Hexaly Planted Benchmarking

import time
import numpy as np
import hexaly.optimizer
import os

def hexaly_solver(Q,c,sum_constraint, time_limit= 1800):
    n = len(np.squeeze(c))
    def external_xTQx(x):
        return x @ Q @ x
    def external_2Qx(x):
        return 2 * Q @ x
    
    with hexaly.optimizer.HexalyOptimizer() as optimizer:
        model = optimizer.model
        x = [model.float(0.0,100.0) for _ in range(n)]
        linear_term = model.sum(c[i]*x[i] for i in range(n))
        xTQx_func = model.create_double_external_function(external_xTQx, external_2Qx)
        objective = linear_term + xTQx_func(x)
        model.constraint(model.sum(x) == sum_constraint)
        model.minimize(objective)
        model.close()
        optimizer.param.time_limit = time_limit
        print("Starting Hexaly solver...")
        optimizer.solve()
        solution = [x[i].value for i in range(n)]
        objective_val = objective.value
        print(f"Status: {optimizer.solution.status}")
        return solution, objective_val

def loadQ(path, n):
    tri = np.load(path, mmap_mode="r")
    Q = np.empty((n,n), dtype=tri.dtype)
    iu = np.triu_indices(n)
    Q[iu] = tri
    Q.T[iu] = tri
    return Q

# Instance details
optimal_energy = 12000
sum_constraint = 100
num_var = 2000
k = 44
ub =10
seed =100
name = f"STQP_n_{num_var}_k_{k}_R_{sum_constraint}_seed_{seed}_ub_{ub}"
instance_path = os.path.join(f"Instances/{name}.npy")
c = np.zeros(num_var)
try:
    Q= loadQ(instance_path,num_var)
    print("loaded file sucessfully.")
except FileNotFoundError:
    print(f"File {instance_path} does not exist.")

loaded file sucessfully.

# solver parameters
time_limit = 600

# solve with Hexaly
hexaly_start = time.time()
hex_sol_list, hex_obj = hexaly_solver(Q,c,sum_constraint,time_limit)
hexaly_end = time.time()
hex_sol = np.array(hex_sol_list)
hex_indices = np.where(hex_sol>1e-6)[0]
print(f"Number of non-zero nodes found by Hexaly:{len(hex_indices)}")
print(f"Eenergy value obtained by Hexaly:{hex_obj}")
print(f"Time taken by Hexaly:{hexaly_end- hexaly_start}")

Preprocess model 100%Starting Hexaly solver...
Push initial solution 100%
Model:  expressions = 4009, decisions = 2000, constraints = 1, objectives = 1
Param:  time limit = 600 sec, no iteration limit

