Hexaly QPLIB 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 read_qplib(path):
    with open(path) as fh:
        toks = [t for t in (line.split("#")[0].strip() for line in fh) if t]
    pos = 0
    def nxt():
        nonlocal pos
        val = toks[pos]
        pos += 1
        return val
    def defaulted(length):
        """Read a `default value` / `number of non-defaults` / entries block."""
        arr = np.full(length, float(nxt()))
        for _ in range(int(nxt())):
            i, v = nxt().split()
            arr[int(i) - 1] = float(v)
        return arr
    name = nxt()
    probtype = nxt()
    sense = nxt().lower()
    n = int(nxt())
    m = int(nxt())
    # quadratic terms of the objective (each unordered pair listed once)
    Q = np.zeros((n, n), dtype=np.float32)
    for _ in range(int(nxt())):
        i, j, v = nxt().split()
        i, j, v = int(i) - 1, int(j) - 1, float(v)
        if i == j:
            Q[i, i] = v
        else:
            Q[i, j] = Q[j, i] = 0.5 * v   # split the pair coefficient over both triangles
    b = defaulted(n)            # linear terms of the objective
    obj_const = float(nxt())
    # linear terms of the constraints
    A = np.zeros((m, n))
    for _ in range(int(nxt())):
        k, i, v = nxt().split()
        A[int(k) - 1, int(i) - 1] = float(v)
    inf = float(nxt())
    lhs, rhs = defaulted(m), defaulted(m)
    lb, ub = defaulted(n), defaulted(n)
    return dict(name=name, type=probtype, sense=sense, n=n, m=m,
                Q=Q, b=b, obj_const=obj_const,
                A=A, lhs=lhs, rhs=rhs, lb=lb, ub=ub, inf=inf)

# Instance details
inst_dir = "Instances/"
inst_name = "QPLIB_2761.qplib"
inst = read_qplib(os.path.join(inst_dir, inst_name))
n, Q, b = inst["n"], inst["Q"], inst["b"]
M = 0.5 * Q
c = b.copy()
sum_constraint = float(inst["rhs"][0])   # sum_i x_i = 1

# solver parameters
time_limit = 300

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

Preprocess model 100%Starting Hexaly solver...
Push initial solution 100%
Model:  expressions = 1009, decisions = 500, constraints = 1, objectives = 1
Param:  time limit = 300 sec, no iteration limit

[objective direction ]:     minimize

[  0 sec,       0 itr]: No feasible solution found (infeas = 1)
[  1 sec,     226 itr]:     0.481681
[  2 sec,    1417 itr]:     0.415455
[  3 sec,    1417 itr]:     0.415455
[  4 sec,    2207 itr]:    0.0669736
[  5 sec,    2713 itr]:    0.0669736
[  6 sec,    3123 itr]:   0.00109363
[  7 sec,    3513 itr]:   0.00109363
[  8 sec,    4202 itr]:   0.00109363
[  9 sec,    4202 itr]:   0.00109363
[ 10 sec,    4521 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[ 11 sec,    5075 itr]:   0.00109363
[ 12 sec,    5357 itr]:   0.00109363
[ 13 sec,    5357 itr]:   0.00109363
[ 14 sec,    5608 itr]:   0.00109363
[ 15 sec,    5866 itr]:   0.00109363
[ 16 sec,    6135 itr]:   0.00109363
[ 17 sec,    6641 itr]:   0.00109363
[ 18 sec,    6911 itr]:   0.00109363
