176 lines
4.5 KiB
Python
176 lines
4.5 KiB
Python
# Copyright 2011 Hakan Kjellerstrand hakank@bonetmail.com
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""
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3 jugs problem using MIP in Google or-tools.
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A.k.a. water jugs problem.
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Problem from Taha 'Introduction to Operations Research',
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page 245f .
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Compare with the CP model:
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http://www.hakank.org/google_or_tools/3_jugs_regular
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This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
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Also see my other Google CP Solver models:
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http://www.hakank.org/google_or_tools/
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"""
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import sys
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from ortools.linear_solver import pywraplp
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def main(sol='CBC'):
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# Create the solver.
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print 'Solver: ', sol
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# using GLPK
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if sol == 'GLPK':
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solver = pywraplp.Solver('CoinsGridGLPK',
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pywraplp.Solver.GLPK_MIXED_INTEGER_PROGRAMMING)
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else:
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# Using CBC
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solver = pywraplp.Solver('CoinsGridCLP',
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pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
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#
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# data
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#
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n = 15
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start = 0 # start node
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end = 14 # end node
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M = 999 # a large number
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nodes = ['8,0,0', # start
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'5,0,3',
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'5,3,0',
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'2,3,3',
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'2,5,1',
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'7,0,1',
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'7,1,0',
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'4,1,3',
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'3,5,0',
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'3,2,3',
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'6,2,0',
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'6,0,2',
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'1,5,2',
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'1,4,3',
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'4,4,0' # goal!
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]
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# distance
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d = [[M, 1, M, M, M, M, M, M, 1, M, M, M, M, M, M],
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[M, M, 1, M, M, M, M, M, M, M, M, M, M, M, M],
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[M, M, M, 1, M, M, M, M, 1, M, M, M, M, M, M],
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[M, M, M, M, 1, M, M, M, M, M, M, M, M, M, M],
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[M, M, M, M, M, 1, M, M, 1, M, M, M, M, M, M],
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[M, M, M, M, M, M, 1, M, M, M, M, M, M, M, M],
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[M, M, M, M, M, M, M, 1, 1, M, M, M, M, M, M],
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[M, M, M, M, M, M, M, M, M, M, M, M, M, M, 1],
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[M, M, M, M, M, M, M, M, M, 1, M, M, M, M, M],
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[M, 1, M, M, M, M, M, M, M, M, 1, M, M, M, M],
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[M, M, M, M, M, M, M, M, M, M, M, 1, M, M, M],
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[M, 1, M, M, M, M, M, M, M, M, M, M, 1, M, M],
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[M, M, M, M, M, M, M, M, M, M, M, M, M, 1, M],
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[M, 1, M, M, M, M, M, M, M, M, M, M, M, M, 1],
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[M, M, M, M, M, M, M, M, M, M, M, M, M, M, M]]
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#
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# variables
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#
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# requirements (right hand statement)
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rhs = [solver.IntVar(-1, 1, 'rhs[%i]' % i) for i in range(n)]
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x = {}
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for i in range(n):
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for j in range(n):
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x[i, j] = solver.IntVar(0, 1, 'x[%i,%i]' % (i, j))
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out_flow = [solver.IntVar(0, 1, 'out_flow[%i]' % i) for i in range(n)]
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in_flow = [solver.IntVar(0, 1, 'in_flow[%i]' % i) for i in range(n)]
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# length of path, to be minimized
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z = solver.Sum([d[i][j] * x[i, j]
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for i in range(n)
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for j in range(n) if d[i][j] < M])
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#
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# constraints
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#
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for i in range(n):
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if i == start:
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solver.Add(rhs[i] == 1)
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elif i == end:
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solver.Add(rhs[i] == -1)
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else:
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solver.Add(rhs[i] == 0)
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# outflow constraint
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for i in range(n):
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solver.Add(out_flow[i] == solver.Sum([x[i, j]
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for j in range(n)
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if d[i][j] < M]))
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# inflow constraint
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for j in range(n):
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solver.Add(in_flow[j] == solver.Sum([x[i, j]
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for i in range(n)
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if d[i][j] < M]))
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# inflow = outflow
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for i in range(n):
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solver.Add(out_flow[i] - in_flow[i] == rhs[i])
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# objective
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objective = solver.Minimize(z)
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#
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# solution and search
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#
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solver.Solve()
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print
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print 'z: ', int(solver.Objective().Value())
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t = start
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while t != end:
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print nodes[t], '->',
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for j in range(n):
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if x[t, j].SolutionValue() == 1:
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print nodes[j]
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t = j
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break
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print
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print 'walltime :', solver.WallTime(), 'ms'
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if sol == 'CBC':
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print 'iterations:', solver.Iterations()
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if __name__ == '__main__':
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sol = 'CBC'
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if len(sys.argv) > 1:
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sol = sys.argv[1]
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if sol != 'GLPK' and sol != 'CBC':
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print 'Solver must be either GLPK or CBC'
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sys.exit(1)
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main(sol)
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