[objective direction ]:     minimize

[  0 sec,       0 itr]: No feasible solution found (infeas = 1)
[  1 sec,       0 itr]: No feasible solution found (infeas = 1)
[  2 sec,     218 itr]:      22859.4
[ optimality gap     ]:      100.00%
[  3 sec,    1294 itr]:      15956.2
[  4 sec,    1519 itr]:      15811.3
[  5 sec,    1796 itr]:      15811.1
[  6 sec,    2012 itr]:        15811
[  7 sec,    2012 itr]:        15811
[  8 sec,    2464 itr]:      15810.6
[  9 sec,    2623 itr]:      15810.3
[ 10 sec,    2623 itr]:      15810.3
[ 11 sec,    2893 itr]:      15810.2
[ 12 sec,    3103 itr]:        15810
[ optimality gap     ]:      100.00%
[ 13 sec,    3431 itr]:      15809.6
[ 14 sec,    3431 itr]:      15809.6
[ 15 sec,    3588 itr]:      15809.3
[ 16 sec,    4014 itr]:      15809.1
[ 17 sec,    4166 itr]:      15808.9
[ 18 sec,    4267 itr]:      15808.6
[ 19 sec,    4450 itr]:      15808.4
[ 20 sec,    4633 itr]:      15808.1
[ 21 sec,    4812 itr]:        15808
[ 22 sec,    4812 itr]:        15808
[ optimality gap     ]:      100.00%
[ 23 sec,    5185 itr]:      12986.9
[ 24 sec,    5185 itr]:      12986.9
[ 25 sec,    5304 itr]:      12986.9
[ 26 sec,    5603 itr]:      12986.9
[ 27 sec,    5724 itr]:      12986.9
[ 28 sec,    5724 itr]:      12986.9
[ 29 sec,    5875 itr]:      12986.9
[ 30 sec,    5963 itr]:      12986.9
[ 31 sec,    6083 itr]:      12986.9
[ 32 sec,    6192 itr]:      12986.9
[ optimality gap     ]:      100.00%
[ 33 sec,    6448 itr]:      12986.9
[ 34 sec,    6448 itr]:      12986.9
[ 35 sec,    6572 itr]:      12986.9
[ 36 sec,    6657 itr]:      12986.9
[ 37 sec,    6743 itr]:      12986.9
[ 38 sec,    6872 itr]:      12986.9
[ 39 sec,    6986 itr]:      12986.9
[ 40 sec,    7238 itr]:      12986.9
[ 41 sec,    7238 itr]:      12986.9
[ 42 sec,    7355 itr]:      12986.9
[ optimality gap     ]:      100.00%
[ 43 sec,    7456 itr]:      12986.9
[ 44 sec,    7551 itr]:      12986.9
[ 45 sec,    7648 itr]:      12986.9
[ 46 sec,    7781 itr]:      12986.9
[ 47 sec,    7920 itr]:      12986.9
[ 48 sec,    8049 itr]:      12986.9
[ 49 sec,    8158 itr]:      12986.9
[ 50 sec,    8324 itr]:      12986.9
[ 51 sec,    8416 itr]:      12986.9
[ 52 sec,    8504 itr]:      12986.9
[ optimality gap     ]:      100.00%
[ 53 sec,    8504 itr]:      12986.9
[ 54 sec,    8623 itr]:      12986.9
[ 55 sec,    8687 itr]:      12986.9
[ 56 sec,    8863 itr]:      12986.9
[ 57 sec,    8863 itr]:      12986.9
[ 58 sec,    8983 itr]:      12986.9
[ 59 sec,    9092 itr]:      12986.9
[ 60 sec,    9217 itr]:      12986.9
[ 61 sec,    9300 itr]:      12986.9
[ 62 sec,    9395 itr]:      12986.9
[ optimality gap     ]:      100.00%
[ 63 sec,    9520 itr]:      12986.9
[ 64 sec,    9746 itr]:      12986.9
[ 65 sec,    9746 itr]:      12986.9
[ 66 sec,    9884 itr]:      12986.9
[ 67 sec,   10083 itr]:      12986.9
[ 68 sec,   10083 itr]:      12986.9
[ 69 sec,   10169 itr]:      12986.9
[ 70 sec,   10405 itr]:      12986.9
[ 71 sec,   10504 itr]:      12986.9
[ 72 sec,   10504 itr]:      12986.9
[ optimality gap     ]:      100.00%
[ 73 sec,   10616 itr]:      12986.9
[ 74 sec,   10721 itr]:      12986.9
[ 75 sec,   10974 itr]:      12986.9
[ 76 sec,   10974 itr]:      12986.9
[ 77 sec,   11203 itr]:      12986.9
[ 78 sec,   11321 itr]:      12986.9
[ 79 sec,   11321 itr]:      12986.9
[ 80 sec,   11561 itr]:      12986.9
[ 81 sec,   11663 itr]:      12986.9
[ 82 sec,   11663 itr]:      12986.9
[ optimality gap     ]:      100.00%
[ 83 sec,   11829 itr]:      12986.9
[ 84 sec,   11901 itr]:      12986.9
[ 85 sec,   11999 itr]:      12986.9
[ 86 sec,   11999 itr]:      12986.9
