Gurobi very slow at solving MIQP

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  • Gayan Lankeshwara

    Hi there,

    I am facing the same issue in solving a MIQP optimisation problem. To be specific I am following Model Predictive Control technique so at each step in the algorithm I need to perform a MIQP with Gurobi. However, I am struggling to solve the optimisation problem at the very first step.

    The log file is as below.

    Academic license - for non-commercial use only
    Optimize a model with 7010 rows, 6010 columns and 16910 nonzeros
    Model has 1010 quadratic objective terms
    Variable types: 2010 continuous, 4000 integer (4000 binary)
    Coefficient statistics:
    Matrix range [4e-02, 2e+00]
    Objective range [5e+01, 4e+02]
    QObjective range [2e+00, 2e+00]
    Bounds range [1e+00, 1e+00]
    RHS range [9e-02, 2e+01]
    Found heuristic solution: objective 104373.43751
    Presolve removed 4100 rows and 1100 columns
    Presolve time: 0.02s
    Presolved: 2910 rows, 4910 columns, 10910 nonzeros
    Presolved model has 1010 quadratic objective terms
    Variable types: 1010 continuous, 3900 integer (3000 binary)

    Root relaxation: objective 2.410519e-01, 7085 iterations, 0.13 seconds

    Nodes | Current Node | Objective Bounds | Work
    Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time

