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qubo_sat.py
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qubo_sat.py
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#!/usr/bin/env python3
# Copyright 2010-2024 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.
"""Solves a Qubo program using the CP-SAT solver."""
from typing import List, Sequence
from absl import app
from ortools.sat.python import cp_model
RAW_DATA: List[List[float]] = [
# fmt:off
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0, 0, 0, 0, 55.2807134, 0, 0, 0, 0, -90.8562594, -43.2271604
],
[
0, 0, 0, 0, 0, 15.2015056, 18.3740448, -11.2614058, 0, 0, 0, 0, 0,
53.0086248, 0, -91.038908, 0, 0, 88.2707986, 3.2580272, 0, 0, 0, 0, 0,
0, 0, 0, 88.8189254, 0, 0, 0, 0, -3.742353, 0, 0, 0, -41.4198488,
90.0966416, 0, -22.474875, 0, -25.610863, -79.5943706, 0, 0, 0, 0, 0, 0,
0, -3.5616438, 0, 0, 0, 88.5984932, 0, 0, 0, 0, 0, 0, 0, 22.4398688, 0,
0, 0, 0, 0, 0, 0, -63.7422676, 0, 0, 0, -82.7150752
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[
0, 0, 75.634243, -60.420708, 0, 0, 0, 0.8383984, 0, 0, -72.2791914, 0,
0, 0, 17.1476022, 0, 0, -14.5930276, 9.4352026, 0, -30.1475326, 0,
-53.7249052, 0, 19.3293368, 0, 0, 0, -80.867335, 0, -3.344608,
71.3546388, -91.098817, 0, 0, 0, -26.83234, 0, 3.7009, 0, 0, 0, 0, 0,
28.4006138, 0, 0, 57.1433046, 14.4086186, 0, 0, 0, 49.5828354, 0, 0, 0,
0, 0, 0, 0, 0, 0, 17.0012008, 0, 30.5581294, -98.7868224, 0, 0, 0,
70.0467486, -9.4444084, 0, 19.9250998, 0, 0, -79.4970662
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[
0, 54.0067274, 0, 0, 0, 37.9936634, 0, -20.1071476, -58.981429, 0, 0,
-83.9927614, 0, 0, 0, 0, 0, 0, -70.8571636, 0, 0, 68.4686496, 0, 0, 0,
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0, 0, 0, 0, 0, 0, 0, 0, 0, 86.4747972, 0, -34.6316042, 0.9788672, 0, 0,
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-5.0425708, 0, 0, 0, 78.9139852, -50.7082204, 0, 34.0684852, 28.2502302
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[
0, 0, 0, 0, 0, 0, 0, 57.544994, 0, 0, -22.4411072, 0, -94.2568866,
-80.7849138, 0, 0, -10.0010618, 33.3160792, 0, 0, 0, 0, 0, 0,
-82.6811248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -11.0390072, 0, 0,
32.0523166, 0, -80.6937396, 0, -94.2671164, 0, 0, -16.2170198, 0, 0, 0,
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-41.9784856, 0, 0, 0, -50.6512854, 0, 78.737702, 0, 0, 0, 0, 0,
9.0618996
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[
0, 0, 0, 0, 0, -94.8072128, 0, 21.9767716, 0, 0, 0, 57.7817378,
35.3840102, 0, 0, 0, 60.4679182, -94.9978498, 0, -18.9377882,
-42.3270372, 0, 0, 0, 0, -3.9058912, 0, 0, 44.440235, 0, 0.41471, 0, 0,
-88.0148602, 53.9755254, 0, 0, 74.7772774, -19.633854, -66.6129164,
-25.4637816, -13.1642082, 0, 0, 0, 0, 57.6068044, 0, 0, -75.9060014,
