + 1) if (i, k, k) in f) == 1, "FlowIn(%s)" % k)
155154

156-
for i in range(2,n+1):
155+
for i in range(2, n + 1):
157156
if i != k:
158-
model.addCons(quicksum(f[j,i,k] for j in range(1,n+1) if (j,i,k) in f) == \
159-
quicksum(f[i,j,k] for j in range(1,n+1) if (i,j,k) in f),
160-
"FlowCons(%s,%s)"%(i,k))
157+
model.addCons(quicksum(f[j, i, k] for j in range(1, n + 1) if (j, i, k) in f) == \
158+
quicksum(f[i, j, k] for j in range(1, n + 1) if (i, j, k) in f),
159+
"FlowCons(%s,%s)" % (i, k))
161160

162-
for (i,j,k) in f:
163-
model.addCons(f[i,j,k] <= x[i,j], "FlowUB(%s,%s,%s)"%(i,j,k))
161+
for (i, j, k) in f:
162+
model.addCons(f[i, j, k] <= x[i, j], "FlowUB(%s,%s,%s)" % (i, j, k))
164163

165-
model.setObjective(quicksum(c[i,j]*x[i,j] for (i,j) in x), "minimize")
164+
model.setObjective(quicksum(c[i, j] * x[i, j] for (i, j) in x), "minimize")
166165

167-
model.data = x,f
166+
model.data = x, f
168167
return model
169168

170169

171-
172170
def sequence(arcs):
173171
"""sequence: make a list of cities to visit, from set of arcs"""
174172
succ = {}
175-
for (i,j) in arcs:
173+
for (i, j) in arcs:
176174
succ[i] = j
177-
curr = 1 # first node being visited
175+
curr = 1 # first node being visited
178176
sol = [curr]
179-
for i in range(len(arcs)-2):
177+
for i in range(len(arcs) - 2):
180178
curr = succ[curr]
181179
sol.append(curr)
182180
return sol
183181

184182

185183
if __name__ == "__main__":
186184
n = 5
187-
c = { (1,1):0, (1,2):1989, (1,3):102, (1,4):102, (1,5):103,
188-
(2,1):104, (2,2):0, (2,3):11, (2,4):104, (2,5):108,
189-
(3,1):107, (3,2):108, (3,3):0, (3,4):19, (3,5):102,
190-
(4,1):109, (4,2):102, (4,3):107, (4,4):0, (4,5):15,
191-
(5,1):13, (5,2):103, (5,3):104, (5,4):101, (5,5):0,
185+
c = {(1, 1): 0, (1, 2): 1989, (1, 3): 102, (1, 4): 102, (1, 5): 103,
186+
(2, 1): 104, (2, 2): 0, (2, 3): 11, (2, 4): 104, (2, 5): 108,
187+
(3, 1): 107, (3, 2): 108, (3, 3): 0, (3, 4): 19, (3, 5): 102,
188+
(4, 1): 109, (4, 2): 102, (4, 3): 107, (4, 4): 0, (4, 5): 15,
189+
(5, 1): 13, (5, 2): 103, (5, 3): 104, (5, 4): 101, (5, 5): 0,
192190
}
193191

194-
model = mtz(n,c)
195-
model.hideOutput() # silent mode
192+
model = mtz(n, c)
193+
model.hideOutput() # silent mode
196194
model.optimize()
197195
cost = model.getObjVal()
198196
print()
199197
print("Miller-Tucker-Zemlin's model:")
200198
print("Optimal value:", cost)
201-
#model.printAttr("X")
199+
# model.printAttr("X")
202200
for v in model.getVars():
203201
if model.getVal(v) > 0.001:
204202
print(v.name, "=", model.getVal(v))
205203

206-
x,u = model.data
207-
sol = [i for (p,i) in sorted([(int(model.getVal(u[i])+.5),i) for i in range(1,n+1)])]
204+
x, u = model.data
205+
sol = [i for (p, i) in sorted([(int(model.getVal(u[i]) + .5), i) for i in range(1, n + 1)])]
208206
print(sol)
209-
arcs = [(i,j) for (i,j) in x if model.getVal(x[i,j]) > .5]
207+
arcs = [(i, j) for (i, j) in x if model.getVal(x[i, j]) > .5]
210208
sol = sequence(arcs)
211209
print(sol)
212210
# assert cost == 5
213211

214-
model = mtz_strong(n,c)
215-
model.hideOutput() # silent mode
212+
model = mtz_strong(n, c)
213+
model.hideOutput() # silent mode
216214
model.optimize()
217215
cost = model.getObjVal()
218216
print()
219217
print("Miller-Tucker-Zemlin's model with stronger constraints:")
220-
print("Optimal value:",cost)
221-
#model.printAttr("X")
218+
print("Optimal value:", cost)
219+
# model.printAttr("X")
222220
for v in model.getVars():
223221
if model.getVal(v) > 0.001:
224222
print(v.name, "=", model.getVal(v))
225223

226-
x,u = model.data
227-
sol = [i for (p,i) in sorted([(int(model.getVal(u[i])+.5),i) for i in range(1,n+1)])]
224+
x, u = model.data
225+
sol = [i for (p, i) in sorted([(int(model.getVal(u[i]) + .5), i) for i in range(1, n + 1)])]
228226
print(sol)
229-
arcs = [(i,j) for (i,j) in x if model.getVal(x[i,j]) > .5]
227+
arcs = [(i, j) for (i, j) in x if model.getVal(x[i, j]) > .5]
230228
sol = sequence(arcs)
231229
print(sol)
232230
# assert cost == 5
233231

234-
model = scf(n,c)
235-
model.hideOutput() # silent mode
232+
model = scf(n, c)
233+
model.hideOutput() # silent mode
236234
model.optimize()
237235
cost = model.getObjVal()
238236
print()
239237
print("Single-commodity flow formulation:")
240-
print("Optimal value:",cost)
241-
#model.printAttr("X")
238+
print("Optimal value:", cost)
239+
# model.printAttr("X")
242240
for v in model.getVars():
243241
if model.getVal(v) > 0.001:
244242
print(v.name, "=", model.getVal(v))
245243

246-
x,f = model.data
247-
arcs = [(i,j) for (i,j) in x if model.getVal(x[i,j]) > .5]
244+
x, f = model.data
245+
arcs = [(i, j) for (i, j) in x if model.getVal(x[i, j]) > .5]
248246
sol = sequence(arcs)
249247
print(sol)
250248
# assert cost == 5
251249

252-
model = mcf(n,c)
253-
model.hideOutput() # silent mode
250+
model = mcf(n, c)
251+
model.hideOutput() # silent mode
254252
model.optimize()
255253
cost = model.getObjVal()
256254
print()
257255
print("Multi-commodity flow formulation:")
258-
print("Optimal value:",cost)
259-
#model.printAttr("X")
256+
print("Optimal value:", cost)
257+
# model.printAttr("X")
260258
for v in model.getVars():
261-
if model.getVal(v)>0.001:
259+
if model.getVal(v) > 0.001:
262260
print(v.name, "=", model.getVal(v))
263261

264-
x,f = model.data
265-
arcs = [(i,j) for (i,j) in x if model.getVal(x[i,j]) > .5]
262+
x, f = model.data
263+
arcs = [(i, j) for (i, j) in x if model.getVal(x[i, j]) > .5]
266264
sol = sequence(arcs)
267265
print(sol)
268266
# assert cost == 5

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