[ 87 sec,   12175 itr]:      12986.9
[ 88 sec,   12315 itr]:      12986.9
[ 89 sec,   12419 itr]:      12986.9
[ 90 sec,   12419 itr]:      12986.9
[ 91 sec,   12492 itr]:      12986.9
[ 92 sec,   12626 itr]:      12986.9
[ optimality gap     ]:      100.00%
[ 93 sec,   12626 itr]:      12986.9
[ 94 sec,   12720 itr]:      12986.9
[ 95 sec,   12775 itr]:      12986.9
[ 96 sec,   12987 itr]:      12986.9
[ 97 sec,   12987 itr]:      12986.9
[ 98 sec,   13177 itr]:      12986.9
[ 99 sec,   13177 itr]:      12986.9
[100 sec,   13341 itr]:      12986.9
[101 sec,   13435 itr]:      12986.9
[102 sec,   13537 itr]:      12986.9
[ optimality gap     ]:      100.00%
[103 sec,   13537 itr]:      12986.9
[104 sec,   13735 itr]:      12986.9
[105 sec,   13861 itr]:      12986.9
[106 sec,   13965 itr]:      12986.9
[107 sec,   13965 itr]:      12986.9
[108 sec,   14185 itr]:      12938.7
[109 sec,   14271 itr]:      12938.7
[110 sec,   14383 itr]:      12938.7
[111 sec,   14504 itr]:      12938.7
[112 sec,   14624 itr]:      12938.7
[ optimality gap     ]:      100.00%
[113 sec,   14699 itr]:      12938.7
[114 sec,   14805 itr]:      12938.7
[115 sec,   14885 itr]:      12938.7
[116 sec,   14885 itr]:      12938.7
[117 sec,   15127 itr]:      12938.7
[118 sec,   15191 itr]:      12938.7
[119 sec,   15191 itr]:      12938.7
[120 sec,   15413 itr]:      12938.7
[121 sec,   15537 itr]:      12938.7
[122 sec,   15537 itr]:      12938.7
[ optimality gap     ]:      100.00%
[123 sec,   15646 itr]:      12938.7
[124 sec,   15932 itr]:      12938.7
[125 sec,   16026 itr]:      12938.7
[126 sec,   16114 itr]:        12855
[127 sec,   16208 itr]:        12855
[128 sec,   16304 itr]:        12855
[129 sec,   16416 itr]:        12855
[130 sec,   16556 itr]:        12855
[131 sec,   16556 itr]:        12855
[132 sec,   16765 itr]:        12855
[ optimality gap     ]:      100.00%
[133 sec,   16765 itr]:        12855
[134 sec,   17033 itr]:        12000
[135 sec,   17146 itr]:        12000
[136 sec,   17278 itr]:        12000
[137 sec,   17436 itr]:        12000
[138 sec,   17567 itr]:        12000
[139 sec,   17690 itr]:        12000
[140 sec,   17690 itr]:        12000
[141 sec,   17802 itr]:        12000
[142 sec,   17891 itr]:        12000
[ optimality gap     ]:      100.00%
[143 sec,   18078 itr]:        12000
[144 sec,   18203 itr]:        12000
[145 sec,   18203 itr]:        12000
[146 sec,   18465 itr]:        12000
[147 sec,   18465 itr]:        12000
[148 sec,   18570 itr]:        12000
[149 sec,   18682 itr]:        12000
[150 sec,   18921 itr]:        12000
[151 sec,   18921 itr]:        12000
[152 sec,   19137 itr]:        12000
[ optimality gap     ]:      100.00%
[153 sec,   19137 itr]:        12000
[154 sec,   19385 itr]:        12000
[155 sec,   19525 itr]:        12000
[156 sec,   19525 itr]:        12000
[157 sec,   19628 itr]:        12000
[158 sec,   19717 itr]:        12000
[159 sec,   19970 itr]:        12000
[160 sec,   20066 itr]:        12000
[161 sec,   20218 itr]:        12000
[162 sec,   20218 itr]:        12000
[ optimality gap     ]:      100.00%
[163 sec,   20346 itr]:        12000
[164 sec,   20488 itr]:        12000
[165 sec,   20557 itr]:        12000
[166 sec,   20789 itr]:        12000
[167 sec,   20789 itr]:        12000
[168 sec,   20883 itr]:        12000
[169 sec,   20981 itr]:        12000
[170 sec,   21233 itr]:        12000
[171 sec,   21405 itr]:        12000
[172 sec,   21560 itr]:        12000
[ optimality gap     ]:      100.00%
[173 sec,   21640 itr]:        12000
[174 sec,   21640 itr]:        12000