24.0447026, 0, 0, 29.9750648, 0, 0, 0, -54.938857, -4.4090126, 0, 0, 0,
0, 0, 0, -57.1202194, 0, -11.130658, 0, 0, 95.6177756, -78.5403868, 0,
0, 30.4589622, -93.6950296
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[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -50.308444, 0, 0, 0, 0, 0, 0, 0,
-20.3462364, 0, 0, 25.6081088, 0, 0, 0, 0, 0, 0, 90.9877902, 0,
-56.0922542, 99.2456868, 0, 45.4316172, 0, 70.1339288, -54.576692, 0, 0,
0, -73.6910292, 0, 0, 0, 0, 0, 0, 38.6032202, 0, 0, 0, 60.7387286, 0, 0,
0, 0, 0, 0, 0, 0, 95.207832, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
58.4721284
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[
0.3163476, 0, 0, 13.0918568, 5.13089, 0, 40.7266308, 0, 0, 0, 0, 0,
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5.846105, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56.7568638, 0, 0,
66.7588344, 0, 0, 0, 99.284785, 0, 0, 0, 0, 0, 0, -99.2850048,
-85.4466004
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[
0, 0, -34.544278, 0, 0, -36.135124, -33.4259354, 0, 0, -60.4256326, 0,
44.7734168, 0, 0, 0, 0, -88.6744704, 0, 0, 0, 0, 0, 0, 0, 0,
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0, 0, 0, 0, 0, 1.6872456, 0, 0, 0, 0, 0, 0, 0, -37.4782422, 0, 0, 0, 0,
0, 0, 0, 0, 4.7642096, 0, 0, -33.6313218, 0, 0, 72.977526, 0, 0, 0, 0,
0, 0, 2.5063252, 0, 0, 0, 0, 0, -64.8677902
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[
0, 0, 0, 3.718989, 0, 0, 49.3814782, 77.868826, 0, 0, 0, 0, 0, 0, 0, 0,
-49.7008846, 0, 4.696494, 0, 0, 0, 0, 0, 0, 0, -59.4928602, 0, 0, 0, 0,
0, 82.6840644, -0.996624, -15.8014198, -93.098215, 0, 0, 41.2709314, 0,
-90.9633198, -56.911012, 0, 0, 0, 0, 0, 0, 0, 0, 0, -26.02585, 0, 0, 0,
0, 0, 0, 61.2353938, 0, 0, 0, 0, 21.376448, 0, 0, 0, 0, 0, 0, 0,
97.0578858, 0, 0, 0, 5.1265226
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[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -19.5643656, 0,
0, -92.0307416, 0, 0, 0, 0, 55.003856, 0, 0, -20.4708104, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54.4588824, 0, 0, 0, 0, 0, 0, 0,
0, -57.0182252, 0, 0, -48.3222128, 0, 0, 0, -41.1121382, 0, 0, 0, 0, 0,
0, -12.2773602, 0, -28.6924808, 50.0415338
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[
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74.8739354, 0, 0, -52.9210426, 0, 46.7750368, 63.6311858, 0, 0, 0, 0,
25.5310902, 0, -3.0369126, 0, 32.5437816, 0, 0, 78.9107496, 32.0416448,
0, 0, 15.9408846, 0, 0, 0, 0, -67.7582854, -52.6103086, 0, 0, 0, 0, 0,
0, 11.8676176, 0, 0, -41.8820812, 43.608357, 0, 0, -64.3752572
],
[
0, -15.1648222, -57.5273074, -94.2919124, -3.0777222, -77.345826,
91.2777856, 0, 0, 0, 0, 13.5044774, 0, 0, 0, 0, 0, 0, 0, 0, 33.5509618,
0, 0, -33.291092, -60.3050638, 0, 0, 0, 94.610171, 0, 0, 0, 0, 0, 0,