[ 19 sec,    6911 itr]:   0.00109363
[ 20 sec,    7476 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[ 21 sec,    7720 itr]:   0.00109363
[ 22 sec,    7993 itr]:   0.00109363
[ 23 sec,    7993 itr]:   0.00109363
[ 24 sec,    8506 itr]:   0.00109363
[ 25 sec,    8774 itr]:   0.00109363
[ 26 sec,    9058 itr]:   0.00109363
[ 27 sec,    9058 itr]:   0.00109363
[ 28 sec,    9331 itr]:   0.00109363
[ 29 sec,    9881 itr]:   0.00109363
[ 30 sec,    9881 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[ 31 sec,   10457 itr]:   0.00109363
[ 32 sec,   10801 itr]:   0.00109363
[ 33 sec,   11175 itr]:   0.00109363
[ 34 sec,   11590 itr]:   0.00109363
[ 35 sec,   11983 itr]:   0.00109363
[ 36 sec,   12306 itr]:   0.00109363
[ 37 sec,   12690 itr]:   0.00109363
[ 38 sec,   12690 itr]:   0.00109363
[ 39 sec,   13509 itr]:   0.00109363
[ 40 sec,   13509 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[ 41 sec,   14379 itr]:   0.00109363
[ 42 sec,   14904 itr]:   0.00109363
[ 43 sec,   14904 itr]:   0.00109363
[ 44 sec,   16026 itr]:   0.00109363
[ 45 sec,   16026 itr]:   0.00109363
[ 46 sec,   16584 itr]:   0.00109363
[ 47 sec,   17206 itr]:   0.00109363
[ 48 sec,   18305 itr]:   0.00109363
[ 49 sec,   18305 itr]:   0.00109363
[ 50 sec,   19054 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[ 51 sec,   19663 itr]:   0.00109363
[ 52 sec,   21035 itr]:   0.00109363
[ 53 sec,   21035 itr]:   0.00109363
[ 54 sec,   22329 itr]:   0.00109363
[ 55 sec,   22920 itr]:   0.00109363
[ 56 sec,   22920 itr]:   0.00109363
[ 57 sec,   24618 itr]:   0.00109363
[ 58 sec,   24618 itr]:   0.00109363
[ 59 sec,   25489 itr]:   0.00109363
[ 60 sec,   26174 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[ 61 sec,   26985 itr]:   0.00109363
[ 62 sec,   28708 itr]:   0.00109363
[ 63 sec,   29571 itr]:   0.00109363
[ 64 sec,   30660 itr]:   0.00109363
[ 65 sec,   30660 itr]:   0.00109363
[ 66 sec,   33161 itr]:   0.00109363
[ 67 sec,   34620 itr]:   0.00109363
[ 68 sec,   35427 itr]:   0.00109363
[ 69 sec,   36331 itr]:   0.00109363
[ 70 sec,   36331 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[ 71 sec,   37300 itr]:   0.00109363
[ 72 sec,   39734 itr]:   0.00109363
[ 73 sec,   39734 itr]:   0.00109363
[ 74 sec,   42357 itr]:   0.00109363
[ 75 sec,   43777 itr]:   0.00109363
[ 76 sec,   43777 itr]:   0.00109363
[ 77 sec,   46432 itr]:   0.00109363
[ 78 sec,   48014 itr]:   0.00109363
[ 79 sec,   49675 itr]:   0.00109363
[ 80 sec,   50939 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[ 81 sec,   52229 itr]:   0.00109363
[ 82 sec,   53510 itr]:   0.00109363
[ 83 sec,   54838 itr]:   0.00109363
[ 84 sec,   56219 itr]:   0.00109363
[ 85 sec,   57598 itr]:   0.00109363
[ 86 sec,   59114 itr]:   0.00109363
[ 87 sec,   60794 itr]:   0.00109363
[ 88 sec,   60794 itr]:   0.00109363
[ 89 sec,   62586 itr]:   0.00109363
[ 90 sec,   65484 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[ 91 sec,   66984 itr]:   0.00109363
