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knapsack_2d_sat.py
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knapsack_2d_sat.py
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#!/usr/bin/env python3
# Copyright 2010-2021 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.
"""Solver a 2D rectangle knapsack problem.
This code is adapted from
https://yetanothermathprogrammingconsultant.blogspot.com/2021/10/2d-knapsack-problem.html
"""
import io
from absl import app
from absl import flags
import numpy as np
import pandas as pd
from google.protobuf import text_format
from ortools.sat.python import cp_model
FLAGS = flags.FLAGS
flags.DEFINE_string('output_proto', '',
'Output file to write the cp_model proto to.')
flags.DEFINE_string('params', 'num_search_workers:16,log_search_progress:true',
'Sat solver parameters.')
flags.DEFINE_string('model', 'rotation',
'\'duplicate\' or \'rotation\' or \'optional\'')
def build_data():
"""Build the data frame."""
data = """
item width height available value color
k1 20 4 2 338.984 blue
k2 12 17 6 849.246 orange
k3 20 12 2 524.022 green
k4 16 7 9 263.303 red
k5 3 6 3 113.436 purple
k6 13 5 3 551.072 brown
k7 4 7 6 86.166 pink
k8 6 18 8 755.094 grey
k9 14 2 7 223.516 olive
k10 9 11 5 369.560 cyan
"""
data = pd.read_table(io.StringIO(data), sep=r'\s+')
print('Input data')
print(data)
max_height = 20
max_width = 30
print(f'Container max_width:{max_width} max_height:{max_height}')
print(f'#Items: {len(data.index)}')
return (data, max_height, max_width)
def solve_with_duplicate_items(data, max_height, max_width):
"""Solve the problem by building 2 items (rotated or not) for each item."""
# Derived data (expanded to individual items).
data_widths = data['width'].to_numpy()
data_heights = data['height'].to_numpy()
data_availability = data['available'].to_numpy()
data_values = data['value'].to_numpy()
# Non duplicated items data.
base_item_widths = np.repeat(data_widths, data_availability)
base_item_heights = np.repeat(data_heights, data_availability)
base_item_values = np.repeat(data_values, data_availability)
num_data_items = len(base_item_values)
# Create rotated items by duplicating.
item_widths = np.concatenate((base_item_widths, base_item_heights))
item_heights = np.concatenate((base_item_heights, base_item_widths))
item_values = np.concatenate((base_item_values, base_item_values))
num_items = len(item_values)
# OR-Tools model
model = cp_model.CpModel()
# Variables
x_starts = []
x_ends = []
y_starts = []
y_ends = []
is_used = []
x_intervals = []
y_intervals = []
for i in range(num_items):
## Is the item used?
is_used.append(model.NewBoolVar(f'is_used{i}'))
## Item coordinates.
x_starts.append(model.NewIntVar(0, max_width, f'x_start{i}'))
x_ends.append(model.NewIntVar(0, max_width, f'x_end{i}'))
y_starts.append(model.NewIntVar(0, max_height, f'y_start{i}'))
y_ends.append(model.NewIntVar(0, max_height, f'y_end{i}'))
## Interval variables.
x_intervals.append(
model.NewIntervalVar(x_starts[i], item_widths[i] * is_used[i],
x_ends[i], f'x_interval{i}'))
y_intervals.append(
model.NewIntervalVar(y_starts[i], item_heights[i] * is_used[i],
y_ends[i], f'y_interval{i}'))
# Constraints.
## Only one of non-rotated/rotated pair can be used.
for i in range(num_data_items):
model.Add(is_used[i] + is_used[i + num_data_items] <= 1)
## 2D no overlap.
model.AddNoOverlap2D(x_intervals, y_intervals)
## Objective.
model.Maximize(cp_model.LinearExpr.ScalProd(is_used, item_values))
# Output proto to file.
if FLAGS.output_proto:
print('Writing proto to %s' % FLAGS.output_proto)
with open(FLAGS.output_proto, 'w') as text_file:
text_file.write(str(model))
# Solve model.
solver = cp_model.CpSolver()
if FLAGS.params:
text_format.Parse(FLAGS.params, solver.parameters)
status = solver.Solve(model)
