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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.
"""Cutting stock problem with the objective to minimize wasted space."""
from __future__ import print_function
import argparse
import collections
import time
from ortools.linear_solver import pywraplp
from ortools.sat.python import cp_model
PARSER = argparse.ArgumentParser()
PARSER.add_argument(
'--solver', default='sat', help='Method used to solve: sat, mip.')
PARSER.add_argument(
'--output_proto',
default='',
help='Output file to write the cp_model proto to.')
DESIRED_LENGTHS = [
2490, 3980, 2490, 3980, 2391, 2391, 2391, 596, 596, 596, 2456, 2456, 3018,
938, 3018, 938, 943, 3018, 943, 3018, 2490, 3980, 2490, 3980, 2391, 2391,
2391, 596, 596, 596, 2456, 2456, 3018, 938, 3018, 938, 943, 3018, 943,
3018, 2890, 3980, 2890, 3980, 2391, 2391, 2391, 596, 596, 596, 2856, 2856,
3018, 938, 3018, 938, 943, 3018, 943, 3018, 3290, 3980, 3290, 3980, 2391,
2391, 2391, 596, 596, 596, 3256, 3256, 3018, 938, 3018, 938, 943, 3018,
943, 3018, 3690, 3980, 3690, 3980, 2391, 2391, 2391, 596, 596, 596, 3656,
3656, 3018, 938, 3018, 938, 943, 3018, 943, 3018, 2790, 3980, 2790, 3980,
2391, 2391, 2391, 596, 596, 596, 2756, 2756, 3018, 938, 3018, 938, 943,
3018, 943, 3018, 2790, 3980, 2790, 3980, 2391, 2391, 2391, 596, 596, 596,
2756, 2756, 3018, 938, 3018, 938, 943
]
POSSIBLE_CAPACITIES = [4000, 5000, 6000, 7000, 8000]
# Toy problem
# DESIRED_LENGTHS = [12, 12, 8, 8, 8]
# POSSIBLE_CAPACITIES = [10, 20]
def regroup_and_count(raw_input):
"""Regroup all equal capacities in a multiset."""
grouped = collections.defaultdict(int)
for i in raw_input:
grouped[i] += 1
output = []
for size, count in grouped.items():
output.append([size, count])
output.sort(reverse=False)
return output
def price_usage(usage, capacities):
"""Compute the best price for a given usage and possible capacities."""
price = max(capacities)
for capacity in capacities:
if capacity < usage:
continue
price = min(capacity - usage, price)
return price
def create_state_graph(items, max_capacity):
"""Create a state graph from a multiset of items, and a maximum capacity."""
states = []
state_to_index = {}
states.append(0)
state_to_index[0] = 0
transitions = []
for item_index, size_and_count in enumerate(items):
size, count = size_and_count
num_states = len(states)
for state_index in range(num_states):
current_state = states[state_index]
current_state_index = state_index
for card in range(count):
new_state = current_state + size * (card + 1)
if new_state > max_capacity:
break
new_state_index = -1
if new_state in state_to_index:
new_state_index = state_to_index[new_state]
else:
new_state_index = len(states)
states.append(new_state)
state_to_index[new_state] = new_state_index
# Add the transition
transitions.append([
current_state_index, new_state_index, item_index, card + 1
])
return states, transitions
def solve_cutting_stock_with_arc_flow_and_sat(output_proto):
"""Solve the cutting stock with arc-flow and the CP-SAT solver."""
