173 lines
3.9 KiB
Python
173 lines
3.9 KiB
Python
# Copyright 2010 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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Simple coloring problem using MIP in Google CP Solver.
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Inspired by the GLPK:s model color.mod
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'''
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COLOR, Graph Coloring Problem
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Written in GNU MathProg by Andrew Makhorin <mao@mai2.rcnet.ru>
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Given an undirected loopless graph G = (V, E), where V is a set of
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nodes, E <= V x V is a set of arcs, the Graph Coloring Problem is to
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find a mapping (coloring) F: V -> C, where C = {1, 2, ... } is a set
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of colors whose cardinality is as small as possible, such that
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F(i) != F(j) for every arc (i,j) in E, that is adjacent nodes must
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be assigned different colors.
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'''
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Compare with the MiniZinc model:
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http://www.hakank.org/minizinc/coloring_ip.mzn
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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: http://www.hakank.org/google_or_tools/
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"""
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import sys
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from linear_solver import pywraplp
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def main(sol = 'GLPK'):
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# Create the solver.
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print 'Solver: ', sol
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if sol == 'GLPK':
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# using 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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# max number of colors
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# [we know that 4 suffices for normal maps]
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nc = 5
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# number of nodes
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n = 11
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# set of nodes
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V = range(n)
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num_edges = 20
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#
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# Neighbours
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#
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# This data correspond to the instance myciel3.col from:
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# http://mat.gsia.cmu.edu/COLOR/instances.html
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#
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# Note: 1-based (adjusted below)
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E = [[1, 2],
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[1, 4],
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[1, 7],
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[1, 9],
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[2, 3],
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[2, 6],
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[2, 8],
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[3, 5],
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[3, 7],
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[3, 10],
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[4, 5],
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[4, 6],
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[4, 10],
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[5, 8],
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[5, 9],
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[6, 11],
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[7, 11],
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[8, 11],
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[9, 11],
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[10, 11]]
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#
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# declare variables
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#
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# x[i,c] = 1 means that node i is assigned color c
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x = {}
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for v in V:
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for j in range(nc):
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x[v,j] = solver.IntVar(0, 1, 'v[%i,%i]' % (v, j))
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# u[c] = 1 means that color c is used, i.e. assigned to some node
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u = [solver.IntVar(0, 1, 'u[%i]' % i) for i in range(nc)]
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# number of colors used, to minimize
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obj = solver.Sum(u)
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#
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# constraints
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#
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# each node must be assigned exactly one color
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for i in V:
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solver.Add(solver.Sum([x[i,c] for c in range(nc)]) == 1)
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# adjacent nodes cannot be assigned the same color
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# (and adjust to 0-based)
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for i in range(num_edges):
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for c in range(nc):
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solver.Add(x[E[i][0]-1,c] + x[E[i][1]-1,c] <= u[c])
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# objective
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objective = solver.Minimize(obj)
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#
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# solution
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#
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solver.Solve()
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print
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print "number of colors:", int(solver.objective_value())
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print "colors used:", [int(u[i].solution_value()) for i in range(nc)]
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print
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for v in V:
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print 'v%i' % v, ' color ',
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for c in range(nc):
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if int(x[v,c].solution_value()) == 1:
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print c
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print
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print "wall_time:", solver.wall_time()
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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 = 'GLPK'
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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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