qubo_sat.py

#!/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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        0.3163476, 0, 0, 13.0918568, 5.13089, 0, 40.7266308, 0, 0, 0, 0, 0,
        -98.7077428, 0, 81.000503, 0, 0, 76.3945372, 0, 0, 0, 0, 0, 0,
        -10.2289084, -70.592702, 0, 0, 0, 0, 0, 0, 69.59571, 0, 0, 0, 0, 0,
        -61.4746908, 53.4041094, 0, 90.4397278, -33.1874988, 0, 0, 71.5512744,
        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
    ],
    [
        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,
        -95.3752508, 4.596855, 85.2924422, 70.9081648, 22.0390844, 0, 0, 0, 0,
        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
    ],
    [
        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
    ],
    [
        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
    ],
    [
        0, 0, 0, -73.9719246, 0, 0, 0, 0, 0, 0, 0, 39.4110332, 0, 0,
        -21.6757132, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
        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
    ],
    [
        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)