[175 sec,   21988 itr]:        12000
[176 sec,   22091 itr]:        12000
[177 sec,   22091 itr]:        12000
[178 sec,   22226 itr]:        12000
[179 sec,   22430 itr]:        12000
[180 sec,   22556 itr]:        12000
[181 sec,   22556 itr]:        12000
[182 sec,   22647 itr]:        12000
[ optimality gap     ]:      100.00%
[183 sec,   22895 itr]:        12000
[184 sec,   22895 itr]:        12000
[185 sec,   23109 itr]:        12000
[186 sec,   23109 itr]:        12000
[187 sec,   23388 itr]:        12000
[188 sec,   23550 itr]:        12000
[189 sec,   23694 itr]:        12000
[190 sec,   23870 itr]:        12000
[191 sec,   23990 itr]:        12000
[192 sec,   23990 itr]:        12000
[ optimality gap     ]:      100.00%
[193 sec,   24115 itr]:        12000
[194 sec,   24263 itr]:        12000
[195 sec,   24393 itr]:        12000
[196 sec,   24577 itr]:        12000
[197 sec,   24684 itr]:        12000
[198 sec,   24684 itr]:        12000
[199 sec,   24894 itr]:        12000
[200 sec,   24894 itr]:        12000
[201 sec,   25140 itr]:        12000
[202 sec,   25265 itr]:        12000
[ optimality gap     ]:      100.00%
[203 sec,   25265 itr]:        12000
[204 sec,   25356 itr]:        12000
[205 sec,   25665 itr]:        12000
[206 sec,   25665 itr]:        12000
[207 sec,   25851 itr]:        12000
[208 sec,   26105 itr]:        12000
[209 sec,   26105 itr]:        12000
[210 sec,   26428 itr]:        12000
[211 sec,   26428 itr]:        12000
[212 sec,   26695 itr]:        12000
[ optimality gap     ]:      100.00%
[213 sec,   26695 itr]:        12000
[214 sec,   26855 itr]:        12000
[215 sec,   27019 itr]:        12000
[216 sec,   27208 itr]:        12000
[217 sec,   27339 itr]:        12000
[218 sec,   27600 itr]:        12000
[219 sec,   27716 itr]:        12000
[220 sec,   27716 itr]:        12000
[221 sec,   27943 itr]:        12000
[222 sec,   27943 itr]:        12000
[ optimality gap     ]:      100.00%
[223 sec,   28088 itr]:        12000
[224 sec,   28291 itr]:        12000
[225 sec,   28419 itr]:        12000
[226 sec,   28419 itr]:        12000
[227 sec,   28657 itr]:        12000
[228 sec,   28791 itr]:        12000
[229 sec,   28915 itr]:        12000
[230 sec,   28915 itr]:        12000
[231 sec,   29250 itr]:        12000
[232 sec,   29415 itr]:        12000
[ optimality gap     ]:      100.00%
[233 sec,   29546 itr]:        12000
[234 sec,   29649 itr]:        12000
[235 sec,   29649 itr]:        12000
[236 sec,   29898 itr]:        12000
[237 sec,   30023 itr]:        12000
[238 sec,   30023 itr]:        12000
[239 sec,   30098 itr]:        12000
[240 sec,   30263 itr]:        12000
[241 sec,   30492 itr]:        12000
[242 sec,   30642 itr]:        12000
[ optimality gap     ]:      100.00%
[243 sec,   30787 itr]:        12000
[244 sec,   30787 itr]:        12000
[245 sec,   30902 itr]:        12000
[246 sec,   31110 itr]:        12000
[247 sec,   31221 itr]:        12000
[248 sec,   31383 itr]:        12000
[249 sec,   31519 itr]:        12000
[250 sec,   31653 itr]:        12000
[251 sec,   31810 itr]:        12000
[252 sec,   31810 itr]:        12000
[ optimality gap     ]:      100.00%
[253 sec,   32131 itr]:        12000
[254 sec,   32268 itr]:        12000
[255 sec,   32420 itr]:        12000
[256 sec,   32420 itr]:        12000
[257 sec,   32703 itr]:        12000
[258 sec,   32703 itr]:        12000
[259 sec,   32822 itr]:        12000
[260 sec,   33087 itr]:        12000
[261 sec,   33227 itr]:        12000
[262 sec,   33357 itr]:        12000
[ optimality gap     ]:      100.00%
[263 sec,   33550 itr]:        12000
