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balance_group_sat.py
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# Copyright 2010-2018 Google LLC
# 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.
"""We are trying to group items in equal sized groups.
Each item has a color and a value. We want the sum of values of each group to
be as close to the average as possible.
Furthermore, if one color is an a group, at least k items with this color must
be in that group.
"""
from __future__ import print_function
from __future__ import division
from ortools.sat.python import cp_model
# Create a solution printer.
class SolutionPrinter(cp_model.CpSolverSolutionCallback):
"""Print intermediate solutions."""
def __init__(self, values, colors, all_groups, all_items, item_in_group):
cp_model.CpSolverSolutionCallback.__init__(self)
self.__solution_count = 0
self.__values = values
self.__colors = colors
self.__all_groups = all_groups
self.__all_items = all_items
self.__item_in_group = item_in_group
def on_solution_callback(self):
print('Solution %i' % self.__solution_count)
self.__solution_count += 1
print(' objective value = %i' % self.ObjectiveValue())
groups = {}
sums = {}
for g in self.__all_groups:
groups[g] = []
sums[g] = 0
for item in self.__all_items:
if self.BooleanValue(self.__item_in_group[(item, g)]):
groups[g].append(item)
sums[g] += self.__values[item]
for g in self.__all_groups:
group = groups[g]
print('group %i: sum = %0.2f [' % (g, sums[g]), end='')
for item in group:
value = self.__values[item]
color = self.__colors[item]
print(' (%i, %i, %i)' % (item, value, color), end='')
print(']')
def main():
# Data.
num_groups = 10
num_items = 100
num_colors = 3
min_items_of_same_color_per_group = 4
all_groups = range(num_groups)
all_items = range(num_items)
all_colors = range(num_colors)
# Values for each items.
values = [1 + i + (i * i // 200) for i in all_items]
# Color for each item (simple modulo).
colors = [i % num_colors for i in all_items]
sum_of_values = sum(values)
average_sum_per_group = sum_of_values // num_groups
num_items_per_group = num_items // num_groups
# Collect all items in a given color.
items_per_color = {}
for c in all_colors:
items_per_color[c] = []
for i in all_items:
if colors[i] == c:
items_per_color[c].append(i)
print('Model has %i items, %i groups, and %i colors' %
(num_items, num_groups, num_colors))
print(' average sum per group = %i' % average_sum_per_group)
# Model.
model = cp_model.CpModel()
item_in_group = {}
for i in all_items:
for g in all_groups:
item_in_group[(i, g)] = model.NewBoolVar('item %d in group %d' %
(i, g))
# Each group must have the same size.
for g in all_groups:
model.Add(
sum(item_in_group[(i, g)]
for i in all_items) == num_items_per_group)
# One item must belong to exactly one group.
for i in all_items:
model.Add(sum(item_in_group[(i, g)] for g in all_groups) == 1)
# The deviation of the sum of each items in a group against the average.
e = model.NewIntVar(0, 550, 'epsilon')
# Constrain the sum of values in one group around the average sum per group.
for g in all_groups:
model.Add(
sum(item_in_group[(i, g)] * values[i]
for i in all_items) <= average_sum_per_group + e)
model.Add(
sum(item_in_group[(i, g)] * values[i]
for i in all_items) >= average_sum_per_group - e)
# color_in_group variables.
color_in_group = {}
for g in all_groups:
for c in all_colors:
color_in_group[(c, g)] = model.NewBoolVar(
'color %d is in group %d' % (c, g))
# Item is in a group implies its color is in that group.
for i in all_items:
for g in all_groups:
model.AddImplication(item_in_group[(i, g)],
color_in_group[(colors[i], g)])
# If a color is in a group, it must contains at least
# min_items_of_same_color_per_group items from that color.
for c in all_colors:
for g in all_groups:
literal = color_in_group[(c, g)]
model.Add(
sum(item_in_group[(i, g)] for i in items_per_color[c]) >=
min_items_of_same_color_per_group).OnlyEnforceIf(literal)
# Compute the maximum number of colors in a group.
max_color = num_items_per_group // min_items_of_same_color_per_group
# Redundant contraint: The problem does not solve in reasonable time without it.
if max_color < num_colors:
for g in all_groups:
model.Add(
sum(color_in_group[(c, g)] for c in all_colors) <= max_color)
# Minimize epsilon
model.Minimize(e)
solver = cp_model.CpSolver()
solution_printer = SolutionPrinter(values, colors, all_groups, all_items,
item_in_group)
status = solver.SolveWithSolutionCallback(model, solution_printer)
if status == cp_model.OPTIMAL:
print('Optimal epsilon: %i' % solver.ObjectiveValue())
print('Statistics')
print(' - conflicts : %i' % solver.NumConflicts())
print(' - branches : %i' % solver.NumBranches())
print(' - wall time : %f s' % solver.WallTime())
else:
print('No solution found')
if __name__ == '__main__':
main()