    0 0 0.24105 0 1250 104373.438 0.24105 100% - 0s
    H 0 0 1421.0937571 0.24105 100% - 0s
    H 0 0 970.3784353 0.24105 100% - 0s
    0 0 0.24105 0 1250 970.37844 0.24105 100% - 0s
    H 0 0 13.3088811 0.24105 98.2% - 1s
    H 0 0 13.1119684 0.24105 98.2% - 2s
    0 2 0.24105 0 1250 13.11197 0.24105 98.2% - 2s
    H 1 4 2.5391907 0.24105 90.5% 0.0 2s
    H 2 4 2.4837433 0.24105 90.3% 1.5 2s
    H 168 169 2.4770202 0.24105 90.3% 2.6 3s
    H 200 200 2.4751562 0.24105 90.3% 2.6 4s
    H 202 202 2.4709689 0.24105 90.2% 2.6 4s
    H 204 204 2.4337335 0.24105 90.1% 2.6 4s
    H 206 206 2.3969387 0.24105 89.9% 2.6 4s
    H 208 208 2.2607556 0.24105 89.3% 2.6 4s
    H 232 233 1.5884368 0.24105 84.8% 2.7 5s
    H 233 234 1.1954716 0.24105 79.8% 2.7 5s
    H 239 240 1.1782665 0.24105 79.5% 2.7 5s
    H 240 241 1.1327982 0.24105 78.7% 2.7 5s
    H 242 243 1.0993180 0.24105 78.1% 2.7 5s
    H 274 275 1.0984273 0.24105 78.1% 2.7 6s
    H 276 277 1.0907321 0.24105 77.9% 2.7 6s
    H 300 299 0.8630261 0.24105 72.1% 2.7 7s
    H 316 317 0.8630261 0.24105 72.1% 2.7 7s
    H 318 319 0.8629522 0.24105 72.1% 2.7 7s
    H 520 521 0.8604217 0.24105 72.0% 2.9 8s
    H 524 525 0.8573929 0.24105 71.9% 2.9 8s
    H 591 592 0.8573322 0.24105 71.9% 3.0 9s
    592 593 0.24968 101 1212 0.85733 0.24105 71.9% 3.0 10s
    H 600 593 0.8023654 0.24105 70.0% 3.0 10s
    H 609 602 0.7538245 0.24105 68.0% 3.0 10s
    H 1132 1118 0.7516816 0.24105 67.9% 3.8 11s
    H 1204 1190 0.7512557 0.24105 67.9% 4.0 11s
    H 1400 1386 0.7443362 0.24105 67.6% 4.0 12s
    H 1448 1434 0.6360757 0.24105 62.1% 3.9 12s
    H 1520 1502 0.6015006 0.24105 59.9% 3.9 13s
    H 1560 1542 0.5978622 0.24105 59.7% 3.8 13s
    1878 1878 0.31499 312 988 0.59786 0.24105 59.7% 3.8 15s
    H 1946 1925 0.5927228 0.24105 59.3% 3.9 15s
    H 1992 1971 0.5729533 0.24105 57.9% 3.9 15s
    H 2958 2935 0.5566761 0.24105 56.7% 4.0 15s
    H 3089 3090 0.5496940 0.24105 56.1% 4.0 17s
    H 3100 3092 0.5477793 0.24105 56.0% 4.0 18s
    H 3111 3103 0.5477793 0.24105 56.0% 4.0 18s
    3156 3157 0.32337 533 667 0.54778 0.24105 56.0% 4.0 20s
    H 3200 3157 0.5456818 0.24105 55.8% 4.0 20s
    H 3245 3202 0.5354913 0.24105 55.0% 4.0 20s
    H 3335 3293 0.5351017 0.24105 55.0% 4.0 20s
    H 3925 3902 0.4911755 0.24105 50.9% 4.0 23s
    4026 4027 0.32529 677 464 0.49118 0.24105 50.9% 4.0 25s
    H 4100 4027 0.4752007 0.24105 49.3% 4.1 25s
    H 4525 4502 0.4713088 0.24105 48.9% 4.1 27s
    H 4700 4628 0.4690689 0.24105 48.6% 4.1 28s
    H 5075 5002 0.4674786 0.24105 48.4% 4.2 28s
    5076 5077 0.38353 849 354 0.46748 0.24105 48.4% 4.2 30s
    H 5175 5150 0.4450028 0.24105 45.8% 4.2 30s
    H 5450 5375 0.4421985 0.24105 45.5% 4.1 32s
    H 5750 5727 0.4416897 0.24105 45.4% 4.2 33s
    H 5826 5824 0.4411571 0.24105 45.4% 4.2 34s
    5832 5829 0.38441 964 248 0.44116 0.24105 45.4% 4.2 36s
    H 5900 5829 0.4400315 0.24105 45.2% 4.2 36s
    H 6107 6037 0.4395533 0.24105 45.2% 4.3 36s
    H 6176 6105 0.4311664 0.24105 44.1% 4.3 36s
    H 6246 6243 0.4297099 0.24105 43.9% 4.3 37s
    H 6250 5933 0.4291423 0.24105 43.8% 4.3 39s
    H 6252 5640 0.4248724 0.24105 43.3% 5.4 39s
    H 6253 5358 0.4221323 0.24105 42.9% 5.4 39s
    6278 5386 0.24135 17 1249 0.42213 0.24105 42.9% 5.4 40s
    H 6340 5149 0.4218470 0.24105 42.9% 5.4 41s
    H 6604 5068 0.4218470 0.24105 42.9% 5.3 41s
    H 6684 4877 0.4204196 0.24105 42.7% 5.2 43s
    H 6694 4658 0.4200950 0.24105 42.6% 5.2 43s
    H 6890 4570 0.4169799 0.24105 42.2% 5.2 43s
    7012 4647 0.24782 43 1216 0.41698 0.24105 42.2% 5.2 46s
    H 7054 4465 0.4148401 0.24105 41.9% 5.2 47s
    H 7056 4269 0.4145561 0.24105 41.9% 5.2 47s
    H 7067 4090 0.4130168 0.24105 41.6% 5.2 48s
    H 7069 3913 0.4117717 0.24105 41.5% 5.2 48s
    H 7070 3745 0.4096722 0.24105 41.2% 5.2 48s
    7261 3859 0.25110 53 1197 0.40967 0.24105 41.2% 5.1 51s
    H 7268 3707 0.4090244 0.24105 41.1% 5.1 51s
    H 7488 3684 0.4075136 0.24105 40.8% 5.1 52s
    H 7502 3545 0.4065043 0.24105 40.7% 5.1 54s
    7623 3613 0.25701 65 1161 0.40650 0.24105 40.7% 5.1 55s
    H 7931 3653 0.4046611 0.24105 40.4% 5.0 56s
    H 8069 3608 0.4031296 0.24105 40.2% 5.0 57s
    H 8270 3606 0.4023847 0.24105 40.1% 5.1 58s
    8527 3760 0.25911 91 1143 0.40238 0.24105 40.1% 5.3 60s
    H 8533 3648 0.4013390 0.24105 39.9% 5.3 60s
    H 8685 3638 0.4009273 0.24105 39.9% 5.3 61s
    H 8732 3539 0.3996373 0.24105 39.7% 5.3 63s
    8789 3598 0.25945 99 1142 0.39964 0.24105 39.7% 5.3 65s
    H 8860 3534 0.3984287 0.24105 39.5% 5.3 65s
    H 9025 3539 0.3965691 0.24105 39.2% 5.3 66s
    9590 3863 0.29649 121 1144 0.39657 0.24105 39.2% 5.3 71s
    H 9600 3768 0.3952559 0.24105 39.0% 5.4 71s
    10769 4508 0.27239 148 1145 0.39526 0.24105 39.0% 5.4 75s
    H10855 4448 0.3929197 0.24105 38.7% 5.4 75s
    H11967 5448 0.3929197 0.24105 38.7% 5.4 77s
    H12001 5482 0.3927632 0.24105 38.6% 5.4 77s
    H12069 5550 0.3927275 0.24105 38.6% 5.4 77s
    12138 5648 0.29799 181 1142 0.39273 0.24105 38.6% 5.4 80s
    H12347 5797 0.3917445 0.24105 38.5% 5.4 80s
    12933 6444 0.33049 203 1128 0.39174 0.24105 38.5% 5.4 85s
    H13508 6954 0.3914108 0.24105 38.4% 5.4 85s
    H13878 7309 0.3912308 0.24105 38.4% 5.3 88s
    H14062 7492 0.3890542 0.24105 38.0% 5.4 88s
    14523 8023 0.33230 251 1038 0.38905 0.24105 38.0% 5.3 90s
    H15551 8975 0.3890542 0.24105 38.0% 5.3 93s
    H15755 9172 0.3886318 0.24105 38.0% 5.3 93s
    H15857 9274 0.3886318 0.24105 38.0% 5.3 93s
    16062 9487 0.33380 316 895 0.38863 0.24105 38.0% 5.3 96s
    H16334 9705 0.3881272 0.24105 37.9% 5.3 96s
    H16600 9840 0.3849535 0.24105 37.4% 5.3 99s
    H17481 10586 0.3843688 0.24105 37.3% 5.2 99s
    17482 10654 0.33505 371 799 0.38437 0.24105 37.3% 5.2 101s
    H17576 10725 0.3840332 0.24105 37.2% 5.3 101s
    H17709 10861 0.3830885 0.24105 37.1% 5.3 101s
    17710 10885 0.33696 380 810 0.38309 0.24105 37.1% 5.3 105s
    H18901 11844 0.3809896 0.24105 36.7% 5.3 105s
    H19000 11855 0.3777322 0.24105 36.2% 5.3 108s
    H19263 12111 0.3757423 0.24105 35.8% 5.4 108s
    20021 12948 0.35221 475 637 0.37574 0.24105 35.8% 5.4 112s
    H20500 13326 0.3753090 0.24105 35.8% 5.4 112s
    H20700 13516 0.3742276 0.24105 35.6% 5.4 112s