[ 92 sec,   68386 itr]:   0.00109363
[ 93 sec,   68386 itr]:   0.00109363
[ 94 sec,   71087 itr]:   0.00109363
[ 95 sec,   72642 itr]:   0.00109363
[ 96 sec,   74305 itr]:   0.00109363
[ 97 sec,   75964 itr]:   0.00109363
[ 98 sec,   77668 itr]:   0.00109363
[ 99 sec,   77668 itr]:   0.00109363
[100 sec,   81322 itr]:   0.00109363
[ optimality gap     ]:      100.00%
[101 sec,   82982 itr]:   0.00109363
[102 sec,   82982 itr]:   0.00109363
[103 sec,   86483 itr]:   0.00109363
[104 sec,   86483 itr]:   0.00109363
[105 sec,   89652 itr]:   0.00109363
[106 sec,   89652 itr]:   0.00109363
[107 sec,   91377 itr]:   0.00109363
[108 sec,   93075 itr]:   0.00109363
[109 sec,   95746 itr]:   0.00108351
[110 sec,   95746 itr]:   0.00108351
[ optimality gap     ]:      100.00%
[111 sec,   99102 itr]:   0.00108265
[112 sec,   99102 itr]:   0.00108265
[113 sec,  102479 itr]:   0.00108171
[114 sec,  102479 itr]:   0.00108171
[115 sec,  105824 itr]:   0.00108171
[116 sec,  107631 itr]:   0.00108171
[117 sec,  109239 itr]:   0.00107665
[118 sec,  110889 itr]:   0.00107386
[119 sec,  112638 itr]:   0.00107386
[120 sec,  114778 itr]:   0.00107386
[ optimality gap     ]:      100.00%
[121 sec,  114778 itr]:   0.00107386
[122 sec,  116787 itr]:   0.00107386
[123 sec,  120536 itr]:   0.00107386
[124 sec,  122390 itr]:   0.00107386
[125 sec,  122390 itr]:   0.00107386
[126 sec,  123826 itr]:   0.00107386
[127 sec,  125606 itr]:   0.00107386
[128 sec,  128956 itr]:   0.00107385
[129 sec,  130493 itr]:   0.00107385
[130 sec,  132310 itr]:   0.00107373
[ optimality gap     ]:      100.00%
[131 sec,  133881 itr]:   0.00107373
[132 sec,  133881 itr]:   0.00107373
[133 sec,  137501 itr]:   0.00107373
[134 sec,  137501 itr]:   0.00107373
[135 sec,  139124 itr]:   0.00107235
[136 sec,  142470 itr]:    0.0010687
[137 sec,  144210 itr]:    0.0010658
[138 sec,  145961 itr]:   0.00106533
[139 sec,  147824 itr]:   0.00106481
[140 sec,  149423 itr]:   0.00106481
[ optimality gap     ]:      100.00%
[141 sec,  149423 itr]:   0.00106481
[142 sec,  152758 itr]:   0.00106481
[143 sec,  154299 itr]:   0.00106481
[144 sec,  155888 itr]:   0.00106481
[145 sec,  157490 itr]:   0.00106481
[146 sec,  157490 itr]:   0.00106481
[147 sec,  158915 itr]:   0.00106481
[148 sec,  161981 itr]:   0.00106481
[149 sec,  161981 itr]:   0.00106481
[150 sec,  164929 itr]:   0.00106118
[ optimality gap     ]:      100.00%
[151 sec,  166352 itr]:   0.00106118
[152 sec,  167652 itr]:   0.00106118
[153 sec,  169150 itr]:   0.00106118
[154 sec,  170646 itr]:   0.00106118
[155 sec,  170646 itr]:   0.00106118
[156 sec,  172551 itr]:   0.00105954
[157 sec,  176568 itr]:   0.00105954
[158 sec,  178443 itr]:   0.00105954
[159 sec,  178443 itr]:   0.00105954
[160 sec,  182133 itr]:   0.00105954
[ optimality gap     ]:      100.00%
[161 sec,  182133 itr]:   0.00105954
[162 sec,  184086 itr]:   0.00105954
[163 sec,  187527 itr]:   0.00105954
