How to solve MIQP faster?

GUROBI

MOSEK

CPLEX

Optimal value

2.5059e+3

2.5101e+3

2.5101e+3

Solving time

475s

29s

27s

Note: Optimality gap for all the solvers are 0.1%; All the other parameters are default; The platform is MATLAB 2020b

Even though GUROBI provides better solution than that of MOSEK and CPLEX, its solution time is much lower than that of MOSEK and CPLEX. The MIQP problem is as following:

I guess the slower solving time may stem from the long root relaxation.

Could you please provide any suggestions for tunning the parameters or solving mode of GUROBI? Following is the GUROBI solving information:

Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (mac64)
Thread count: 8 physical cores, 16 logical processors, using up to 16 threads
Optimize a model with 96492 rows, 40704 columns and 330384 nonzeros
Model fingerprint: 0xfcbb0052
Model has 384 quadratic objective terms
Variable types: 32064 continuous, 8640 integer (8640 binary)
Coefficient statistics:
Matrix range [2e-01, 2e+04]
Objective range [2e-02, 8e+00]
QObjective range [2e+03, 2e+03]
Bounds range [1e+00, 1e+00]
RHS range [1e+00, 3e+06]

No start values specified in MIP start

Found heuristic solution: objective 4519759.5855
Presolve removed 67050 rows and 11205 columns
Presolve time: 0.82s
Presolved: 29442 rows, 29499 columns, 164082 nonzeros
Presolved model has 384 quadratic objective terms
Variable types: 21879 continuous, 7620 integer (7620 binary)

Root simplex log...