    20861 13765 0.35301 515 567 0.37423 0.24105 35.6% 5.4 115s
    H20940 13805 0.3742276 0.24105 35.6% 5.4 115s
    H21520 14216 0.3719106 0.24105 35.2% 5.5 118s
    H22161 14901 0.3717775 0.24105 35.2% 5.5 122s
    H22201 14936 0.3708983 0.24105 35.0% 5.5 122s
    H22241 14969 0.3705738 0.24105 35.0% 5.5 122s
    22641 15337 0.35423 585 417 0.37057 0.24105 35.0% 5.5 125s
    H22700 15238 0.3687503 0.24105 34.6% 5.5 125s
    H23540 15934 0.3677783 0.24105 34.5% 5.5 128s
    24041 16400 0.35536 635 307 0.36778 0.24105 34.5% 5.5 132s
    H24700 16941 0.3677436 0.24105 34.5% 5.6 132s
    24761 17041 0.35588 665 280 0.36774 0.24105 34.5% 5.6 135s
    H25080 17246 0.3672407 0.24105 34.4% 5.6 135s
    H25360 17399 0.3666663 0.24105 34.3% 5.6 139s
    H25880 17758 0.3663976 0.24105 34.2% 5.6 139s
    26061 17974 0.35604 715 240 0.36640 0.24105 34.2% 5.6 142s
    H26100 17917 0.3651768 0.24105 34.0% 5.6 142s
    26641 18377 0.35900 735 235 0.36518 0.24105 34.0% 5.7 145s
    H27336 18865 0.3651171 0.24105 34.0% 5.7 145s
    H27600 18596 0.3625397 0.24105 33.5% 5.7 149s
    28470 19453 0.35929 802 193 0.36254 0.24105 33.5% 5.7 152s
    29180 20128 0.35918 818 197 0.36254 0.24105 33.5% 5.7 156s
    H29601 20409 0.3618351 0.24105 33.4% 5.7 156s
    H29720 20506 0.3616458 0.24105 33.3% 5.7 156s
    30095 20917 0.36006 838 186 0.36165 0.24105 33.3% 5.7 161s
    H30123 20916 0.3612371 0.24105 33.3% 5.7 161s
    H30601 21181 0.3599682 0.24105 33.0% 5.7 161s
    31020 21577 cutoff 849 0.35997 0.24105 33.0% 5.7 166s
    H31100 21408 0.3588971 0.24105 32.8% 5.7 166s
    32686 23088 0.24854 98 1214 0.35890 0.24105 32.8% 5.7 172s
    H32800 23028 0.3584732 0.24105 32.8% 5.7 172s
    H32815 22986 0.3577178 0.24105 32.6% 5.7 172s
    33948 23972 0.25151 213 1129 0.35772 0.24105 32.6% 5.7 178s
    H34274 24201 0.3575482 0.24105 32.6% 5.7 178s
    35623 25529 0.26375 366 958 0.35755 0.24105 32.6% 5.6 183s
    H35720 25625 0.3575276 0.24105 32.6% 5.6 183s
    H35721 25540 0.3570697 0.24105 32.5% 5.6 183s
    H36721 26147 0.3557409 0.24105 32.2% 5.6 184s
    36977 26314 0.26524 462 794 0.35574 0.24105 32.2% 5.6 189s
    H37124 26337 0.3551684 0.24105 32.1% 5.6 189s
    H37720 26732 0.3547534 0.24105 32.1% 5.6 189s
    38369 27445 0.26878 586 669 0.35475 0.24105 32.1% 5.6 194s
    H38532 27569 0.3546466 0.24105 32.0% 5.6 194s
    H38896 27696 0.3538100 0.24105 31.9% 5.6 194s
    39892 28732 0.27040 718 490 0.35381 0.24105 31.9% 5.6 199s
    H39900 28709 0.3536087 0.24105 31.8% 5.6 199s
    H40946 29544 0.3532519 0.24105 31.8% 5.6 199s
    41183 29891 0.27144 827 410 0.35325 0.24105 31.8% 5.6 204s
    H41418 29886 0.3523701 0.24105 31.6% 5.6 204s
    H42495 30869 0.3514137 0.24105 31.4% 5.6 205s
    H42595 30793 0.3508061 0.24105 31.3% 5.6 205s
    42696 31008 0.27464 945 280 0.35081 0.24105 31.3% 5.6 210s
    H42905 31104 0.3506635 0.24105 31.3% 5.6 210s
    H42910 31177 0.3501381 0.24105 31.2% 5.6 210s
    44147 32389 0.28238 1050 152 0.35014 0.24105 31.2% 5.6 216s
    H45391 33535 0.3499254 0.24105 31.1% 5.6 216s
    45954 34147 0.32230 1201 34 0.34993 0.24105 31.1% 5.6 221s
    H47088 35180 0.3495196 0.24105 31.0% 5.6 221s
    47591 35681 0.25702 70 1154 0.34952 0.24105 31.0% 5.6 227s
    H48413 36394 0.3486554 0.24105 30.9% 5.6 227s
    48954 36953 0.27283 125 1133 0.34866 0.24105 30.9% 5.6 232s
    H49167 37025 0.3486554 0.24105 30.9% 5.6 232s
    H49436 37404 0.3486554 0.24105 30.9% 5.6 232s
    H49596 37526 0.3485910 0.24105 30.8% 5.6 232s
    H49685 37606 0.3484318 0.24105 30.8% 5.6 232s
    50392 38338 0.31864 160 1130 0.34843 0.24105 30.8% 5.6 238s
    H51590 39039 0.3457246 0.24105 30.3% 5.6 238s
    51700 39225 0.29785 215 1091 0.34572 0.24105 30.3% 5.6 244s
    H52202 39505 0.3455679 0.24105 30.2% 5.6 244s
    H53010 40378 0.3454030 0.24105 30.2% 5.6 244s
    53112 40572 0.29903 265 967 0.34540 0.24105 30.2% 5.6 250s
    H53767 40961 0.3439099 0.24105 29.9% 5.6 250s
    55461 42511 0.30150 360 771 0.34391 0.24105 29.9% 5.6 256s
    H56530 43343 0.3435564 0.24105 29.8% 5.6 256s
    57191 44103 0.31248 430 619 0.34356 0.24105 29.8% 5.6 261s
    H57630 44374 0.3431843 0.24105 29.8% 5.6 262s
    H58511 45226 0.3423715 0.24105 29.6% 5.6 267s
    H58618 45253 0.3419763 0.24105 29.5% 5.6 267s
    60482 47083 0.31533 538 347 0.34198 0.24105 29.5% 5.6 272s
    H61430 47695 0.3411162 0.24105 29.3% 5.6 272s
    61888 48139 0.31586 598 371 0.34112 0.24105 29.3% 5.6 278s
    63206 49370 0.31639 654 319 0.34112 0.24105 29.3% 5.6 283s
    H65279 51048 0.3404322 0.24105 29.2% 5.6 284s
    65566 51405 0.31701 752 229 0.34043 0.24105 29.2% 5.6 289s
    67154 52985 0.32189 819 191 0.34043 0.24105 29.2% 5.7 294s
    H67240 52951 0.3399960 0.24105 29.1% 5.7 294s
    68699 54226 0.32176 859 184 0.34000 0.24105 29.1% 5.7 299s
    H69196 54597 0.3398602 0.24105 29.1% 5.7 299s
    H69846 55220 0.3398602 0.24105 29.1% 5.7 304s
    H69900 55220 0.3398602 0.24105 29.1% 5.7 304s
    H70008 55171 0.3396575 0.24105 29.0% 5.7 304s
    H70058 55025 0.3392336 0.24105 28.9% 5.7 304s
    70819 55812 0.26583 722 491 0.33923 0.24105 28.9% 5.7 305s
    71217 56251 0.24405 38 1229 0.33923 0.24105 28.9% 5.7 310s
    H71384 55772 0.3380371 0.24105 28.7% 5.7 310s
    73262 57555 0.25623 80 1149 0.33804 0.24105 28.7% 5.7 316s
    H73592 57444 0.3374838 0.24105 28.6% 5.7 316s
    74802 58753 0.26076 108 1129 0.33748 0.24105 28.6% 5.7 321s
    H75392 58811 0.3366477 0.24105 28.4% 5.7 321s
    H75674 58647 0.3359925 0.24105 28.3% 5.7 321s
    76809 59755 0.27326 158 1050 0.33599 0.24105 28.3% 5.7 325s
    H78299 61087 0.3359925 0.24105 28.3% 5.8 326s
    78784 61550 0.27531 231 842 0.33599 0.24105 28.3% 5.8 330s
    H79225 61400 0.3349799 0.24105 28.0% 5.8 330s
    80075 62170 0.27675 290 694 0.33498 0.24105 28.0% 5.8 335s
    H80267 62255 0.3347949 0.24105 28.0% 5.8 335s
    81485 63362 0.27713 310 641 0.33479 0.24105 28.0% 5.8 340s
    H81494 63362 0.3347949 0.24105 28.0% 5.8 340s
    H81633 63486 0.3347758 0.24105 28.0% 5.8 340s
    H81769 63415 0.3343654 0.24105 27.9% 5.8 340s
    82370 63959 0.27726 320 638 0.33437 0.24105 27.9% 5.8 345s
    H82771 64141 0.3338842 0.24105 27.8% 5.8 345s
    H82869 64134 0.3336610 0.24105 27.8% 5.8 345s
    83795 65021 0.27921 374 522 0.33366 0.24105 27.8% 5.8 350s
