examples/notebook/contrib/3_jugs_mip.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
3 jugs problem using MIP in Google or-tools.
A.k.a. water jugs problem.
Problem from Taha 'Introduction to Operations Research', page 245f .
Compare with the CP model: http://www.hakank.org/google_or_tools/3_jugs_regular
This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
import sys
from ortools.linear_solver import pywraplp
def main(sol='CBC'):
# Create the solver.
print('Solver: ', sol)
solver = pywraplp.Solver.CreateSolver(sol)
if not solver:
return
#
# data
#
n = 15
start = 0 # start node
end = 14 # end node
M = 999 # a large number
nodes = [
'8,0,0', # start
'5,0,3',
'5,3,0',
'2,3,3',
'2,5,1',
'7,0,1',
'7,1,0',
'4,1,3',
'3,5,0',
'3,2,3',
'6,2,0',
'6,0,2',
'1,5,2',
'1,4,3',
'4,4,0' # goal!
]
# distance
d = [[M, 1, M, M, M, M, M, M, 1, M, M, M, M, M, M],
[M, M, 1, M, M, M, M, M, M, M, M, M, M, M, M],
[M, M, M, 1, M, M, M, M, 1, M, M, M, M, M, M],
[M, M, M, M, 1, M, M, M, M, M, M, M, M, M, M],
[M, M, M, M, M, 1, M, M, 1, M, M, M, M, M, M],
[M, M, M, M, M, M, 1, M, M, M, M, M, M, M, M],
[M, M, M, M, M, M, M, 1, 1, M, M, M, M, M, M],
[M, M, M, M, M, M, M, M, M, M, M, M, M, M, 1],
[M, M, M, M, M, M, M, M, M, 1, M, M, M, M, M],
[M, 1, M, M, M, M, M, M, M, M, 1, M, M, M, M],
[M, M, M, M, M, M, M, M, M, M, M, 1, M, M, M],
[M, 1, M, M, M, M, M, M, M, M, M, M, 1, M, M],
[M, M, M, M, M, M, M, M, M, M, M, M, M, 1, M],
[M, 1, M, M, M, M, M, M, M, M, M, M, M, M, 1],
[M, M, M, M, M, M, M, M, M, M, M, M, M, M, M]]
#
# variables
#
# requirements (right hand statement)
rhs = [solver.IntVar(-1, 1, 'rhs[%i]' % i) for i in range(n)]
x = {}
for i in range(n):
for j in range(n):
x[i, j] = solver.IntVar(0, 1, 'x[%i,%i]' % (i, j))
out_flow = [solver.IntVar(0, 1, 'out_flow[%i]' % i) for i in range(n)]
in_flow = [solver.IntVar(0, 1, 'in_flow[%i]' % i) for i in range(n)]
# length of path, to be minimized
z = solver.Sum(
[d[i][j] * x[i, j] for i in range(n) for j in range(n) if d[i][j] < M])
#
# constraints
#
for i in range(n):
if i == start:
solver.Add(rhs[i] == 1)
elif i == end:
solver.Add(rhs[i] == -1)
else:
solver.Add(rhs[i] == 0)
# outflow constraint
for i in range(n):
solver.Add(
out_flow[i] == solver.Sum([x[i, j] for j in range(n) if d[i][j] < M]))
# inflow constraint
for j in range(n):
solver.Add(
in_flow[j] == solver.Sum([x[i, j] for i in range(n) if d[i][j] < M]))
# inflow = outflow
for i in range(n):
solver.Add(out_flow[i] - in_flow[i] == rhs[i])
# objective
objective = solver.Minimize(z)
#
# solution and search
#
solver.Solve()
print()
print('z: ', int(solver.Objective().Value()))
t = start
while t != end:
print(nodes[t], '->', end=' ')
for j in range(n):
if x[t, j].SolutionValue() == 1:
print(nodes[j])
t = j
break
print()
print('walltime :', solver.WallTime(), 'ms')
if sol == 'CBC':
print('iterations:', solver.Iterations())
sol = 'CBC'
if len(sys.argv) > 1:
sol = sys.argv[1]
if sol != 'GLPK' and sol != 'CBC':
print('Solver must be either GLPK or CBC')
sys.exit(1)
main(sol)