[164 sec,  189551 itr]:   0.00105954
[165 sec,  191438 itr]:   0.00105901
[166 sec,  193582 itr]:   0.00105901
[167 sec,  195791 itr]:   0.00105901
[168 sec,  195791 itr]:   0.00105901
[169 sec,  197645 itr]:   0.00105901
[170 sec,  199747 itr]:   0.00105901
[ optimality gap     ]:      100.00%
[171 sec,  201583 itr]:   0.00105901
[172 sec,  205467 itr]:   0.00105759
[173 sec,  205467 itr]:   0.00105719
[174 sec,  207637 itr]:   0.00105719
[175 sec,  209529 itr]:   0.00105719
[176 sec,  213351 itr]:   0.00105719
[177 sec,  213351 itr]:   0.00105719
[178 sec,  217063 itr]:   0.00105675
[179 sec,  219040 itr]:   0.00105675
[180 sec,  219040 itr]:   0.00105675
[ optimality gap     ]:      100.00%
[181 sec,  223027 itr]:   0.00105675
[182 sec,  224610 itr]:   0.00105675
[183 sec,  224610 itr]:   0.00105675
[184 sec,  227668 itr]:   0.00105675
[185 sec,  227668 itr]:   0.00105675
[186 sec,  230642 itr]:   0.00105675
[187 sec,  232385 itr]:   0.00105675
[188 sec,  233903 itr]:   0.00105675
[189 sec,  235543 itr]:   0.00105576
[190 sec,  237198 itr]:   0.00105576
[ optimality gap     ]:      100.00%
[191 sec,  238802 itr]:   0.00105576
[192 sec,  240200 itr]:   0.00105576
[193 sec,  241847 itr]:   0.00105576
[194 sec,  243559 itr]:   0.00105576
[195 sec,  245162 itr]:   0.00105576
[196 sec,  245162 itr]:   0.00105576
[197 sec,  246973 itr]:   0.00105576
[198 sec,  250640 itr]:   0.00105576
[199 sec,  250640 itr]:   0.00105576
[200 sec,  254464 itr]:   0.00105576
[ optimality gap     ]:      100.00%
[201 sec,  256204 itr]:   0.00105576
[202 sec,  256204 itr]:   0.00105576
[203 sec,  258275 itr]:   0.00105576
[204 sec,  262095 itr]:   0.00105576
[205 sec,  262095 itr]:   0.00105576
[206 sec,  263891 itr]:   0.00105576
[207 sec,  267570 itr]:   0.00105576
[208 sec,  269614 itr]:   0.00105576
[209 sec,  271398 itr]:   0.00105576
[210 sec,  271398 itr]:   0.00105576
[ optimality gap     ]:      100.00%
[211 sec,  273406 itr]:   0.00105576
[212 sec,  277055 itr]:   0.00105576
[213 sec,  279180 itr]:   0.00105576
[214 sec,  279180 itr]:   0.00105576
[215 sec,  282811 itr]:   0.00105576
[216 sec,  282811 itr]:   0.00105576
[217 sec,  287029 itr]:   0.00105545
[218 sec,  289131 itr]:   0.00105545
[219 sec,  289131 itr]:   0.00105545
[220 sec,  293110 itr]:   0.00105468
[ optimality gap     ]:      100.00%
[221 sec,  293110 itr]:   0.00105468
[222 sec,  296688 itr]:    0.0010539
[223 sec,  298725 itr]:   0.00105371
[224 sec,  300292 itr]:   0.00105371
[225 sec,  300292 itr]:   0.00105371
[226 sec,  302077 itr]:   0.00105371
[227 sec,  306039 itr]:   0.00105226
[228 sec,  306039 itr]:   0.00105226
[229 sec,  307451 itr]:   0.00105226
[230 sec,  308052 itr]:   0.00105226
[ optimality gap     ]:      100.00%
[231 sec,  308623 itr]:   0.00105226
[232 sec,  308623 itr]:   0.00105226
[233 sec,  310032 itr]:   0.00105226
[234 sec,  310032 itr]:   0.00105226
[235 sec,  310945 itr]:   0.00105226