    H83886 64999 0.3334210 0.24105 27.7% 5.8 350s
    H84584 65694 0.3334210 0.24105 27.7% 5.8 350s
    84975 66099 0.28012 417 416 0.33342 0.24105 27.7% 5.8 355s
    H85478 66468 0.3334089 0.24105 27.7% 5.8 355s
    86421 67432 0.28227 480 394 0.33341 0.24105 27.7% 5.8 360s
    H87418 67882 0.3325937 0.24105 27.5% 5.8 360s
    88349 68957 0.28160 538 296 0.33259 0.24105 27.5% 5.8 366s
    H88351 68957 0.3325937 0.24105 27.5% 5.8 366s
    H88421 68794 0.3321122 0.24105 27.4% 5.8 366s
    H89497 69824 0.3321122 0.24105 27.4% 5.8 366s
    H89499 69824 0.3321122 0.24105 27.4% 5.8 366s
    89544 69880 0.28179 564 289 0.33211 0.24105 27.4% 5.8 371s
    H89748 70024 0.3321122 0.24105 27.4% 5.8 371s
    91355 71561 0.28254 638 266 0.33211 0.24105 27.4% 5.9 376s
    H91813 71544 0.3312166 0.24105 27.2% 5.9 376s
    93071 72691 0.29520 699 215 0.33122 0.24105 27.2% 5.9 382s
    94549 74071 0.29758 764 177 0.33122 0.24105 27.2% 5.9 388s
    96307 75617 0.24464 51 1229 0.33122 0.24105 27.2% 5.9 393s
    98287 77475 0.25137 245 1104 0.33122 0.24105 27.2% 5.9 398s
    98983 78179 0.26315 359 917 0.33122 0.24105 27.2% 5.9 404s
    100364 79457 0.26504 477 729 0.33122 0.24105 27.2% 5.8 409s
    101882 80860 0.26903 614 575 0.33122 0.24105 27.2% 5.8 414s
    103283 82243 0.27082 733 429 0.33122 0.24105 27.2% 5.8 420s
    H103543 82070 0.3306340 0.24105 27.1% 5.8 420s
    H103758 82285 0.3306340 0.24105 27.1% 5.8 420s
    104633 83150 0.27221 851 321 0.33063 0.24105 27.1% 5.8 425s
    H104968 83231 0.3304686 0.24105 27.1% 5.8 425s
    H105952 84275 0.3304318 0.24105 27.0% 5.8 425s
    106708 85089 0.28549 1019 141 0.33043 0.24105 27.0% 5.8 431s
    H107379 85571 0.3301261 0.24105 27.0% 5.8 432s
    109208 87275 0.30339 1207 36 0.33013 0.24105 27.0% 5.8 437s
    H109594 87550 0.3301261 0.24105 27.0% 5.8 437s
    111037 88962 0.24906 173 1168 0.33013 0.24105 27.0% 5.8 442s
    H111050 88962 0.3301261 0.24105 27.0% 5.8 442s
    H111296 89148 0.3299165 0.24105 26.9% 5.8 442s
    H112193 90009 0.3298353 0.24105 26.9% 5.8 442s
    112697 90480 0.26851 331 977 0.32984 0.24105 26.9% 5.8 447s
    H112908 90467 0.3292711 0.24105 26.8% 5.8 447s
    113842 91266 0.27017 435 786 0.32927 0.24105 26.8% 5.8 453s
    H114159 91424 0.3292711 0.24105 26.8% 5.8 453s
    115588 92952 0.27436 594 598 0.32927 0.24105 26.8% 5.8 458s
    H115698 93060 0.3292711 0.24105 26.8% 5.8 458s
    H116316 93548 0.3290540 0.24105 26.7% 5.8 458s
    116553 93749 0.27704 703 450 0.32905 0.24105 26.7% 5.8 463s
    118337 95473 0.27857 851 319 0.32905 0.24105 26.7% 5.8 468s
    H119368 96330 0.3289081 0.24105 26.7% 5.8 468s
    120230 97185 0.29193 1013 132 0.32891 0.24105 26.7% 5.8 474s
    H120300 97185 0.3289081 0.24105 26.7% 5.8 474s
    121723 98673 0.24550 73 1228 0.32891 0.24105 26.7% 5.8 479s
    H121955 98793 0.3287024 0.24105 26.7% 5.8 479s
    H121971 98778 0.3286457 0.24105 26.7% 5.8 479s
    H122386 98591 0.3275818 0.24105 26.4% 5.8 479s
    123230 99405 0.24758 151 1205 0.32758 0.24105 26.4% 5.8 485s
    H123471 99472 0.3275738 0.24105 26.4% 5.8 485s
    124743 100824 0.25096 222 1102 0.32757 0.24105 26.4% 5.8 491s
    H124800 100824 0.3275738 0.24105 26.4% 5.8 491s
    126572 102593 0.25679 380 809 0.32757 0.24105 26.4% 5.8 496s
    127944 103954 0.26433 491 720 0.32757 0.24105 26.4% 5.8 501s
    129747 105702 0.28498 648 494 0.32757 0.24105 26.4% 5.7 506s
    H129765 105551 0.3272253 0.24105 26.3% 5.7 506s
    H130989 106549 0.3272000 0.24105 26.3% 5.7 506s
    131225 106786 0.29659 802 310 0.32720 0.24105 26.3% 5.7 512s
    H131300 106644 0.3268833 0.24105 26.3% 5.7 512s
    H131400 106644 0.3268833 0.24105 26.3% 5.7 512s
    133263 108487 0.24407 60 1235 0.32688 0.24105 26.3% 5.7 517s
    134371 109462 0.24596 98 1224 0.32688 0.24105 26.3% 5.7 522s
    H135641 110567 0.3268825 0.24105 26.3% 5.7 522s
    135772 110795 0.25042 213 1113 0.32688 0.24105 26.3% 5.7 527s
    137255 112288 0.25567 342 894 0.32688 0.24105 26.3% 5.7 532s
    138718 113700 0.27328 488 655 0.32688 0.24105 26.3% 5.7 538s
    140823 115790 0.29196 671 402 0.32688 0.24105 26.3% 5.7 543s
    142810 117611 0.31552 958 136 0.32688 0.24105 26.3% 5.7 549s
    144714 119335 0.24735 104 1213 0.32688 0.24105 26.3% 5.7 553s
    H145081 119653 0.3268825 0.24105 26.3% 5.7 553s
    145962 120444 0.26841 191 1162 0.32688 0.24105 26.3% 5.6 558s
    H146832 120960 0.3264049 0.24105 26.1% 5.6 558s
    147412 121545 0.28925 330 1027 0.32640 0.24105 26.1% 5.6 564s
    149341 123454 0.29208 519 676 0.32640 0.24105 26.1% 5.6 569s
    150991 125080 0.29321 628 512 0.32640 0.24105 26.1% 5.6 574s
    152268 126253 0.29720 738 462 0.32640 0.24105 26.1% 5.6 579s
    153423 127416 0.29789 794 391 0.32640 0.24105 26.1% 5.6 584s
    155301 129197 0.30159 972 221 0.32640 0.24105 26.1% 5.6 590s
    H155614 129077 0.3259716 0.24105 26.1% 5.6 590s
    156866 130291 0.32394 1047 160 0.32597 0.24105 26.1% 5.6 595s
    H157947 131306 0.3259716 0.24105 26.1% 5.6 595s
    158411 131741 0.24547 144 1205 0.32597 0.24105 26.1% 5.6 600s
    H159230 132407 0.3259716 0.24105 26.1% 5.6 600s
    160288 133487 0.26668 304 963 0.32597 0.24105 26.1% 5.6 605s
    161245 134417 0.27287 417 749 0.32597 0.24105 26.1% 5.6 610s
    H161924 134971 0.3259716 0.24105 26.1% 5.6 610s
    H162314 135042 0.3254982 0.24105 25.9% 5.6 610s
    162812 135586 0.29619 573 539 0.32550 0.24105 25.9% 5.6 615s
    H162900 135586 0.3254982 0.24105 25.9% 5.6 616s
    H163100 135586 0.3254970 0.24105 25.9% 5.6 616s
    165100 137707 0.32357 862 219 0.32550 0.24105 25.9% 5.6 621s
    H165773 138289 0.3254288 0.24105 25.9% 5.6 621s
    H166076 138199 0.3249900 0.24105 25.8% 5.6 621s
    166278 138389 0.24200 47 1241 0.32499 0.24105 25.8% 5.6 627s
    H167258 139235 0.3249631 0.24105 25.8% 5.6 627s
    167414 139360 0.24643 102 1221 0.32496 0.24105 25.8% 5.6 632s
    H167433 139360 0.3249631 0.24105 25.8% 5.6 632s
    H167590 139533 0.3249631 0.24105 25.8% 5.6 632s
    168702 140586 0.24836 189 1179 0.32496 0.24105 25.8% 5.6 637s
    H169298 140903 0.3248948 0.24105 25.8% 5.6 637s
    H169397 141063 0.3248554 0.24105 25.8% 5.6 637s
    170912 142504 0.32029 387 937 0.32486 0.24105 25.8% 5.6 642s
    H172624 144037 0.3248554 0.24105 25.8% 5.5 643s