items = regroup_and_count(DESIRED_LENGTHS)
print('Items:', items)
num_items = len(DESIRED_LENGTHS)
max_capacity = max(POSSIBLE_CAPACITIES)
states, transitions = create_state_graph(items, max_capacity)
print('Dynamic programming has generated', len(states), 'states and',
len(transitions), 'transitions')
incoming_vars = collections.defaultdict(list)
outgoing_vars = collections.defaultdict(list)
incoming_sink_vars = []
item_vars = collections.defaultdict(list)
item_coeffs = collections.defaultdict(list)
transition_vars = []
model = cp_model.CpModel()
objective_vars = []
objective_coeffs = []
for outgoing, incoming, item_index, card in transitions:
count = items[item_index][1]
max_count = count // card
count_var = model.NewIntVar(
0, max_count,
'i%i_f%i_t%i_C%s' % (item_index, incoming, outgoing, card))
incoming_vars[incoming].append(count_var)
outgoing_vars[outgoing].append(count_var)
item_vars[item_index].append(count_var)
item_coeffs[item_index].append(card)
transition_vars.append(count_var)
for state_index, state in enumerate(states):
if state_index == 0:
continue
exit_var = model.NewIntVar(0, num_items, 'e%i' % state_index)
outgoing_vars[state_index].append(exit_var)
incoming_sink_vars.append(exit_var)
price = price_usage(state, POSSIBLE_CAPACITIES)
objective_vars.append(exit_var)
objective_coeffs.append(price)
# Flow conservation
for state_index in range(1, len(states)):
model.Add(
sum(incoming_vars[state_index]) == sum(outgoing_vars[state_index]))
# Flow going out of the source must go in the sink
model.Add(sum(outgoing_vars[0]) == sum(incoming_sink_vars))
# Items must be placed
for item_index, size_and_count in enumerate(items):
num_arcs = len(item_vars[item_index])
model.Add(
sum(item_vars[item_index][i] * item_coeffs[item_index][i]
for i in range(num_arcs)) == size_and_count[1])
# Objective is the sum of waste
model.Minimize(
sum(objective_vars[i] * objective_coeffs[i]
for i in range(len(objective_vars))))
# Output model proto to file.
if output_proto:
output_file = open(output_proto, 'w')
output_file.write(str(model.Proto()))
output_file.close()
# Solve model.
solver = cp_model.CpSolver()
solver.parameters.log_search_progress = True
solver.parameters.num_search_workers = 8
status = solver.Solve(model)
print(solver.ResponseStats())
def solve_cutting_stock_with_arc_flow_and_mip():
"""Solve the cutting stock with arc-flow and a MIP solver."""
items = regroup_and_count(DESIRED_LENGTHS)
print('Items:', items)
num_items = len(DESIRED_LENGTHS)
max_capacity = max(POSSIBLE_CAPACITIES)
states, transitions = create_state_graph(items, max_capacity)
print('Dynamic programming has generated', len(states), 'states and',
len(transitions), 'transitions')
incoming_vars = collections.defaultdict(list)
outgoing_vars = collections.defaultdict(list)
incoming_sink_vars = []
item_vars = collections.defaultdict(list)
item_coeffs = collections.defaultdict(list)
start_time = time.time()
solver = pywraplp.Solver('Steel',
pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
objective_vars = []
objective_coeffs = []
var_index = 0
for outgoing, incoming, item_index, card in transitions:
count = items[item_index][1]
count_var = solver.IntVar(
0, count, 'a%i_i%i_f%i_t%i_c%i' % (var_index, item_index, incoming,
outgoing, card))
var_index += 1
incoming_vars[incoming].append(count_var)
outgoing_vars[outgoing].append(count_var)
item_vars[item_index].append(count_var)
item_coeffs[item_index].append(card)
for state_index, state in enumerate(states):
if state_index == 0:
continue
exit_var = solver.IntVar(0, num_items, 'e%i' % state_index)
outgoing_vars[state_index].append(exit_var)
incoming_sink_vars.append(exit_var)
price = price_usage(state, POSSIBLE_CAPACITIES)
objective_vars.append(exit_var)
objective_coeffs.append(price)
# Flow conservation
for state_index in range(1, len(states)):
solver.Add(
sum(incoming_vars[state_index]) == sum(outgoing_vars[state_index]))
# Flow going out of the source must go in the sink
solver.Add(sum(outgoing_vars[0]) == sum(incoming_sink_vars))
# Items must be placed
for item_index, size_and_count in enumerate(items):
num_arcs = len(item_vars[item_index])
solver.Add(
sum(item_vars[item_index][i] * item_coeffs[item_index][i]
for i in range(num_arcs)) == size_and_count[1])
# Objective is the sum of waste
solver.Minimize(
sum(objective_vars[i] * objective_coeffs[i]
for i in range(len(objective_vars))))
solver.EnableOutput()
status = solver.Solve()
### Output the solution.
if status == pywraplp.Solver.OPTIMAL:
print('Objective value = %f found in %.2f s' %
(solver.Objective().Value(), time.time() - start_time))
else:
print('No solution')
"""Main function"""
if args.solver == 'sat':
solve_cutting_stock_with_arc_flow_and_sat(args.output_proto)
else: # 'mip'
solve_cutting_stock_with_arc_flow_and_mip()