[264 sec,   33550 itr]:        12000
[265 sec,   33899 itr]:        12000
[266 sec,   33899 itr]:        12000
[267 sec,   34043 itr]:        12000
[268 sec,   34286 itr]:        12000
[269 sec,   34286 itr]:        12000
[270 sec,   34458 itr]:        12000
[271 sec,   34705 itr]:        12000
[272 sec,   34705 itr]:        12000
[ optimality gap     ]:      100.00%
[273 sec,   34969 itr]:        12000
[274 sec,   35127 itr]:        12000
[275 sec,   35273 itr]:        12000
[276 sec,   35273 itr]:        12000
[277 sec,   35561 itr]:        12000
[278 sec,   35561 itr]:        12000
[279 sec,   35824 itr]:        12000
[280 sec,   35979 itr]:        12000
[281 sec,   36114 itr]:        12000
[282 sec,   36287 itr]:        12000
[ optimality gap     ]:      100.00%
[283 sec,   36287 itr]:        12000
[284 sec,   36444 itr]:        12000
[285 sec,   36540 itr]:        12000
[286 sec,   36761 itr]:        12000
[287 sec,   36888 itr]:        12000
[288 sec,   37034 itr]:        12000
[289 sec,   37195 itr]:        12000
[290 sec,   37195 itr]:        12000
[291 sec,   37339 itr]:        12000
[292 sec,   37454 itr]:        12000
[ optimality gap     ]:      100.00%
[293 sec,   37727 itr]:        12000
[294 sec,   37871 itr]:        12000
[295 sec,   38003 itr]:        12000
[296 sec,   38003 itr]:        12000
[297 sec,   38232 itr]:        12000
[298 sec,   38342 itr]:        12000
[299 sec,   38342 itr]:        12000
[300 sec,   38455 itr]:        12000
[301 sec,   38738 itr]:        12000
[302 sec,   38886 itr]:        12000
[ optimality gap     ]:      100.00%
[303 sec,   39016 itr]:        12000
[304 sec,   39165 itr]:        12000
[305 sec,   39165 itr]:        12000
[306 sec,   39399 itr]:        12000
[307 sec,   39514 itr]:        12000
[308 sec,   39639 itr]:        12000
[309 sec,   39639 itr]:        12000
[310 sec,   39714 itr]:        12000
[311 sec,   39997 itr]:        12000
[312 sec,   39997 itr]:        12000
[ optimality gap     ]:      100.00%
[313 sec,   40261 itr]:        12000
[314 sec,   40421 itr]:        12000
[315 sec,   40567 itr]:        12000
[316 sec,   40742 itr]:        12000
[317 sec,   40742 itr]:        12000
[318 sec,   41012 itr]:        12000
[319 sec,   41248 itr]:        12000
[320 sec,   41466 itr]:        12000
[321 sec,   41650 itr]:        12000
[322 sec,   41852 itr]:        12000
[ optimality gap     ]:      100.00%
[323 sec,   41852 itr]:        12000
[324 sec,   42027 itr]:        12000
[325 sec,   42323 itr]:        12000
[326 sec,   42441 itr]:        12000
[327 sec,   42614 itr]:        12000
[328 sec,   42614 itr]:        12000
[329 sec,   42782 itr]:        12000
[330 sec,   43009 itr]:        12000
[331 sec,   43152 itr]:        12000
[332 sec,   43274 itr]:        12000
[ optimality gap     ]:      100.00%
[333 sec,   43421 itr]:        12000
[334 sec,   43421 itr]:        12000
[335 sec,   43695 itr]:        12000
[336 sec,   43809 itr]:        12000
[337 sec,   43943 itr]:        12000
[338 sec,   44083 itr]:        12000
[339 sec,   44083 itr]:        12000
[340 sec,   44358 itr]:        12000
[341 sec,   44520 itr]:        12000
[342 sec,   44622 itr]:        12000
[ optimality gap     ]:      100.00%
[343 sec,   44622 itr]:        12000
[344 sec,   44888 itr]:        12000
[345 sec,   45047 itr]:        12000
[346 sec,   45215 itr]:        12000
[347 sec,   45215 itr]:        12000
[348 sec,   45492 itr]:        12000
[349 sec,   45492 itr]:        12000
[350 sec,   45746 itr]:        12000
[351 sec,   45899 itr]:        12000
[352 sec,   45987 itr]:        12000
[ optimality gap     ]:      100.00%