# Report solution.
if status == cp_model.OPTIMAL:
used = {i for i in range(num_items) if solver.BooleanValue(is_used[i])}
data = pd.DataFrame({
'x_start': [solver.Value(x_starts[i]) for i in used],
'y_start': [solver.Value(y_starts[i]) for i in used],
'item_width': [item_widths[i] for i in used],
'item_height': [item_heights[i] for i in used],
'x_end': [solver.Value(x_ends[i]) for i in used],
'y_end': [solver.Value(y_ends[i]) for i in used],
'item_value': [item_values[i] for i in used]
})
print(data)
def solve_with_duplicate_optional_items(data, max_height, max_width):
"""Solve the problem by building 2 optional items (rotated or not) for each item."""
# Derived data (expanded to individual items).
data_widths = data['width'].to_numpy()
data_heights = data['height'].to_numpy()
data_availability = data['available'].to_numpy()
data_values = data['value'].to_numpy()
# Non duplicated items data.
base_item_widths = np.repeat(data_widths, data_availability)
base_item_heights = np.repeat(data_heights, data_availability)
base_item_values = np.repeat(data_values, data_availability)
num_data_items = len(base_item_values)
# Create rotated items by duplicating.
item_widths = np.concatenate((base_item_widths, base_item_heights))
item_heights = np.concatenate((base_item_heights, base_item_widths))
item_values = np.concatenate((base_item_values, base_item_values))
num_items = len(item_values)
# OR-Tools model
model = cp_model.CpModel()
# Variables
x_starts = []
y_starts = []
is_used = []
x_intervals = []
y_intervals = []
for i in range(num_items):
## Is the item used?
is_used.append(model.NewBoolVar(f'is_used{i}'))
## Item coordinates.
x_starts.append(
model.NewIntVar(0, max_width - int(item_widths[i]), f'x_start{i}'))
y_starts.append(
model.NewIntVar(0, max_height - int(item_heights[i]),
f'y_start{i}'))
## Interval variables.
x_intervals.append(
model.NewOptionalFixedSizeIntervalVar(x_starts[i], item_widths[i],
is_used[i], f'x_interval{i}'))
y_intervals.append(
model.NewOptionalFixedSizeIntervalVar(y_starts[i], item_heights[i],
is_used[i], f'y_interval{i}'))
# Constraints.
## Only one of non-rotated/rotated pair can be used.
for i in range(num_data_items):
model.Add(is_used[i] + is_used[i + num_data_items] <= 1)
## 2D no overlap.
model.AddNoOverlap2D(x_intervals, y_intervals)
## Objective.
model.Maximize(cp_model.LinearExpr.ScalProd(is_used, item_values))
# Output proto to file.
if FLAGS.output_proto:
print('Writing proto to %s' % FLAGS.output_proto)
with open(FLAGS.output_proto, 'w') as text_file:
text_file.write(str(model))
# Solve model.
solver = cp_model.CpSolver()
if FLAGS.params:
text_format.Parse(FLAGS.params, solver.parameters)
status = solver.Solve(model)
# Report solution.
if status == cp_model.OPTIMAL:
used = {i for i in range(num_items) if solver.BooleanValue(is_used[i])}
data = pd.DataFrame({
'x_start': [solver.Value(x_starts[i]) for i in used],
'y_start': [solver.Value(y_starts[i]) for i in used],
'item_width': [item_widths[i] for i in used],
'item_height': [item_heights[i] for i in used],
'x_end': [solver.Value(x_starts[i]) + item_widths[i] for i in used],
'y_end': [
solver.Value(y_starts[i]) + item_heights[i] for i in used
],
'item_value': [item_values[i] for i in used]
})
print(data)
def solve_with_rotations(data, max_height, max_width):
"""Solve the problem by rotating items."""
