new example
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Laurent Perron
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examples/python/wedding_optimal_chart_sat.py
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examples/python/wedding_optimal_chart_sat.py
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#
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# Copyright 2018 Google.
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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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from __future__ import print_function
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from ortools.sat.python import cp_model
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import time
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"""
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Finding an optimal wedding seating chart.
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From
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Meghan L. Bellows and J. D. Luc Peterson
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"Finding an optimal seating chart for a wedding"
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http://www.improbable.com/news/2012/Optimal-seating-chart.pdf
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http://www.improbable.com/2012/02/12/finding-an-optimal-seating-chart-for-a-wedding
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Every year, millions of brides (not to mention their mothers, future
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mothers-in-law, and occasionally grooms) struggle with one of the
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most daunting tasks during the wedding-planning process: the
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seating chart. The guest responses are in, banquet hall is booked,
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menu choices have been made. You think the hard parts are over,
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but you have yet to embark upon the biggest headache of them all.
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In order to make this process easier, we present a mathematical
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formulation that models the seating chart problem. This model can
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be solved to find the optimal arrangement of guests at tables.
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At the very least, it can provide a starting point and hopefully
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minimize stress and arguments.
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Adapted from https://github.com/google/or-tools/blob/master/examples/csharp/wedding_optimal_chart.cs
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"""
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class WeddingChartPrinter(cp_model.CpSolverSolutionCallback):
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"""Print intermediate solutions."""
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def __init__(self, seats, names, num_tables, num_guests):
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self.__solution_count = 0
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self.__start_time = time.time()
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self.__seats = seats
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self.__names = names
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self.__num_tables = num_tables
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self.__num_guests = num_guests
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def NewSolution(self):
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current_time = time.time()
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objective = self.ObjectiveValue()
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print('Solution %i, time = %f s, objective = %i' %
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(self.__solution_count, current_time - self.__start_time, objective))
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self.__solution_count += 1
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for t in range(self.__num_tables):
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print("Table %d: " % t);
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for g in range(self.__num_guests):
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if self.Value(self.__seats[(t, g)]):
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print(' ' + self.__names[g])
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def NumSolutions(self):
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return self.__solution_count
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def main():
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#
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# Data
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#
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# Easy problem (from the paper)
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# num_tables = 2
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# table_capacity = 10
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# min_known_neighbors = 1
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# Slightly harder problem (also from the paper)
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num_tables = 5
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table_capacity = 4
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min_known_neighbors = 1
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# Connection matrix: who knows who, and how strong
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# is the relation
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C = [
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[ 1,50, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
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[50, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
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[ 1, 1, 1,50, 1, 1, 1, 1,10, 0, 0, 0, 0, 0, 0, 0, 0],
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[ 1, 1,50, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
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[ 1, 1, 1, 1, 1,50, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
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[ 1, 1, 1, 1,50, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
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[ 1, 1, 1, 1, 1, 1, 1,50, 1, 0, 0, 0, 0, 0, 0, 0, 0],
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[ 1, 1, 1, 1, 1, 1,50, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
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[ 1, 1,10, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,50, 1, 1, 1, 1, 1, 1],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0,50, 1, 1, 1, 1, 1, 1, 1],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1]
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]
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# Names of the guests. B: Bride side, G: Groom side
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names = [
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"Deb (B)",
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"John (B)",
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"Martha (B)",
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"Travis (B)",
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"Allan (B)",
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"Lois (B)",
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"Jayne (B)",
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"Brad (B)",
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"Abby (B)",
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"Mary Helen (G)",
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"Lee (G)",
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"Annika (G)",
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"Carl (G)",
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"Colin (G)",
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"Shirley (G)",
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"DeAnn (G)",
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"Lori (G)"
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]
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num_guests = len(C)
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all_tables = range(num_tables)
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all_guests = range(num_guests)
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# Create the cp model.
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model = cp_model.CpModel()
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#
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# Decision variables
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#
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seats = {}
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for t in all_tables:
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for g in all_guests:
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seats[(t, g)] = model.NewBoolVar('guest %i seats on table %i' % (g, t))
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colocated = {}
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for g1 in range(num_guests - 1):
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for g2 in range(g1 + 1, num_guests):
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colocated[(g1, g2)] = model.NewBoolVar(
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'guest %i seats with guest %i' % (g1, g2))
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same_table = {}
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for g1 in range(num_guests - 1):
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for g2 in range(g1 + 1, num_guests):
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for t in all_tables:
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same_table[(g1, g2, t)] = model.NewBoolVar(
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'guest %i seats with guest %i on table %i' % (g1, g2, t))
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# Objective
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model.Maximize(sum(C[g1][g2] * colocated[g1, g2]
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for g1 in range(num_guests - 1)
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for g2 in range(g1 + 1, num_guests)
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if C[g1][g2] > 0))
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#
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# Constraints
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#
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# Everybody seats at one table.
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for g in all_guests:
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model.Add(sum(seats[(t, g)] for t in all_tables) == 1)
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# Tables have a max capacity.
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for t in all_tables:
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model.Add(sum(seats[(t, g)] for g in all_guests) <= table_capacity)
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# Link colocated with seats
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for g1 in range(num_guests - 1):
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for g2 in range(g1 + 1, num_guests):
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for t in all_tables:
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# Maintain same_table.
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model.AddBoolOr([seats[(t, g1)].Not(),
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seats[(t, g2)].Not(),
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same_table[(g1, g2, t)]])
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# Link colocated and same_table.
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model.Add(sum(same_table[(g1, g2, t)]
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for t in all_tables) == colocated[(g1, g2)])
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# Min known neighbors rule.
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for t in all_tables:
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model.Add(sum(same_table[(g1, g2, t)]
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for g1 in range(num_guests - 1)
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for g2 in range(g1 + 1, num_guests)
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for t in all_tables
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if C[g1][g2] > 0) >= min_known_neighbors)
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# Symmetry breaking. First guest seats on the first table.
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model.Add(seats[(0, 0)] == 1)
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### Solve model.
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solver = cp_model.CpSolver()
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solution_printer = WeddingChartPrinter(seats, names, num_tables, num_guests)
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status = solver.SolveWithSolutionObserver(model, solution_printer)
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print('Statistics')
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print(' - conflicts : %i' % solver.NumConflicts())
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print(' - branches : %i' % solver.NumBranches())
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print(' - wall time : %f ms' % solver.WallTime())
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print(' - num solutions: %i' % solution_printer.NumSolutions())
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if __name__ == '__main__':
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main()
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