-47.270154, -81.403122, 0, 0, 47.829269, 0, 0, 0, 0, -47.4699122, 0, 0,
-31.0161918, 0, 0, -54.993563, -9.6544012, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-17.0644648, 0, 0, 0, 0, 0, 0, 49.0555938, -82.4686508, 0, 0,
97.7299292, 0, 0, -93.1718028
],
[
0, 0, 0, 45.5639954, 0, 0, 0, 0, 0, 92.3127826, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, -5.8746296, 22.9079182, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
25.2727812, 0, 0, 0, 0, 0, 0, 65.0012614, 0, 67.4376806, 0, 0,
14.0298002, 0, 0, 0, 0, 0, 33.432514, 43.000429, 0, 0, 0, 0, 0, 0, 0, 0,
0, 20.2757068, 4.0567932, 0, 0, -15.8737758, 0, 0, 0, 0, 29.8957398,
50.0218946, 17.0262346
],
[
46.1658228, 19.630724, 0, 0, 0, 0, 0, 80.6073204, 24.5091878, 0, 0, 0,
73.9258848, 0, 0, 0, -98.2044476, 0, 0, 0, 0, -59.2213968, 0,
-70.1450004, 0, 0, 0, 42.4721292, 0, -73.0346074, 0, 67.9829686, 0, 0,
0, 0, 6.6597886, 39.7215082, 0, 0, 0, 52.505292, 95.9204336, 0, 0,
5.8797776, 0, 0, 0, 36.0738246, 0, -15.2667614, 0, 0, 0, 0, 0, 0, 0, 0,
0, 50.963131, 0, 0, 0, 49.3354032, 13.7868492, 0, 77.3708062,
26.0888548, 0, 0, 0, 0, -60.0881692, 24.2459968
],
[
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56.562023, 0, 0, 24.9145996, 0, 0, 0,
0, 32.8196724, -75.8879774, -12.4005106, 0, 0, 0, 0, -18.824482,
-45.0330046, 0, 0, -47.5493022, 0, 0, 0, 8.1879572, 0, 0, 4.5700222,
-28.6731266, 0, 0, 0, 0, -83.2735948, 5.4624948, 0, 0, 0, 0, 0, 0, 0,
83.664375, -52.8630198, 58.5805764, 0, 0, 0, 45.5781336, 0, 0,
-1.9768322, 0, 0, 0, 0, 91.1151128, 0, 0, 0, 0, 0, 0, -65.5158586, 0,
-22.12762
],
[
0, 0, 0, 0, 0, -50.8301006, 0, -57.183698, -24.666489, 43.0557936, 0, 0,
0, -44.0812116, 0, 0, 0, 97.1670056, 0, 0, 0, 0, 83.4511366, 0,
-96.8912356, -6.1095452, 87.6643268, 0, 0, 0, -32.5223614, 0, 0, 0, 0,
-18.5596964, 0, 56.1790224, 0, 25.6035684, 0, 0, 0, 0, -46.8740154, 0,
0, 0, 0, 0, 0, 0, -44.4329434, -34.719678, 85.6384822, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 48.9669952, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28.2571694
],
[
0, 0, 0, 0, 42.1192158, 18.3800218, 0, 0, 33.4475094, 0, -39.4713432, 0,
54.9744572, 0, -6.6305664, 79.0252374, 77.6908818, -61.5099746, 0, 0,
38.4501814, 0, 0, -96.4250704, -27.809694, -34.9250884, 63.2997728, 0,
-98.8800042, 0, -7.682428, 0, 0, 0, 0, 0, 0, 7.7256608, 0, 48.5546152,
0, 0, 0, 0, 0, 0, -58.963373, 0, 0, 0, 0, 0, 86.5062664, 7.0006556, 0,
0, 0, 0, 0, 0, 3.1958572, 0, -46.2861844, 0, 0, 0, 0, 30.0710902,
46.6948898, 0, 68.4681908, 0, 0, 0, 0, -51.3930766
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[
7.1969236, 0, -79.6160432, -39.947334, -15.2636342, 0, 10.0645898,
-57.8968238, -31.9945476, 0, 91.5839662, -52.777566, 0, 0, 0, 0,
-40.9252974, 0, 0, 0, -45.5113982, 70.585349, 0, 0, 0, 0, 0, 0, 0, 0,