    172914 144409 0.24774 133 1207 0.32486 0.24105 25.8% 5.5 648s
    174837 146340 0.29655 320 1016 0.32486 0.24105 25.8% 5.5 654s
    176513 147947 0.30209 484 726 0.32486 0.24105 25.8% 5.5 659s
    178551 149944 0.30664 672 558 0.32486 0.24105 25.8% 5.5 664s
    H179409 150608 0.3248554 0.24105 25.8% 5.5 664s
    179974 151248 0.31533 813 415 0.32486 0.24105 25.8% 5.5 669s
    H180227 151373 0.3248554 0.24105 25.8% 5.5 669s
    181270 152543 0.31877 939 271 0.32486 0.24105 25.8% 5.5 674s
    H181311 152219 0.3245494 0.24105 25.7% 5.5 674s
    181871 152737 0.32229 996 214 0.32455 0.24105 25.7% 5.5 679s
    H182130 152842 0.3245494 0.24105 25.7% 5.5 679s
    H182260 152972 0.3245494 0.24105 25.7% 5.5 679s
    H182978 153578 0.3244530 0.24105 25.7% 5.5 679s
    183339 153950 0.24778 126 1200 0.32445 0.24105 25.7% 5.5 684s
    184823 155364 0.24845 188 1174 0.32445 0.24105 25.7% 5.5 690s
    186908 157394 0.25979 366 962 0.32445 0.24105 25.7% 5.5 695s
    H187365 157570 0.3243848 0.24105 25.7% 5.5 695s
    188954 159285 0.26131 459 807 0.32438 0.24105 25.7% 5.5 701s
    H190223 160341 0.3242944 0.24105 25.7% 5.5 701s
    190672 160722 0.26383 606 633 0.32429 0.24105 25.7% 5.5 706s
    192274 162285 0.26736 735 478 0.32429 0.24105 25.7% 5.5 711s
    193653 163658 0.30584 862 322 0.32429 0.24105 25.7% 5.5 715s
    H193658 163658 0.3242944 0.24105 25.7% 5.5 715s
    H193665 163658 0.3242944 0.24105 25.7% 5.5 715s
    H193755 163180 0.3239186 0.24105 25.6% 5.5 715s
    H194033 163131 0.3237082 0.24105 25.5% 5.5 715s
    194381 163501 0.30884 927 256 0.32371 0.24105 25.5% 5.5 720s
    H195720 164570 0.3237082 0.24105 25.5% 5.5 720s
    195721 164692 0.32343 1045 38 0.32371 0.24105 25.5% 5.5 726s
    197859 166704 0.24973 203 1149 0.32371 0.24105 25.5% 5.5 731s
    199612 168319 0.25659 345 1009 0.32371 0.24105 25.5% 5.5 736s
    201384 170014 0.25944 534 693 0.32371 0.24105 25.5% 5.4 743s
    202306 170909 0.26371 651 590 0.32371 0.24105 25.5% 5.4 749s
    204166 172711 0.30288 846 355 0.32371 0.24105 25.5% 5.4 754s
    205786 174323 0.31150 980 194 0.32371 0.24105 25.5% 5.4 760s
    207162 175624 0.24567 92 1227 0.32371 0.24105 25.5% 5.4 765s
    H207301 175762 0.3237082 0.24105 25.5% 5.4 765s
    208796 177249 0.25039 231 1097 0.32371 0.24105 25.5% 5.4 771s
    H209156 176102 0.3227803 0.24105 25.3% 5.4 771s
    209987 176921 0.25945 336 921 0.32278 0.24105 25.3% 5.4 776s
    211355 178245 0.26105 450 747 0.32278 0.24105 25.3% 5.4 782s
    213129 179910 0.26344 595 590 0.32278 0.24105 25.3% 5.4 788s
    H213544 179988 0.3226444 0.24105 25.3% 5.4 788s
    215162 181589 0.26838 767 410 0.32264 0.24105 25.3% 5.4 793s
    216725 183113 0.27199 906 272 0.32264 0.24105 25.3% 5.4 799s
    H218430 183121 0.3218367 0.24105 25.1% 5.4 799s
    218712 183562 0.24822 166 1181 0.32184 0.24105 25.1% 5.4 804s
    H219093 183789 0.3218176 0.24105 25.1% 5.4 804s
    H219526 184099 0.3217544 0.24105 25.1% 5.4 804s
    220718 185323 0.25963 355 882 0.32175 0.24105 25.1% 5.4 810s
    H220733 185323 0.3217544 0.24105 25.1% 5.4 810s
    H220800 185323 0.3217544 0.24105 25.1% 5.4 810s
    H220987 185587 0.3217544 0.24105 25.1% 5.4 810s
    H221024 185544 0.3217353 0.24105 25.1% 5.4 810s
    222514 186898 0.26252 538 611 0.32174 0.24105 25.1% 5.4 816s
    H223697 187923 0.3217353 0.24105 25.1% 5.4 816s
    H224316 188437 0.3217353 0.24105 25.1% 5.4 816s
    224469 188749 0.26722 725 456 0.32174 0.24105 25.1% 5.4 821s
    H224600 188568 0.3216285 0.24105 25.1% 5.4 821s
    225810 189845 0.26877 857 314 0.32163 0.24105 25.1% 5.4 826s
    227806 191652 0.24795 149 1194 0.32163 0.24105 25.1% 5.4 831s
    229664 193403 0.26276 311 1012 0.32163 0.24105 25.1% 5.4 836s
    230825 194491 0.26492 448 764 0.32163 0.24105 25.1% 5.4 841s
    232461 196020 0.26632 524 643 0.32163 0.24105 25.1% 5.4 847s
    H232484 195118 0.3210901 0.24105 24.9% 5.4 847s
    H232661 194040 0.3203864 0.24105 24.8% 5.4 847s
    232941 194285 0.26691 564 549 0.32039 0.24105 24.8% 5.4 852s
    H233000 194285 0.3203864 0.24105 24.8% 5.4 852s
    234655 195933 0.27062 694 447 0.32039 0.24105 24.8% 5.4 857s
    236481 197538 0.27208 840 338 0.32039 0.24105 24.8% 5.4 862s
    237702 198697 0.28557 960 206 0.32039 0.24105 24.8% 5.4 867s
    239802 200743 0.24738 137 1202 0.32039 0.24105 24.8% 5.4 872s
    241537 202467 0.26482 299 1056 0.32039 0.24105 24.8% 5.4 877s
    243021 203872 0.26890 463 749 0.32039 0.24105 24.8% 5.4 883s
    H243029 203872 0.3203864 0.24105 24.8% 5.4 883s
    H243519 204365 0.3203864 0.24105 24.8% 5.4 883s
    H243810 203588 0.3198328 0.24105 24.6% 5.4 883s
    244384 204202 0.27013 553 641 0.31983 0.24105 24.6% 5.4 888s
    H245524 204122 0.3192583 0.24105 24.5% 5.4 888s
    245765 204376 0.29373 670 501 0.31926 0.24105 24.5% 5.4 893s
    247272 205865 0.29518 806 377 0.31926 0.24105 24.5% 5.4 898s
    H247421 205993 0.3192583 0.24105 24.5% 5.3 898s
    H247639 206195 0.3192583 0.24105 24.5% 5.3 898s
    248280 206837 0.30481 935 186 0.31926 0.24105 24.5% 5.3 903s
    249579 208123 0.24441 89 1231 0.31926 0.24105 24.5% 5.3 908s
    251043 209593 0.24862 211 1161 0.31926 0.24105 24.5% 5.3 914s
    252884 211374 0.26349 369 959 0.31926 0.24105 24.5% 5.3 919s
    254257 212682 0.26544 486 746 0.31926 0.24105 24.5% 5.3 924s
    255949 214392 0.26913 630 605 0.31926 0.24105 24.5% 5.3 929s
    257795 216112 0.28935 782 413 0.31926 0.24105 24.5% 5.3 935s
    H257940 214673 0.3186187 0.24105 24.3% 5.3 935s
    258531 215269 0.28977 851 342 0.31862 0.24105 24.3% 5.3 941s
    H258700 215269 0.3186187 0.24105 24.3% 5.3 941s
    H259620 215682 0.3184194 0.24105 24.3% 5.3 941s
    260514 216539 0.30691 1021 132 0.31842 0.24105 24.3% 5.3 946s
    262169 218173 0.24439 156 1198 0.31842 0.24105 24.3% 5.3 952s
    263613 219506 0.25007 282 977 0.31842 0.24105 24.3% 5.3 957s
    265725 221476 0.25163 360 909 0.31842 0.24105 24.3% 5.3 962s
    H266328 221599 0.3182764 0.24105 24.3% 5.3 962s
    267735 223013 0.26000 528 665 0.31828 0.24105 24.3% 5.3 968s
    H267966 223178 0.3182764 0.24105 24.3% 5.3 968s
    269544 224650 0.28929 694 442 0.31828 0.24105 24.3% 5.3 973s
    270957 226048 0.31466 897 207 0.31828 0.24114 24.2% 5.3 979s
