always-cautious/ortools-clone
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

add arc_flow version of cutting stock problem with different capacities

Browse Source
This commit is contained in:
Laurent Perron
2019-05-31 21:42:45 +02:00
parent 4ac9172f9f
commit 9e5a83ae05
1 changed files with 259 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files

259
examples/python/arc_flow_cutting_stock_sat.py Normal file
View File

@@ -0,0 +1,259 @@
# 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):
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=True)
return output
def price_capacity(capacity, capacities):
price = max(capacities)
for c in capacities:
if c < capacity:
continue
price = min(c - capacity, price)
return price
def create_state_graph(items, max_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):
previous_state = states[state_index]
previous_state_index = state_index
for _ in range(count):
new_state = previous_state + size
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(
[previous_state_index, new_state_index, item_index])
# And update counters
previous_state_index = new_state_index
previous_state = new_state
return states, transitions
def solve_cutting_stock_with_arc_flow_with_sat(output_proto):
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)
model = cp_model.CpModel()
objective_vars = []
objective_coeffs = []
for outgoing, incoming, item_index in transitions:
count = items[item_index][1]
count_var = model.NewIntVar(
0, count, 'i%i_f%i_t%i' % (item_index, incoming, outgoing))
incoming_vars[incoming].append(count_var)
outgoing_vars[outgoing].append(count_var)
item_vars[item_index].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_capacity(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):
size, count = size_and_count
model.Add(sum(item_vars[item_index]) == count)
# 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_with_mip():
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)
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 in transitions:
count = items[item_index][1]
count_var = solver.IntVar(
0, count,
'a%i_i%i_f%i_t%i' % (var_index, item_index, incoming, outgoing))
var_index += 1
incoming_vars[incoming].append(count_var)
outgoing_vars[outgoing].append(count_var)
item_vars[item_index].append(count_var)
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_capacity(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):
size, count = size_and_count
solver.Add(sum(item_vars[item_index]) == count)
# 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')
def main(args):
"""Main function"""
if args.solver == 'sat':
solve_cutting_stock_with_arc_flow_with_sat(args.output_proto)
else: # 'mip'
solve_cutting_stock_with_arc_flow_with_mip()
if __name__ == '__main__':
main(PARSER.parse_args())