examples/notebook/contrib/stable_marriage.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Stable marriage problem in Google CP Solver.
Problem and OPL model from Pascal Van Hentenryck 'The OPL Optimization Programming Language', page 43ff.
Also, see http://www.comp.rgu.ac.uk/staff/ha/ZCSP/additional_problems/stable_marriage/stable_marriage.pdf
Note: This model is translated from my Comet model http://www.hakank.org/comet/stable_marriage.co I have kept some of the constraint from that code.
Compare with the following models:
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.constraint_solver import pywrapcp
def main(ranks, problem_name):
# Create the solver
solver = pywrapcp.Solver("Stable marriage")
#
# data
#
print("Problem name:", problem_name)
rankMen = ranks["rankMen"]
rankWomen = ranks["rankWomen"]
n = len(rankMen)
#
# declare variables
#
wife = [solver.IntVar(0, n - 1, "wife[%i]" % i) for i in range(n)]
husband = [solver.IntVar(0, n - 1, "husband[%i]" % i) for i in range(n)]
#
# constraints
#
# forall(m in Men)
# cp.post(husband[wife[m]] == m);
for m in range(n):
solver.Add(solver.Element(husband, wife[m]) == m)
# forall(w in Women)
# cp.post(wife[husband[w]] == w);
for w in range(n):
solver.Add(solver.Element(wife, husband[w]) == w)
# forall(m in Men, o in Women)
# cp.post(rankMen[m,o] < rankMen[m, wife[m]] => rankWomen[o,husband[o]] <
# rankWomen[o,m]);
for m in range(n):
for o in range(n):
b1 = solver.IsGreaterCstVar(
solver.Element(rankMen[m], wife[m]), rankMen[m][o])
b2 = (
solver.IsLessCstVar(
solver.Element(rankWomen[o], husband[o]), rankWomen[o][m]))
solver.Add(b1 - b2 <= 0)
# forall(w in Women, o in Men)
# cp.post(rankWomen[w,o] < rankWomen[w,husband[w]] => rankMen[o,wife[o]] <
# rankMen[o,w]);
for w in range(n):
for o in range(n):
b1 = solver.IsGreaterCstVar(
solver.Element(rankWomen[w], husband[w]), rankWomen[w][o])
b2 = solver.IsLessCstVar(
solver.Element(rankMen[o], wife[o]), rankMen[o][w])
solver.Add(b1 - b2 <= 0)
#
# solution and search
#
solution = solver.Assignment()
solution.Add(wife)
solution.Add(husband)
db = solver.Phase(wife + husband, solver.CHOOSE_FIRST_UNBOUND,
solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db)
num_solutions = 0
solutions = []
while solver.NextSolution():
# solutions.append([x[i].Value() for i in range(x_len)])
print("wife : ", [wife[i].Value() for i in range(n)])
print("husband: ", [husband[i].Value() for i in range(n)])
print()
num_solutions += 1
solver.EndSearch()
print()
print("num_solutions:", num_solutions)
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
print("#############")
print()
#
# From Van Hentenryck's OPL book
#
van_hentenryck = {
"rankWomen": [[1, 2, 4, 3, 5], [3, 5, 1, 2, 4], [5, 4, 2, 1, 3],
[1, 3, 5, 4, 2], [4, 2, 3, 5, 1]],
"rankMen": [[5, 1, 2, 4, 3], [4, 1, 3, 2, 5], [5, 3, 2, 4, 1],
[1, 5, 4, 3, 2], [4, 3, 2, 1, 5]]
}
#
# Data from MathWorld
# http://mathworld.wolfram.com/StableMarriageProblem.html
#
mathworld = {
"rankWomen": [[3, 1, 5, 2, 8, 7, 6, 9, 4], [9, 4, 8, 1, 7, 6, 3, 2, 5],
[3, 1, 8, 9, 5, 4, 2, 6, 7], [8, 7, 5, 3, 2, 6, 4, 9, 1],
[6, 9, 2, 5, 1, 4, 7, 3, 8], [2, 4, 5, 1, 6, 8, 3, 9, 7],
[9, 3, 8, 2, 7, 5, 4, 6, 1], [6, 3, 2, 1, 8, 4, 5, 9, 7],
[8, 2, 6, 4, 9, 1, 3, 7, 5]],
"rankMen": [[7, 3, 8, 9, 6, 4, 2, 1, 5], [5, 4, 8, 3, 1, 2, 6, 7, 9],
[4, 8, 3, 9, 7, 5, 6, 1, 2], [9, 7, 4, 2, 5, 8, 3, 1, 6],
[2, 6, 4, 9, 8, 7, 5, 1, 3], [2, 7, 8, 6, 5, 3, 4, 1, 9],
[1, 6, 2, 3, 8, 5, 4, 9, 7], [5, 6, 9, 1, 2, 8, 4, 3, 7],
[6, 1, 4, 7, 5, 8, 3, 9, 2]]
}
#
# Data from
# http://www.csee.wvu.edu/~ksmani/courses/fa01/random/lecnotes/lecture5.pdf
#
problem3 = {
"rankWomen": [[1, 2, 3, 4], [4, 3, 2, 1], [1, 2, 3, 4], [3, 4, 1, 2]],
"rankMen": [[1, 2, 3, 4], [2, 1, 3, 4], [1, 4, 3, 2], [4, 3, 1, 2]]
}
#
# Data from
# http://www.comp.rgu.ac.uk/staff/ha/ZCSP/additional_problems/stable_marriage/stable_marriage.pdf
# page 4
#
problem4 = {
"rankWomen": [[1, 5, 4, 6, 2, 3], [4, 1, 5, 2, 6, 3], [6, 4, 2, 1, 5, 3],
[1, 5, 2, 4, 3, 6], [4, 2, 1, 5, 6, 3], [2, 6, 3, 5, 1, 4]],
"rankMen": [[1, 4, 2, 5, 6, 3], [3, 4, 6, 1, 5, 2], [1, 6, 4, 2, 3, 5],
[6, 5, 3, 4, 2, 1], [3, 1, 2, 4, 5, 6], [2, 3, 1, 6, 5, 4]]
}
main(van_hentenryck, "Van Hentenryck")
main(mathworld, "MathWorld")
main(problem3, "Problem 3")
main(problem4, "Problem4")