    272499 227509 0.24565 121 1214 0.31828 0.24114 24.2% 5.3 984s
    273443 228388 0.24734 167 1179 0.31828 0.24114 24.2% 5.3 989s
    H273447 228388 0.3182764 0.24114 24.2% 5.3 989s
    H273466 228126 0.3181796 0.24114 24.2% 5.3 989s
    H274185 228753 0.3181623 0.24114 24.2% 5.3 989s
    H274216 227998 0.3178857 0.24114 24.1% 5.3 989s
    274316 228123 0.26281 225 1143 0.31789 0.24114 24.1% 5.3 995s
    H275610 229192 0.3178857 0.24114 24.1% 5.3 995s
    276510 230262 0.26847 410 914 0.31789 0.24114 24.1% 5.3 1000s
    278212 231957 0.27096 572 674 0.31789 0.24114 24.1% 5.3 1006s
    280425 234071 0.27713 761 496 0.31789 0.24114 24.1% 5.3 1011s
    281905 235497 0.29014 937 283 0.31789 0.24114 24.1% 5.3 1016s
    283859 237396 0.24391 108 1228 0.31789 0.24114 24.1% 5.3 1021s
    284928 238312 0.24671 159 1179 0.31789 0.24114 24.1% 5.3 1025s
    286392 239629 0.24156 76 1245 0.31789 0.24114 24.1% 5.3 1031s
    287642 240771 0.24591 129 1202 0.31789 0.24114 24.1% 5.3 1035s
    288987 242001 0.24722 188 1178 0.31789 0.24114 24.1% 5.3 1040s
    290187 243191 0.29119 302 1078 0.31789 0.24114 24.1% 5.3 1045s
    291023 244008 0.30830 416 894 0.31789 0.24114 24.1% 5.3 1051s
    292927 245898 0.31081 594 632 0.31789 0.24114 24.1% 5.3 1056s
    294704 247623 0.31414 759 402 0.31789 0.24114 24.1% 5.3 1061s
    296639 249421 cutoff 856 0.31789 0.24114 24.1% 5.3 1066s
    298170 250852 0.24591 134 1197 0.31789 0.24114 24.1% 5.3 1071s
    299283 251898 0.26930 224 1131 0.31789 0.24114 24.1% 5.3 1076s
    300247 252818 0.28836 317 1071 0.31789 0.24114 24.1% 5.3 1081s
    301918 254409 0.29038 471 809 0.31789 0.24114 24.1% 5.3 1087s
    303856 256181 0.29286 654 572 0.31789 0.24114 24.1% 5.3 1092s
    305379 257574 0.29714 799 430 0.31789 0.24114 24.1% 5.3 1097s
    307004 259002 0.31594 1008 218 0.31789 0.24114 24.1% 5.3 1103s
    H307030 258930 0.3178677 0.24114 24.1% 5.3 1103s
    H307803 259251 0.3177613 0.24114 24.1% 5.3 1103s
    H308103 258528 0.3174898 0.24114 24.0% 5.3 1103s
    H308228 258083 0.3173402 0.24114 24.0% 5.3 1103s
    308268 258208 0.24668 141 1179 0.31734 0.24114 24.0% 5.3 1108s
    H309654 259421 0.3173402 0.24114 24.0% 5.3 1108s
    309788 259707 0.30379 231 1136 0.31734 0.24114 24.0% 5.3 1114s
    H310691 260489 0.3173402 0.24114 24.0% 5.3 1114s
    311144 260947 0.30561 344 949 0.31734 0.24114 24.0% 5.3 1120s
    H312870 261575 0.3170701 0.24114 23.9% 5.3 1120s
    313028 261909 0.31254 498 741 0.31707 0.24114 23.9% 5.3 1126s
    315001 263687 0.31527 670 513 0.31707 0.24114 23.9% 5.3 1131s
    H316172 264422 0.3169818 0.24114 23.9% 5.3 1132s
    316907 265167 0.24182 75 1242 0.31698 0.24114 23.9% 5.3 1137s
    H317434 264773 0.3167483 0.24114 23.9% 5.3 1137s
    318442 265789 0.24556 107 1210 0.31675 0.24114 23.9% 5.3 1142s
    319865 267210 0.24672 132 1189 0.31675 0.24114 23.9% 5.3 1147s
    H320102 266691 0.3165412 0.24114 23.8% 5.3 1147s
    321151 267758 0.24926 157 1165 0.31654 0.24114 23.8% 5.3 1152s
    322678 269177 0.25281 179 1147 0.31654 0.24114 23.8% 5.3 1157s
    H323867 270206 0.3165412 0.24114 23.8% 5.3 1157s
    323991 270392 0.28510 190 1128 0.31654 0.24114 23.8% 5.3 1161s
    H324197 269928 0.3163332 0.24114 23.8% 5.3 1161s
    H324350 270040 0.3163138 0.24114 23.8% 5.3 1161s
    324479 270161 0.28596 200 1111 0.31631 0.24114 23.8% 5.3 1168s
    H324963 270499 0.3163138 0.24114 23.8% 5.3 1168s
    325940 271442 0.28831 227 1065 0.31631 0.24114 23.8% 5.3 1174s
    H326278 271728 0.3163138 0.24114 23.8% 5.3 1174s
    327118 272520 0.24428 112 1227 0.31631 0.24114 23.8% 5.3 1175s
    327662 273058 0.28887 250 1010 0.31631 0.24114 23.8% 5.3 1180s
    329110 274466 0.28965 281 936 0.31631 0.24114 23.8% 5.3 1186s
    H329874 274936 0.3162974 0.24114 23.8% 5.3 1186s
    H331093 274928 0.3159559 0.24114 23.7% 5.3 1186s
    331094 275115 0.29282 340 792 0.31596 0.24114 23.7% 5.3 1191s
    H331299 275316 0.3159559 0.24114 23.7% 5.3 1191s
    H331355 274546 0.3157543 0.24114 23.6% 5.3 1191s
    H331383 274242 0.3156761 0.24114 23.6% 5.3 1191s
    332050 274921 0.29348 361 738 0.31568 0.24114 23.6% 5.3 1197s
    333860 276568 0.29423 384 691 0.31568 0.24114 23.6% 5.3 1203s
    335365 278017 0.29770 408 629 0.31568 0.24114 23.6% 5.3 1209s
    336895 279413 0.29862 426 605 0.31568 0.24114 23.6% 5.3 1214s
    H336900 277353 0.3151259 0.24114 23.5% 5.3 1214s
    338134 278611 0.30015 442 587 0.31513 0.24114 23.5% 5.3 1220s
    339364 279705 0.30086 451 567 0.31513 0.24114 23.5% 5.3 1226s
    H339400 278457 0.3147486 0.24114 23.4% 5.3 1226s
    340985 280022 0.30257 470 546 0.31475 0.24114 23.4% 5.3 1232s
    342238 281210 0.30423 498 495 0.31475 0.24114 23.4% 5.3 1238s
    344238 282969 0.30541 523 450 0.31475 0.24114 23.4% 5.3 1245s
    H344300 282969 0.3147486 0.24114 23.4% 5.3 1245s
    H345052 282755 0.3145451 0.24114 23.3% 5.3 1245s
    H346013 281476 0.3139316 0.24114 23.2% 5.3 1245s
    346277 281766 0.30730 545 430 0.31393 0.24114 23.2% 5.3 1251s
    347925 283202 0.30921 569 361 0.31393 0.24114 23.2% 5.3 1257s
    H348000 283202 0.3139316 0.24114 23.2% 5.3 1257s
    H349076 282470 0.3134672 0.24114 23.1% 5.3 1257s
    349793 283266 0.31079 602 309 0.31347 0.24114 23.1% 5.3 1262s
    351129 284462 0.31256 638 254 0.31347 0.24114 23.1% 5.3 1269s
    H351834 282952 0.3128192 0.24114 22.9% 5.3 1269s
    352786 283882 0.24563 144 1190 0.31282 0.24114 22.9% 5.3 1274s
    354093 285086 0.27766 259 1087 0.31282 0.24114 22.9% 5.3 1280s
    355294 286280 0.27906 367 921 0.31282 0.24114 22.9% 5.3 1286s
    H355296 286280 0.3128192 0.24114 22.9% 5.3 1286s
    H355301 285185 0.3125152 0.24114 22.8% 5.3 1286s
    356303 286162 0.28038 474 792 0.31252 0.24114 22.8% 5.3 1292s
    358474 288204 0.30297 672 455 0.31252 0.24114 22.8% 5.3 1298s
    H359636 288529 0.3123130 0.24114 22.8% 5.3 1299s
    359976 288878 0.30456 799 344 0.31231 0.24114 22.8% 5.3 1306s
    H360000 288878 0.3123130 0.24114 22.8% 5.3 1306s
    H360750 289100 0.3121860 0.24114 22.8% 5.3 1306s
    361476 289809 0.30824 924 225 0.31219 0.24114 22.8% 5.3 1312s
    362976 291198 0.24417 125 1218 0.31219 0.24114 22.8% 5.3 1318s
    H364091 292264 0.3121860 0.24114 22.8% 5.3 1318s
    364460 292587 0.25028 228 1135 0.31219 0.24114 22.8% 5.3 1324s