# Derived data (expanded to individual items).
data_widths = data['width'].to_numpy()
data_heights = data['height'].to_numpy()
data_availability = data['available'].to_numpy()
data_values = data['value'].to_numpy()
item_widths = np.repeat(data_widths, data_availability)
item_heights = np.repeat(data_heights, data_availability)
item_values = np.repeat(data_values, data_availability)
num_items = len(item_widths)
# OR-Tools model.
model = cp_model.CpModel()
# Coordinate variables for each rectangle.
x_starts = []
x_sizes = []
x_ends = []
y_starts = []
y_sizes = []
y_ends = []
x_intervals = []
y_intervals = []
for i in range(num_items):
sizes = [0, int(item_widths[i]), int(item_heights[i])]
# X coordinates.
x_starts.append(model.NewIntVar(0, max_width, f'x_start{i}'))
x_sizes.append(
model.NewIntVarFromDomain(cp_model.Domain.FromValues(sizes),
f'x_size{i}'))
x_ends.append(model.NewIntVar(0, max_width, f'x_end{i}'))
# Y coordinates.
y_starts.append(model.NewIntVar(0, max_height, f'y_start{i}'))
y_sizes.append(
model.NewIntVarFromDomain(cp_model.Domain.FromValues(sizes),
f'y_size{i}'))
y_ends.append(model.NewIntVar(0, max_height, f'y_end{i}'))
## Interval variables
x_intervals.append(
model.NewIntervalVar(x_starts[i], x_sizes[i], x_ends[i],
f'x_interval{i}'))
y_intervals.append(
model.NewIntervalVar(y_starts[i], y_sizes[i], y_ends[i],
f'y_interval{i}'))
# is_used[i] == True if and only if item i is selected.
is_used = []
# Constraints.
## for each item, decide is unselected, no_rotation, rotated.
for i in range(num_items):
not_selected = model.NewBoolVar(f'not_selected_{i}')
no_rotation = model.NewBoolVar(f'no_rotation_{i}')
rotated = model.NewBoolVar(f'rotated_{i}')
### Exactly one state must be chosen.
model.Add(not_selected + no_rotation + rotated == 1)
### Define height and width according to the state.
dim1 = item_widths[i]
dim2 = item_heights[i]
model.Add(x_sizes[i] == 0).OnlyEnforceIf(not_selected)
model.Add(y_sizes[i] == 0).OnlyEnforceIf(not_selected)
model.Add(x_sizes[i] == dim1).OnlyEnforceIf(no_rotation)
model.Add(y_sizes[i] == dim2).OnlyEnforceIf(no_rotation)
model.Add(x_sizes[i] == dim2).OnlyEnforceIf(rotated)
model.Add(y_sizes[i] == dim1).OnlyEnforceIf(rotated)
is_used.append(not_selected.Not())
## 2D no overlap.
model.AddNoOverlap2D(x_intervals, y_intervals)
# Objective.
model.Maximize(cp_model.LinearExpr.ScalProd(is_used, item_values))
# Output proto to file.
if FLAGS.output_proto:
print('Writing proto to %s' % FLAGS.output_proto)
with open(FLAGS.output_proto, 'w') as text_file:
text_file.write(str(model))
# Solve model.
solver = cp_model.CpSolver()
if FLAGS.params:
text_format.Parse(FLAGS.params, solver.parameters)
status = solver.Solve(model)
# Report solution.
if status == cp_model.OPTIMAL:
used = {i for i in range(num_items) if solver.BooleanValue(is_used[i])}
data = pd.DataFrame({
'x_start': [solver.Value(x_starts[i]) for i in used],
'y_start': [solver.Value(y_starts[i]) for i in used],
'item_width': [solver.Value(x_sizes[i]) for i in used],
'item_height': [solver.Value(y_sizes[i]) for i in used],
'x_end': [solver.Value(x_ends[i]) for i in used],
'y_end': [solver.Value(y_ends[i]) for i in used],
'item_value': [item_values[i] for i in used]
})
print(data)
def main(_):
"""Solve the problem with all models."""
data, max_height, max_width = build_data()
if FLAGS.model == 'duplicate':
solve_with_duplicate_items(data, max_height, max_width)
elif FLAGS.model == 'optional':
solve_with_duplicate_optional_items(data, max_height, max_width)
else:
solve_with_rotations(data, max_height, max_width)
if __name__ == '__main__':
app.run(main)