[236 sec,  312453 itr]:   0.00105226
[237 sec,  312453 itr]:   0.00105226
[238 sec,  313325 itr]:   0.00105226
[239 sec,  314915 itr]:   0.00105207
[240 sec,  314915 itr]:   0.00105207
[ optimality gap     ]:      100.00%
[241 sec,  316404 itr]:   0.00105207
[242 sec,  316404 itr]:   0.00105207
[243 sec,  317962 itr]:   0.00105207
[244 sec,  318588 itr]:   0.00105194
[245 sec,  318588 itr]:   0.00105194
[246 sec,  319434 itr]:   0.00105194
[247 sec,  321013 itr]:   0.00105194
[248 sec,  321664 itr]:   0.00105194
[249 sec,  321664 itr]:   0.00105194
[250 sec,  323117 itr]:   0.00105194
[ optimality gap     ]:      100.00%
[251 sec,  323117 itr]:   0.00105194
[252 sec,  323873 itr]:   0.00105194
[253 sec,  324492 itr]:   0.00105194
[254 sec,  326056 itr]:   0.00105194
[255 sec,  326056 itr]:   0.00105194
[256 sec,  327720 itr]:   0.00105194
[257 sec,  327720 itr]:   0.00105194
[258 sec,  329303 itr]:   0.00105194
[259 sec,  329303 itr]:   0.00105194
[260 sec,  330739 itr]:   0.00105194
[ optimality gap     ]:      100.00%
[261 sec,  330739 itr]:   0.00105194
[262 sec,  331689 itr]:   0.00105194
[263 sec,  332457 itr]:   0.00105194
[264 sec,  333244 itr]:   0.00105194
[265 sec,  333933 itr]:   0.00105183
[266 sec,  335300 itr]:   0.00105168
[267 sec,  335300 itr]:   0.00105168
[268 sec,  335975 itr]:   0.00105168
[269 sec,  336859 itr]:   0.00105168
[270 sec,  337513 itr]:   0.00105168
[ optimality gap     ]:      100.00%
[271 sec,  339052 itr]:   0.00105168
[272 sec,  339788 itr]:   0.00105168
[273 sec,  339788 itr]:   0.00105168
[274 sec,  341046 itr]:   0.00105168
[275 sec,  341046 itr]:   0.00105168
[276 sec,  342387 itr]:   0.00105168
[277 sec,  342387 itr]:   0.00105168
[278 sec,  343024 itr]:   0.00105155
[279 sec,  343786 itr]:   0.00105155
[280 sec,  345023 itr]:   0.00105135
[ optimality gap     ]:      100.00%
[281 sec,  345698 itr]:   0.00105135
[282 sec,  345698 itr]:   0.00105135
[283 sec,  346353 itr]:   0.00105135
[284 sec,  347952 itr]:   0.00105076
[285 sec,  348619 itr]:   0.00105066
[286 sec,  348619 itr]:   0.00105066
[287 sec,  349403 itr]:   0.00105066
[288 sec,  350132 itr]:   0.00105066
[289 sec,  350790 itr]:   0.00105066
[290 sec,  352171 itr]:   0.00105066
[ optimality gap     ]:      100.00%
[291 sec,  352856 itr]:   0.00105066
[292 sec,  352856 itr]:   0.00105066
[293 sec,  354243 itr]:   0.00104905
[294 sec,  355071 itr]:   0.00104905
[295 sec,  355809 itr]:   0.00104905
[296 sec,  355809 itr]:   0.00104905
[297 sec,  357257 itr]:   0.00104905
[298 sec,  357927 itr]:   0.00104905
[299 sec,  358644 itr]:   0.00104905
[300 sec,  359308 itr]:   0.00104905
[ optimality gap     ]:      100.00%
[300 sec,  359308 itr]:   0.00104905
[ optimality gap     ]:      100.00%

359308 iterations performed in 300 seconds

Feasible solution: 
  obj    =   0.00104905
  gap    =      100.00%
  bounds =         -inf
Status: HxSolutionStatus.FEASIBLE
Eenergy value obtained by Hexaly:0.001049053329335798