130 lines
3.4 KiB
Python
130 lines
3.4 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
|
|
#
|
|
# Licensed under the Apache License, Version 2.0 (the 'License');
|
|
# you may not use this file except in compliance with the License.
|
|
# You may obtain a copy of the License at
|
|
#
|
|
# http://www.apache.org/licenses/LICENSE-2.0
|
|
#
|
|
# Unless required by applicable law or agreed to in writing, software
|
|
# distributed under the License is distributed on an 'AS IS' BASIS,
|
|
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
# See the License for the specific language governing permissions and
|
|
# limitations under the License.
|
|
|
|
"""
|
|
|
|
Max flow problem in Google CP Solver.
|
|
|
|
From Taha 'Introduction to Operations Research', Example 6.4-2
|
|
|
|
Translated from the AMPL code at
|
|
http://taha.ineg.uark.edu/maxflo.txt
|
|
|
|
Compare with the following model:
|
|
* MiniZinc: http://www.hakank.org/minizinc/max_flow_taha.mzn
|
|
|
|
This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
|
|
Also see my other Google CP Solver models:
|
|
http://www.hakank.org/google_or_tools/
|
|
"""
|
|
from __future__ import print_function
|
|
from ortools.constraint_solver import pywrapcp
|
|
|
|
|
|
def main():
|
|
|
|
# Create the solver.
|
|
solver = pywrapcp.Solver('Max flow problem, Taha')
|
|
|
|
#
|
|
# data
|
|
#
|
|
n = 5
|
|
start = 0
|
|
end = n - 1
|
|
|
|
nodes = list(range(n))
|
|
|
|
# cost matrix
|
|
c = [
|
|
[0, 20, 30, 10, 0],
|
|
[0, 0, 40, 0, 30],
|
|
[0, 0, 0, 10, 20],
|
|
[0, 0, 5, 0, 20],
|
|
[0, 0, 0, 0, 0]
|
|
]
|
|
|
|
#
|
|
# declare variables
|
|
#
|
|
x = {}
|
|
for i in nodes:
|
|
for j in nodes:
|
|
x[i, j] = solver.IntVar(0, c[i][j], 'x[%i,%i]' % (i, j))
|
|
|
|
x_flat = [x[i, j] for i in nodes for j in nodes]
|
|
out_flow = [solver.IntVar(0, 10000, 'out_flow[%i]' % i) for i in nodes]
|
|
in_flow = [solver.IntVar(0, 10000, 'in_flow[%i]' % i) for i in nodes]
|
|
|
|
total = solver.IntVar(0, 10000, 'z')
|
|
|
|
#
|
|
# constraints
|
|
#
|
|
cost_sum = solver.Sum([x[start, j] for j in nodes if c[start][j] > 0])
|
|
solver.Add(total == cost_sum)
|
|
|
|
for i in nodes:
|
|
in_flow_sum = solver.Sum([x[j, i] for j in nodes if c[j][i] > 0])
|
|
solver.Add(in_flow[i] == in_flow_sum)
|
|
|
|
out_flow_sum = solver.Sum([x[i, j] for j in nodes if c[i][j] > 0])
|
|
solver.Add(out_flow[i] == out_flow_sum)
|
|
|
|
# in_flow == out_flow
|
|
for i in nodes:
|
|
if i != start and i != end:
|
|
solver.Add(out_flow[i] - in_flow[i] == 0)
|
|
|
|
s1 = [x[i, start] for i in nodes if c[i][start] > 0]
|
|
if len(s1) > 0:
|
|
solver.Add(solver.Sum([x[i, start]
|
|
for i in nodes if c[i][start] > 0] == 0))
|
|
|
|
s2 = [x[end, j] for j in nodes if c[end][j] > 0]
|
|
if len(s2) > 0:
|
|
solver.Add(solver.Sum([x[end, j]
|
|
for j in nodes if c[end][j] > 0]) == 0)
|
|
|
|
# objective: maximize total cost
|
|
objective = solver.Maximize(total, 1)
|
|
|
|
#
|
|
# solution and search
|
|
#
|
|
db = solver.Phase(x_flat,
|
|
solver.INT_VAR_DEFAULT,
|
|
solver.ASSIGN_MAX_VALUE)
|
|
|
|
solver.NewSearch(db, [objective])
|
|
num_solutions = 0
|
|
while solver.NextSolution():
|
|
num_solutions += 1
|
|
print('total:', total.Value())
|
|
print('in_flow:', [in_flow[i].Value() for i in nodes])
|
|
print('out_flow:', [out_flow[i].Value() for i in nodes])
|
|
for i in nodes:
|
|
for j in nodes:
|
|
print('%2i' % x[i, j].Value(), end=' ')
|
|
print()
|
|
print()
|
|
|
|
print('num_solutions:', num_solutions)
|
|
print('failures:', solver.Failures())
|
|
print('branches:', solver.Branches())
|
|
print('WallTime:', solver.WallTime(), 'ms')
|
|
|
|
if __name__ == '__main__':
|
|
main()
|