[353 sec,   46065 itr]:        12000
[354 sec,   46206 itr]:        12000
[355 sec,   46206 itr]:        12000
[356 sec,   46339 itr]:        12000
[357 sec,   46667 itr]:        12000
[358 sec,   46814 itr]:        12000
[359 sec,   46814 itr]:        12000
[360 sec,   47042 itr]:        12000
[361 sec,   47164 itr]:        12000
[362 sec,   47290 itr]:        12000
[ optimality gap     ]:      100.00%
[363 sec,   47415 itr]:        12000
[364 sec,   47548 itr]:        12000
[365 sec,   47724 itr]:        12000
[366 sec,   47896 itr]:        12000
[367 sec,   47896 itr]:        12000
[368 sec,   48152 itr]:        12000
[369 sec,   48279 itr]:        12000
[370 sec,   48401 itr]:        12000
[371 sec,   48401 itr]:        12000
[372 sec,   48688 itr]:        12000
[ optimality gap     ]:      100.00%
[373 sec,   48846 itr]:        12000
[374 sec,   48998 itr]:        12000
[375 sec,   49156 itr]:        12000
[376 sec,   49156 itr]:        12000
[377 sec,   49312 itr]:        12000
[378 sec,   49474 itr]:        12000
[379 sec,   49474 itr]:        12000
[380 sec,   49602 itr]:        12000
[381 sec,   49746 itr]:        12000
[382 sec,   49874 itr]:        12000
[ optimality gap     ]:      100.00%
[383 sec,   50040 itr]:        12000
[384 sec,   50040 itr]:        12000
[385 sec,   50212 itr]:        12000
[386 sec,   50519 itr]:        12000
[387 sec,   50604 itr]:        12000
[388 sec,   50749 itr]:        12000
[389 sec,   50749 itr]:        12000
[390 sec,   50958 itr]:        12000
[391 sec,   51139 itr]:        12000
[392 sec,   51285 itr]:        12000
[ optimality gap     ]:      100.00%
[393 sec,   51468 itr]:        12000
[394 sec,   51468 itr]:        12000
[395 sec,   51725 itr]:        12000
[396 sec,   51943 itr]:        12000
[397 sec,   51943 itr]:        12000
[398 sec,   52149 itr]:        12000
[399 sec,   52149 itr]:        12000
[400 sec,   52264 itr]:        12000
[401 sec,   52484 itr]:        12000
[402 sec,   52484 itr]:        12000
[ optimality gap     ]:      100.00%
[403 sec,   52768 itr]:        12000
[404 sec,   52865 itr]:        12000
[405 sec,   52865 itr]:        12000
[406 sec,   53065 itr]:        12000
[407 sec,   53195 itr]:        12000
[408 sec,   53195 itr]:        12000
[409 sec,   53340 itr]:        12000
[410 sec,   53577 itr]:        12000
[411 sec,   53577 itr]:        12000
[412 sec,   53682 itr]:        12000
[ optimality gap     ]:      100.00%
[413 sec,   53886 itr]:        12000
[414 sec,   53886 itr]:        12000
[415 sec,   54157 itr]:        12000
[416 sec,   54351 itr]:        12000
[417 sec,   54485 itr]:        12000
[418 sec,   54485 itr]:        12000
[419 sec,   54834 itr]:        12000
[420 sec,   54950 itr]:        12000
[421 sec,   54950 itr]:        12000
[422 sec,   55177 itr]:        12000
[ optimality gap     ]:      100.00%
[423 sec,   55356 itr]:        12000
[424 sec,   55356 itr]:        12000
[425 sec,   55490 itr]:        12000
[426 sec,   55645 itr]:        12000
[427 sec,   55718 itr]:        12000
[428 sec,   55744 itr]:        12000
[429 sec,   55827 itr]:        12000
[430 sec,   55827 itr]:        12000
[431 sec,   55941 itr]:        12000
[432 sec,   55941 itr]:        12000
[ optimality gap     ]:      100.00%
[433 sec,   56090 itr]:        12000
[434 sec,   56142 itr]:        12000
[435 sec,   56234 itr]:        12000
[436 sec,   56234 itr]:        12000
[437 sec,   56338 itr]:        12000
[438 sec,   56418 itr]:        12000
[439 sec,   56527 itr]:        12000
[440 sec,   56617 itr]:        12000
[441 sec,   56686 itr]:        12000
[442 sec,   56765 itr]:        12000