    365729 293853 cutoff 567 0.31219 0.24114 22.8% 5.3 1325s
    366152 294209 0.25323 359 940 0.31219 0.24114 22.8% 5.3 1330s
    367925 295825 0.25549 498 630 0.31219 0.24114 22.8% 5.3 1337s
    369631 297366 0.26017 660 496 0.31219 0.24114 22.8% 5.3 1343s
    371365 298890 0.26144 820 379 0.31219 0.24114 22.8% 5.3 1349s
    H372158 298525 0.3118679 0.24114 22.7% 5.3 1349s
    372874 299248 0.26297 927 286 0.31187 0.24114 22.7% 5.3 1354s
    374212 300453 0.26408 938 259 0.31187 0.24114 22.7% 5.3 1360s
    376449 302468 0.26788 992 217 0.31187 0.24114 22.7% 5.3 1366s
    378206 303975 0.26959 1028 202 0.31187 0.24115 22.7% 5.3 1372s
    H378495 303549 0.3117132 0.24115 22.6% 5.3 1372s
    380342 305167 0.24185 109 1234 0.31171 0.24115 22.6% 5.3 1378s
    H380352 305167 0.3117132 0.24115 22.6% 5.3 1378s
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    H380368 305167 0.3117132 0.24115 22.6% 5.3 1378s
    H380507 305237 0.3117132 0.24115 22.6% 5.3 1379s
    H380829 304692 0.3114761 0.24115 22.6% 5.3 1379s
    381150 305029 0.24349 165 1181 0.31148 0.24115 22.6% 5.3 1385s
    H381804 305493 0.3114761 0.24115 22.6% 5.3 1385s
    382962 306572 0.31108 288 1039 0.31148 0.24115 22.6% 5.3 1390s
    384517 308016 0.24647 181 1175 0.31148 0.24115 22.6% 5.3 1396s
    386629 309922 0.30972 357 956 0.31148 0.24115 22.6% 5.3 1401s
    388490 311677 0.24123 90 1243 0.31148 0.24115 22.6% 5.3 1407s
    389689 312868 0.24452 137 1211 0.31148 0.24115 22.6% 5.3 1413s
    390981 314115 0.27074 245 1100 0.31148 0.24115 22.6% 5.3 1418s
    392521 315665 0.27521 365 937 0.31148 0.24115 22.6% 5.3 1424s
    394681 317683 0.27816 545 596 0.31148 0.24115 22.6% 5.3 1430s
    H395131 317923 0.3114149 0.24115 22.6% 5.3 1430s
    H395507 318222 0.3113902 0.24115 22.6% 5.3 1430s
    395628 318358 0.27845 584 576 0.31139 0.24115 22.6% 5.3 1437s
    H396392 319036 0.3113902 0.24115 22.6% 5.3 1437s
    397677 320295 0.28268 757 458 0.31139 0.24115 22.6% 5.3 1442s
    399198 321746 0.28405 881 334 0.31139 0.24115 22.6% 5.3 1448s
    400486 322999 0.24848 178 1176 0.31139 0.24119 22.5% 5.3 1455s
    401866 324311 0.24516 146 1195 0.31139 0.24119 22.5% 5.3 1461s
    403586 325971 0.29283 281 1086 0.31139 0.24119 22.5% 5.3 1467s
    405066 327377 0.30129 396 930 0.31139 0.24119 22.5% 5.3 1474s
    H405198 326945 0.3112627 0.24119 22.5% 5.3 1474s
    406001 327738 0.30237 472 775 0.31126 0.24119 22.5% 5.3 1480s
    H406200 327738 0.3112627 0.24119 22.5% 5.3 1480s
    408401 330051 0.30557 672 513 0.31126 0.24123 22.5% 5.3 1487s
    410692 332169 0.25121 184 1177 0.31126 0.24124 22.5% 5.3 1492s
    411897 333154 0.28110 259 1108 0.31126 0.24124 22.5% 5.3 1498s
    413089 334325 0.28233 360 952 0.31126 0.24124 22.5% 5.3 1504s
    414486 335671 0.28396 463 753 0.31126 0.24124 22.5% 5.3 1510s
    H414600 335671 0.3112627 0.24124 22.5% 5.3 1510s
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    415966 337124 0.28547 564 622 0.31126 0.24124 22.5% 5.3 1517s
    H416939 337609 0.3111587 0.24124 22.5% 5.3 1517s
    417580 338300 0.28754 691 472 0.31116 0.24124 22.5% 5.3 1523s
    419075 339620 0.28878 791 384 0.31116 0.24124 22.5% 5.3 1529s
    420683 341112 0.30210 873 306 0.31116 0.24124 22.5% 5.3 1536s
    H420778 341174 0.3111587 0.24124 22.5% 5.3 1536s
    421751 342124 0.30244 925 278 0.31116 0.24124 22.5% 5.3 1543s
    423430 343659 0.30549 956 252 0.31116 0.24124 22.5% 5.3 1550s
    425579 345679 0.30809 990 192 0.31116 0.24124 22.5% 5.3 1556s
    H427063 346888 0.3111587 0.24124 22.5% 5.3 1556s
    427186 347125 0.30928 1031 158 0.31116 0.24124 22.5% 5.3 1562s
    428521 348401 0.30979 1132 49 0.31116 0.24128 22.5% 5.3 1568s
    430567 350330 0.30550 235 1029 0.31116 0.24128 22.5% 5.3 1574s
    H430734 349202 0.3108687 0.24128 22.4% 5.3 1574s
    432137 350454 0.31001 369 794 0.31087 0.24128 22.4% 5.3 1581s
    434067 352238 0.28623 223 1120 0.31087 0.24128 22.4% 5.3 1588s
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    435644 353420 0.28975 357 925 0.31079 0.24128 22.4% 5.3 1595s
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    437356 355008 0.29215 514 669 0.31079 0.24128 22.4% 5.3 1601s
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    442391 359738 0.30335 952 243 0.31079 0.24128 22.4% 5.3 1621s
    H442616 359772 0.3107666 0.24128 22.4% 5.3 1621s
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    539345 431770 0.27710 823 393 0.30730 0.24129 21.5% 5.3 1984s
    541082 433407 0.28930 979 218 0.30730 0.24129 21.5% 5.3 1990s
    541897 434166 0.24299 99 1234 0.30730 0.24129 21.5% 5.3 1996s
    543145 435407 0.24712 203 1111 0.30730 0.24129 21.5% 5.3 2002s
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    546863 438981 0.26206 543 559 0.30730 0.24129 21.5% 5.3 2014s
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    548522 439489 0.29808 726 326 0.30713 0.24130 21.4% 5.3 2021s
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    559546 441272 0.24164 92 1243 0.30578 0.24130 21.1% 5.3 2060s
    H559619 441327 0.3057817 0.24130 21.1% 5.3 2061s
    560381 442092 0.24550 147 1191 0.30578 0.24130 21.1% 5.3 2067s
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    563398 444942 0.25326 394 788 0.30578 0.24130 21.1% 5.3 2079s
    564634 446069 0.25444 497 611 0.30578 0.24130 21.1% 5.3 2086s
    566638 447893 0.25698 664 412 0.30578 0.24130 21.1% 5.3 2093s
    568694 449657 0.27165 827 307 0.30578 0.24130 21.1% 5.3 2099s
    570078 450960 0.28275 934 143 0.30578 0.24130 21.1% 5.3 2106s
    571478 452314 0.24629 155 1169 0.30578 0.24131 21.1% 5.3 2111s
    572954 453765 0.24946 165 1176 0.30578 0.24131 21.1% 5.3 2118s
    574718 455466 0.28722 312 992 0.30578 0.24131 21.1% 5.3 2125s
    576914 457630 0.29168 495 695 0.30578 0.24131 21.1% 5.3 2132s
    579141 459802 0.29670 682 467 0.30578 0.24131 21.1% 5.3 2139s
    H580229 460547 0.3057487 0.24131 21.1% 5.3 2139s
    580798 461092 0.29963 842 287 0.30575 0.24131 21.1% 5.3 2145s
    H581455 461661 0.3057487 0.24131 21.1% 5.3 2145s
    581643 461873 0.24165 96 1243 0.30575 0.24131 21.1% 5.3 2151s
    583433 463526 0.24603 109 1222 0.30575 0.24131 21.1% 5.3 2158s
    585404 465397 0.29702 277 1076 0.30575 0.24131 21.1% 5.3 2164s

