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cabling.py
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cabling.py
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"""
Cabling problem in cpmpy
From https://yurichev.com/blog/cabling_Z3/
'''
Take a rack cabinet, like this one:
[ an image ]
Let's say, there are 8 1U devices, maybe servers, routers and whatnot, named
as A, B, C, D, E, F, G, H. Devices must be connected by cables: probably
twisted pair or whatever network engineers using today. Some devices must be
connected by several cables (2 cables, 3 or 4):
A <--- 1 cable ---> H
A <--- 2 cables ---> E
B <--- 4 cables ---> F
C <--- 1 cable ---> G
C <--- 1 cable ---> D
C <--- 1 cable ---> E
D <--- 3 cables ---> H
G <--- 1 cable ---> H
The problem: how we can place these 8 devices in such an order, so that sum
of all cable lengths would be as short as possible?
'''
Here are two models:
- cabling1: A port of the original Z3 model
- cabling2: A more general approach.
This model also shows all the 48 optimal
solutions (length = 19)
Model created by Hakan Kjellerstrand, hakank@hakank.com
See also my cpmpy page: http://www.hakank.org/cpmpy/
"""
import sys
import numpy as np
from cpmpy import *
from cpmpy.solvers import *
from cpmpy_hakank import *
def diff(x, y):
return abs(x-y)
# This is a port of the original Z3 model
def cabling_1():
model = Model()
n = 8
x = intvar(0,7,shape=n,name="x")
A, B, C, D, E, F, G, H = x
final_sum = intvar(-1000,1000,name="final_sum")
# all "devices" has distinct positions in rack:
model += [AllDifferent(x)]
# A <--- 1 cable ---> H
diff_A_H = intvar(-7,7,name="diff_A_H")
model += [diff_A_H == diff(A,H)]
# final_sum = diff_A_H
# A <--- 2 cables ---> E
diff_A_E = intvar(-7,7,name="diff_A_E")
model += [diff_A_E == diff(A,E)]
# final_sum = final_sum+diff_A_E*2
# B <--- 4 cables ---> F
diff_B_F = intvar(-7,7,name="diff_B_F")
model += [diff_B_F == diff(B,F)]
# final_sum=final_sum+diff_B_F*4
# C <--- 1 cable ---> G
diff_C_G = intvar(-7,7,name="diff_C_G")
model += [diff_C_G == diff(C,G)]
# final_sum = final_sum+diff_C_G
# C <--- 1 cable ---> D
diff_C_D = intvar(-7,7,name="diff_C_D")
model += [diff_C_D == diff(C,D)]
# final_sum = final_sum+diff_C_D
# C <--- 1 cable ---> E
diff_C_E = intvar(-7,7,name="diff_C_E")
model += [diff_C_E == diff(C,E)]
# final_sum = final_sum+diff_C_E
# D <--- 3 cables ---> H
diff_D_H = intvar(-7,7,name="diff_D_H")
model += [diff_D_H == diff(D,H)]
# final_sum = final_sum+diff_D_H*3
# G <--- 1 cable ---> H
diff_G_H = intvar(-7,7,name="diff_G_H")
model += [diff_G_H == diff(G,H)]
# final_sum = final_sum+diff_G_H
diffs = cpm_array([diff_A_H, diff_A_E, diff_B_F, diff_C_G, diff_C_D,
diff_C_E, diff_D_H, diff_G_H])
model += [final_sum == diff_A_H +
diff_A_E*2 +
diff_B_F*4 +
diff_C_G +
diff_C_D +
diff_C_E +
diff_D_H*3 +
diff_G_H
]
model.minimize(final_sum)
def print_sol():
a_s = ["A","B","C","D","E","F","G","H"]
print("x:", x.value())
print("diffs:",diffs.value())
print("final_sum:", final_sum.value())
order = [a_s[x[i].value()] for i in range(n)]
print("order:","".join(order))
print()
ss = CPM_ortools(model)
# num_solutions = ss.solveAll(display=print_sol)
if ss.solve():
print("ss:",ss.status())
a_s = ["A","B","C","D","E","F","G","H"]
print("x:", x.value())
print("diffs:",diffs.value())
print("final_sum:", final_sum.value())
order = [a_s[x[i].value()] for i in range(n)]
print("order:","".join(order))
print()
else:
print("No solution found")
#
# A more general model
#
def cabling_2(min_val=None):
print("min_val:", min_val)
model = Model()
n = 8
# A <--- 1 cable ---> H
# A <--- 2 cables ---> E
# B <--- 4 cables ---> F
# C <--- 1 cable ---> G
# C <--- 1 cable ---> D
# C <--- 1 cable ---> E
# D <--- 3 cables ---> H
# G <--- 1 cable ---> H
A,B,C,D,E,F,G,H = list(range(n))
cable_struct = [[A,H,1],
[A,E,2],
[B,F,4],
[C,G,1],
[C,D,1],
[C,E,1],
[D,H,3],
[G,H,1]
]
x = intvar(0,n-1,shape=n,name="x")
t = intvar(1,n*n,shape=len(cable_struct),name="t")
final_sum = intvar(0,n*n,name="final_sum")
# all "devices" has distinct positions in rack:
model += [AllDifferent(x),
final_sum == sum(t)]
for i in range(len(cable_struct)):
a,b,num = cable_struct[i]
model += [t[i] == abs(x[a]-x[b])*num]
if min_val == None:
model.minimize(final_sum)
else:
model += [final_sum == min_val]
def print_sol():
a_s = ["A","B","C","D","E","F","G","H"]
print("x:", x.value())
print("t:",t.value())
print("final_sum:", final_sum.value())
order = [a_s[x[i].value()] for i in range(n)]
print("order:","".join(order))
print()
if min_val == None:
ss = CPM_ortools(model)
num_solutions = ss.solve()
print_sol()
return final_sum.value()
else:
ss = CPM_ortools(model)
num_solutions = ss.solveAll(display=print_sol)
print("num_solutions:",num_solutions)
print("cabling_1:")
cabling_1()
print("\ncabling_2:")
min_val = cabling_2()
print("\nFind all optimal solution:")
cabling_2(min_val)