-66.2523308, 0, 0, 0, 0, 0, 0, 0, 0, 85.7454324, -7.1148372, 0,
93.6584844, 0, 0, 0, 0, 0, 0, -8.0414788, 0, 0, 0, 0, 51.3263388, 0, 0,
79.892422, 0, 0, -64.6934098, 0, 0, -45.9577622, 0, 0, 0, -46.8290526,
0, 48.2417506, 0, 0, 0, 0, -2.4115812, -50.7156922
],
[
62.9870494, -81.5584552, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53.7333104, 0,
50.6438202, -57.7938262, 0, 0, 0, 0, -78.1108892, 0, 0, 0, 0, 0, 0, 0,
87.6584692, 0, 58.2960112, -17.5355398, 12.0497204, -60.5414862, 0, 0,
0, 0, 0, 0, 0, 0, 38.586472, -19.7940052, 94.423359, -89.557933, 0, 0,
-77.0715722, 0, -87.707166, 70.8585278, 0, 9.0616914, 91.333051, 0, 0,
0, 5.8166112, 0, 24.7793442, -51.000038, 0, 0, 0, 0, 0, 0, 79.9657776,
97.4969126, 0, 0, 0, 0, -73.8994394
],
[
10.133741, 0, 0, 0, 95.6910336, 0, 0, 0, 0, -22.6696236, 0, 0, 0, 0,
15.137996, 35.7088464, 0, -16.1971956, 0, -29.4834358, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, -89.868739, 24.0040126, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 40.7292396, 35.7709458, 0, 34.690347, 22.3083532, 0, 0, 0, 0, 0,
-48.4224164, 0, 0, 0, 0, 91.7670744, 0, 0, 69.4045014, 0, 60.5937114,
-38.9993134, 0, 0, 0, 0, 0, 55.4599018, 0, 86.689944
],
[
0, 0, -24.842169, -52.997003, 0, 0, 0, 0, 0, 0, 0, 5.9075842, 0, 0,
-91.1447252, -5.3147106, 0, 0, 0, 4.4670454, 34.97343, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, -5.3957052, 0, 0, 0, 0, -19.2118838, 0, 0, 0, 0, 0, 0, 0, 0,
64.9559324, 0, 0, -10.0586402, 0, -74.8523334, 0, 0, 0, 0, 0, 0, 0, 0,
0, 84.8495464, 0, 0, 0, 0, 0, 0, 33.0825986, 46.995148, 0, 0, 0,
-4.243203, 0, 0, -24.0124188
]
# fmt:on
]
def solve_qubo() -> None:
"""solve the Qubo problem."""
# Build the model.
model = cp_model.CpModel()
num_vars = len(RAW_DATA)
all_vars = range(num_vars)
variables = [model.new_bool_var("x_%i" % i) for i in all_vars]
obj_vars = []
obj_coeffs = []
for i in range(num_vars - 1):
x_i = variables[i]
for j in range(i + 1, num_vars):
coeff = RAW_DATA[i][j] + RAW_DATA[j][i]
if coeff == 0.0:
continue
x_j = variables[j]
var = model.new_bool_var("")
model.add_bool_or([~x_i, ~x_j, var])
model.add_implication(var, x_i)
model.add_implication(var, x_j)
obj_vars.append(var)
obj_coeffs.append(coeff)
for i in all_vars:
self_coeff = RAW_DATA[i][i] + RAW_DATA[i][-1]
if self_coeff != 0.0:
obj_vars.append(variables[i])
obj_coeffs.append(self_coeff)
model.minimize(sum(obj_vars[i] * obj_coeffs[i] for i in range(len(obj_vars))))
### Solve model.
solver = cp_model.CpSolver()
solver.parameters.num_search_workers = 16
solver.parameters.log_search_progress = True
solver.parameters.max_time_in_seconds = 30
solver.solve(model)
def main(argv: Sequence[str]) -> None:
if len(argv) > 1:
raise app.UsageError("Too many command-line arguments.")
solve_qubo()
if __name__ == "__main__":
app.run(main)