[ optimality gap     ]:      100.00%
[443 sec,   56825 itr]:        12000
[444 sec,   56876 itr]:        12000
[445 sec,   56961 itr]:        12000
[446 sec,   57023 itr]:        12000
[447 sec,   57091 itr]:        12000
[448 sec,   57217 itr]:        12000
[449 sec,   57315 itr]:        12000
[450 sec,   57375 itr]:        12000
[451 sec,   57422 itr]:        12000
[452 sec,   57474 itr]:        12000
[ optimality gap     ]:      100.00%
[453 sec,   57474 itr]:        12000
[454 sec,   57599 itr]:        12000
[455 sec,   57599 itr]:        12000
[456 sec,   57731 itr]:        12000
[457 sec,   57785 itr]:        12000
[458 sec,   57868 itr]:        12000
[459 sec,   57930 itr]:        12000
[460 sec,   57930 itr]:        12000
[461 sec,   58056 itr]:        12000
[462 sec,   58120 itr]:        12000
[ optimality gap     ]:      100.00%
[463 sec,   58188 itr]:        12000
[464 sec,   58263 itr]:        12000
[465 sec,   58351 itr]:        12000
[466 sec,   58393 itr]:        12000
[467 sec,   58393 itr]:        12000
[468 sec,   58575 itr]:        12000
[469 sec,   58645 itr]:        12000
[470 sec,   58726 itr]:        12000
[471 sec,   58726 itr]:        12000
[472 sec,   58861 itr]:        12000
[ optimality gap     ]:      100.00%
[473 sec,   58929 itr]:        12000
[474 sec,   59058 itr]:        12000
[475 sec,   59133 itr]:        12000
[476 sec,   59243 itr]:        12000
[477 sec,   59314 itr]:        12000
[478 sec,   59314 itr]:        12000
[479 sec,   59433 itr]:        12000
[480 sec,   59433 itr]:        12000
[481 sec,   59593 itr]:        12000
[482 sec,   59690 itr]:        12000
[ optimality gap     ]:      100.00%
[483 sec,   59690 itr]:        12000
[484 sec,   59796 itr]:        12000
[485 sec,   59796 itr]:        12000
[486 sec,   59932 itr]:        12000
[487 sec,   60037 itr]:        12000
[488 sec,   60126 itr]:        12000
[489 sec,   60190 itr]:        12000
[490 sec,   60190 itr]:        12000
[491 sec,   60386 itr]:        12000
[492 sec,   60386 itr]:        12000
[ optimality gap     ]:      100.00%
[493 sec,   60542 itr]:        12000
[494 sec,   60616 itr]:        12000
[495 sec,   60719 itr]:        12000
[496 sec,   60719 itr]:        12000
[497 sec,   60896 itr]:        12000
[498 sec,   60973 itr]:        12000
[499 sec,   61030 itr]:        12000
[500 sec,   61030 itr]:        12000
[501 sec,   61126 itr]:        12000
[502 sec,   61270 itr]:        12000
[ optimality gap     ]:      100.00%
[503 sec,   61270 itr]:        12000
[504 sec,   61403 itr]:        12000
[505 sec,   61475 itr]:        12000
[506 sec,   61475 itr]:        12000
[507 sec,   61563 itr]:        12000
[508 sec,   61685 itr]:        12000
[509 sec,   61685 itr]:        12000
[510 sec,   61820 itr]:        12000
[511 sec,   61890 itr]:        12000
[512 sec,   61890 itr]:        12000
[ optimality gap     ]:      100.00%
[513 sec,   62008 itr]:        12000
[514 sec,   62043 itr]:        12000
[515 sec,   62129 itr]:        12000
[516 sec,   62331 itr]:        12000
[517 sec,   62452 itr]:        12000
[518 sec,   62525 itr]:        12000
[519 sec,   62648 itr]:        12000
[520 sec,   62772 itr]:        12000
[521 sec,   62846 itr]:        12000
[522 sec,   62846 itr]:        12000
[ optimality gap     ]:      100.00%
[523 sec,   62973 itr]:        12000
[524 sec,   63072 itr]:        12000
[525 sec,   63153 itr]:        12000
[526 sec,   63223 itr]:        12000
[527 sec,   63266 itr]:        12000
[528 sec,   63266 itr]:        12000
[529 sec,   63393 itr]:        12000
[530 sec,   63445 itr]:        12000
[531 sec,   63537 itr]:        12000