     

    I tried changing the MIPFocus but does not seem to give me the expected results.

    I would really appreciate if you could give me some suggestions over here to improve the performance.

    Thanks in advance.

     

    Thanks in advance,

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  • Jaromił Najman

    Dear Gayan,

    Could you provide some more information about the problem you are trying to solve? Is it, e.g., a parameter estimation problem? What does the objective and the constraints look like? Do you provide variable bounds for all variables participating in nonlinear terms in your problem?

    Did you try to reformulate your problem in order to reduce the number of nonlinearities? For example, instead of writing \(x_1\cdot x_2 + x_1 \cdot x_3\), you could introduce an auxiliary variable \(w_1\) and reformulate it as \(x_1 \cdot w_1 \) and add the linear equality constraint \( w_1 = x_2 + x_3\). This reduces the number of nonlinear term from 2 to 1 in this simple example.

    Best regards,
    Jaromił

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  • Gayan Lankeshwara

    Hi Jaromil,

    The objective of the optimisation problem is in the quadratic form 

    objective : x^{T}Qx + u^{T}Ru %% quadratic

    where

    u \in {0,1,2,3,4} %% makes the problem MIQP

    %% constraints for u and x

    u_{min} \leq u leq u_{max}
    x_{min} \leq x leq x_{max}

    in addition to the integer constraint for u

    By the way sorry for the inconvenience caused by LaTeX formulation, and I do not how to use the LaTeX formatting here.

    Thank you.

     

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  • Jaromił Najman

    Hi Gayan,

    So the integer variables \(u\) are independent of the continuous variables \(x\). You could try reformulating your problem with binaries and then linearize the multiplication of two binaries since \(x^2 = x \) for \(x \in \{0,1\}\) and \(x \cdot y = z\) can be reformulated exactly by

    \(z \leq x \)
    \(z \leq y\)
    \(x+y \leq z +1. \)

    The above follows directly from the McCormick envelope and the fact that \(x,y \in \{0,1\}\).

    You could also try reducing the number of nonlinear terms by reformulation as proposed in my previous comment. This could have a significant impact on solver performance. 

    Your problem does not have any constraints. Is it possible to add (in best case linear) constraints to shrink the feasible region of the problem?

    Please don't forget that your non-convex MIQP has 2000 continuous and 4000 binary variables which is already considered very large for this problem type even without any constraints.

    You can find a guide to our Support Portal here.


    Best regards,
    Jaromił

     

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  • Gayan Lankeshwara

    Hi Jaromil,

    Sorry for being late to reply.

    I think its better to give a full picture of the mathematical formulation as I was unable to convey the message properly.

    Here is a very brief formulation of the optimisation problem, 

    \[\begin{align}
    \min_{u} \quad (x_{k}&-x_{ref})^{T}Q(x_{k}-x_{ref}) + (P_{k}-P_{ref})^{T}R(P_{k}-P_{ref}) \\
    \text{s.t. } x_{k+1}&=Ax_{k}+Bu_{k} \\
    P_{k} &= \mathbb{I}^{T}u_{k}\\
    u_{k} &\in \{0,1,2,3,4\}\\
    \underline{x}&\leq x_{k}\leq \overline{x}
    \end{align}\]

    Q and R are positive definite matrices, 

    I developed the optimisation problem in YALMIP in MATLAB. In any case, you need to have a look at it, I am happy to share the MWE with you.

    I would really appreciate if you could give me your suggestions based on the above formulation.

    Thanks in advance.

     

    Kind regards

    Gayan

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  • Jaromił Najman

    Hi Gayan,

    Thank you for the clarification. It seems like the lower bound (dual bound/BestBd) is already very good as it does not move much, while the incumbent is being improved very often over during the optimization. Do you have any information or a good guess about the optimal solution point which you could provide to Gurobi as explained in our article on MIP starts? This could help a lot. What is your expected MIPGap and run time for this kind of problem?

    Do you have any additional information about the problem which you could feed into your problem formulation in order to tighten the feasible set, e.g., something like at timestep \(\texttt{i}\) you know or you expect that some variables have to be 0 or similar.

    To me, this problem formulation looks very similar to parameter estimation problems, which are known for their complexity. You could try reducing the size of your problem to see whether smaller problems are solvable in the time you desire and try building up from there.

    Best regards,
    Jaromił

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  • Gayan Lankeshwara

    Hi Jaromil,

    Thank you for your comments and suggestions. MIP starts seems interesting but I need to make look into a possible feasible solution first.

    At the same time I am not sure whether I have any additional information to tighten the feasible set.

    Although I am aware of the fact that each optimisation process should be completeted within 60seconds (1 minute), still I have a certain doubt on the MIPGap that I should allow? Is there any rule of thumb sort of an approach to set the MIPGap?

    I referred to the MIPGap article on Gurobi on how to set the parameters, but I am not sure about the value I should set. For example, whether 1e-2 is bad compared to the default 1e-4 or else whether I should avoid setting 1e-1 sort of value ?

    At the same time, I tried the following approach for setting parameters in Gurobi with YALMIP as follows,

    options = sdpsettings('verbose',2, 'solver', 'gurobi', 'gurobi.MIPFocus',1, 'gurobi.IterationLimit',100000);

    I would really appreciate if you could give me some hints on the following.

    1) Is it a bad approach to set an IterationLimit for the optimisation problem considering the convergence of it ? If No, does it
    need to be a trial and error approach on setting the simplex iteration limit ?

    2) I tried to perform the optimisation problem in the High Performance Computing (HPC) facility. As far as I know, PBS job allocation sort of a process is followed to execute a certain operation at the HPC. Initially I used ncpus =8 and after a while, an error message appeared 

    PBS: job killed: ncpus xxxx exceeded limit 8 (sum)

    What I would like to know is  do I need to manually set Threads in Gurobi if I am performing optimisation on an HPC ? Does it affect the convergence of the problem ?

    Sorry for the whole bunch of questions over here :(

    Thank you.

     

     

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  • Jaromił Najman

    Hi Gayan,

    Regarding the MIPGap setting, it really depends on your application. Do you require the best (or at least a very good) solution or is it OK for your application to proceed with just a "good" solution. You are the one to define what is a "good" and a "very good" solution as you have the knowledge about your model and application. There is always the trade-off between solution quality and time. You state that your optimization problem should be solved within 60 seconds and the gap you reach at that time in your LOG file is 40%, so a MIPGap of 0.4. You could ask yourself if this is enough or if a solution point with lower objective value is required. Since your problem has rather small objective values, it could be useful to use the MIPGapAbs parameter. With that, you can terminate when a specific absolute difference between the best found solution and the lower bound is reached.

    1) Setting the IterationLimit can work in some cases but it often boils down to a trial and error approach. It is better to set a TimeLimit instead.

    2) Gurobi in general uses all cores of a given machine unless you specify the Threads to a fixed value. It seems to be the case with your job that the machine has more than 8 cores and Gurobi tries to use more than 8. Thus, the system kills your job as you only asked for a maximum of 8 CPUs. Setting the Threads parameter may have an impact on the convergence of the problem. In general one tends to say that more Threads are better but 8 Threads should be a good amount for most problems.

    I hope the above could help.

    Best regards,
    Jaromił

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  • Gayan Lankeshwara

    Dear Jaromil,

    Thank you very much for your useful suggestions.

    I will follow them and update in the forum in case I face the same issue.

    Cheers.

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