[532 sec,   63537 itr]:        12000
[ optimality gap     ]:      100.00%
[533 sec,   63702 itr]:        12000
[534 sec,   63780 itr]:        12000
[535 sec,   63876 itr]:        12000
[536 sec,   63962 itr]:        12000
[537 sec,   64035 itr]:        12000
[538 sec,   64035 itr]:        12000
[539 sec,   64139 itr]:        12000
[540 sec,   64315 itr]:        12000
[541 sec,   64315 itr]:        12000
[542 sec,   64499 itr]:        12000
[ optimality gap     ]:      100.00%
[543 sec,   64499 itr]:        12000
[544 sec,   64606 itr]:        12000
[545 sec,   64697 itr]:        12000
[546 sec,   64768 itr]:        12000
[547 sec,   64843 itr]:        12000
[548 sec,   64906 itr]:        12000
[549 sec,   64960 itr]:        12000
[550 sec,   65056 itr]:        12000
[551 sec,   65149 itr]:        12000
[552 sec,   65249 itr]:        12000
[ optimality gap     ]:      100.00%
[553 sec,   65249 itr]:        12000
[554 sec,   65410 itr]:        12000
[555 sec,   65490 itr]:        12000
[556 sec,   65490 itr]:        12000
[557 sec,   65674 itr]:        12000
[558 sec,   65762 itr]:        12000
[559 sec,   65835 itr]:        12000
[560 sec,   65936 itr]:        12000
[561 sec,   66032 itr]:        12000
[562 sec,   66106 itr]:        12000
[ optimality gap     ]:      100.00%
[563 sec,   66195 itr]:        12000
[564 sec,   66195 itr]:        12000
[565 sec,   66257 itr]:        12000
[566 sec,   66402 itr]:        12000
[567 sec,   66497 itr]:        12000
[568 sec,   66497 itr]:        12000
[569 sec,   66652 itr]:        12000
[570 sec,   66739 itr]:        12000
[571 sec,   66817 itr]:        12000
[572 sec,   66893 itr]:        12000
[ optimality gap     ]:      100.00%
[573 sec,   66934 itr]:        12000
[574 sec,   67008 itr]:        12000
[575 sec,   67099 itr]:        12000
[576 sec,   67166 itr]:        12000
[577 sec,   67261 itr]:        12000
[578 sec,   67261 itr]:        12000
[579 sec,   67541 itr]:        12000
[580 sec,   67660 itr]:        12000
[581 sec,   67856 itr]:        12000
[582 sec,   67978 itr]:        12000
[ optimality gap     ]:      100.00%
[583 sec,   68102 itr]:        12000
[584 sec,   68276 itr]:        12000
[585 sec,   68276 itr]:        12000
[586 sec,   68413 itr]:        12000
[587 sec,   68580 itr]:        12000
[588 sec,   68704 itr]:        12000
[589 sec,   69119 itr]:        12000
[590 sec,   69284 itr]:        12000
[591 sec,   69509 itr]:        12000
[592 sec,   69715 itr]:        12000
[ optimality gap     ]:      100.00%
[593 sec,   69715 itr]:        12000
[594 sec,   70098 itr]:        12000
[595 sec,   70270 itr]:        12000
[596 sec,   70270 itr]:        12000
[597 sec,   70413 itr]:        12000
[598 sec,   70722 itr]:        12000
[599 sec,   70722 itr]:        12000
[600 sec,   71091 itr]:        12000
[600 sec,   71091 itr]:        12000
[ optimality gap     ]:      100.00%

71091 iterations performed in 600 seconds

Feasible solution: 
  obj    =        12000
  gap    =      100.00%
  bounds =         -inf
Status: HxSolutionStatus.FEASIBLE
Number of non-zero nodes found by Hexaly:44
Eenergy value obtained by Hexaly:12000.020820610489
Time taken by Hexaly:599.5881824493408

# compute relative gap
tol = 1e-7
abs_gap = hex_obj-optimal_energy
relative_gap = (round(abs_gap,6)*100)/round(optimal_energy,6)

# print result
if abs_gap>tol:
    print(f"Hexaly solution is not optimal")
    print(f"Absolute Gap:{abs_gap}")
    print(f"Relative Gap(%):{abs(relative_gap)}")
else:
    print(f"Optimal solution found:{hex_obj}.")

Hexaly solution is not optimal
Absolute Gap:0.020820610488954117
Relative Gap(%):0.00017350833333333333