Iteration Objective Primal Inf. Dual Inf. Time
107700 3.1618395e+06 0.000000e+00 2.423230e+04 5s
141977 2.8613187e+06 0.000000e+00 9.628881e+03 10s
159095 2.8224688e+06 0.000000e+00 1.256773e+04 15s
174325 2.7782259e+06 0.000000e+00 1.053597e+04 20s
189292 2.7343561e+06 0.000000e+00 9.230604e+03 25s
204238 2.7196319e+06 0.000000e+00 8.636641e+03 30s
219670 2.6724761e+06 0.000000e+00 1.412663e+04 35s
232399 2.6313092e+06 0.000000e+00 8.135329e+03 40s
244563 2.5978751e+06 0.000000e+00 1.075950e+04 45s
255467 2.5830686e+06 0.000000e+00 7.466468e+03 50s
266225 2.5535575e+06 0.000000e+00 3.042182e+04 55s
275532 2.5463826e+06 0.000000e+00 7.780226e+03 60s
284697 2.5425229e+06 0.000000e+00 9.182279e+03 65s
293580 2.5354749e+06 0.000000e+00 1.398105e+04 70s
302181 2.5237613e+06 0.000000e+00 8.289566e+03 75s
311347 2.5090514e+06 0.000000e+00 9.696519e+03 80s
319666 2.5002595e+06 0.000000e+00 8.071407e+03 85s
327844 2.4944801e+06 0.000000e+00 7.656166e+03 90s
335599 2.4920601e+06 0.000000e+00 8.266899e+03 95s
343495 2.4884379e+06 0.000000e+00 7.530097e+03 100s
351109 2.4858823e+06 0.000000e+00 7.831430e+03 105s
359005 2.4764825e+06 0.000000e+00 7.317625e+03 110s
366055 2.4730619e+06 0.000000e+00 9.719391e+03 115s
373105 2.4702949e+06 0.000000e+00 8.866025e+03 120s
380860 2.4679840e+06 0.000000e+00 7.531656e+03 125s
388333 2.4639898e+06 0.000000e+00 7.967690e+03 130s
395947 2.4622089e+06 0.000000e+00 8.295247e+03 135s
403279 2.4588936e+06 0.000000e+00 3.378259e+04 140s
410047 2.4547470e+06 0.000000e+00 1.668496e+04 145s
417097 2.4502438e+06 0.000000e+00 7.325238e+03 150s
423865 2.4479380e+06 0.000000e+00 9.075344e+03 155s
430774 2.4453483e+06 0.000000e+00 7.931693e+03 160s
437824 2.4434848e+06 0.000000e+00 1.124068e+04 165s
444874 2.4411265e+06 0.000000e+00 7.205576e+03 170s
451642 2.4380249e+06 0.000000e+00 1.993734e+04 175s
458410 2.4351876e+06 0.000000e+00 1.087766e+04 180s
465037 2.4327190e+06 0.000000e+00 8.728082e+03 185s
472087 2.4274941e+06 0.000000e+00 8.525905e+03 190s
479278 2.4232843e+06 0.000000e+00 1.142129e+04 195s
486187 2.4189076e+06 0.000000e+00 9.204798e+03 200s
493237 2.4129778e+06 0.000000e+00 6.956072e+03 205s
500569 2.4070199e+06 0.000000e+00 1.333207e+04 210s
507510 2.3989939e+06 0.000000e+00 8.536691e+03 215s
514137 2.3972216e+06 0.000000e+00 1.416488e+04 220s
520905 2.3932145e+06 0.000000e+00 9.157140e+03 225s
527532 2.3880949e+06 0.000000e+00 7.867807e+03 230s
533877 2.3865922e+06 0.000000e+00 8.592409e+03 235s
540222 2.3841987e+06 0.000000e+00 9.780597e+03 240s
546426 2.3826269e+06 0.000000e+00 8.601621e+03 245s
553053 2.3698907e+06 0.000000e+00 7.389552e+03 250s
558975 2.3697431e+06 0.000000e+00 6.634589e+03 255s
565320 2.3676814e+06 0.000000e+00 1.413950e+04 260s
571524 2.3656247e+06 0.000000e+00 7.653701e+03 265s
577869 2.3635849e+06 0.000000e+00 7.580017e+03 270s
584073 2.3617829e+06 0.000000e+00 7.835401e+03 275s
590418 2.3564503e+06 0.000000e+00 8.775089e+03 280s
596764 2.3504195e+06 0.000000e+00 8.535462e+03 285s
603532 2.3429096e+06 0.000000e+00 7.458879e+03 290s
609878 2.3366863e+06 0.000000e+00 1.431712e+04 295s
616224 2.3165772e+06 0.000000e+00 8.301464e+03 300s
622569 2.3145375e+06 0.000000e+00 2.189699e+04 305s
629196 2.3132002e+06 0.000000e+00 1.454158e+04 310s
635682 2.3104804e+06 0.000000e+00 6.753712e+03 315s
642168 2.3080763e+06 0.000000e+00 1.416319e+04 320s
648513 2.3065537e+06 0.000000e+00 1.915734e+04 325s
654858 2.2986163e+06 0.000000e+00 1.296723e+04 330s
661062 2.2969191e+06 0.000000e+00 8.121040e+03 335s
667407 2.2920635e+06 0.000000e+00 2.504730e+04 340s
673752 2.2867899e+06 0.000000e+00 7.564333e+03 345s
679815 2.2792187e+06 0.000000e+00 1.035805e+04 350s
685878 2.2755747e+06 0.000000e+00 2.699358e+04 355s
691800 2.2745207e+06 0.000000e+00 7.443625e+03 360s
697581 2.2694107e+06 0.000000e+00 2.404597e+05 365s
703785 2.2677519e+06 0.000000e+00 8.876582e+03 370s
709848 2.2646340e+06 0.000000e+00 1.080324e+04 375s
715065 2.2607480e+06 0.000000e+00 9.316893e+03 380s
720705 2.2586187e+06 0.000000e+00 1.104085e+04 385s
726768 2.2560430e+06 0.000000e+00 1.838143e+05 390s
732549 2.2548909e+06 0.000000e+00 9.286830e+03 395s
738330 2.2538031e+06 0.000000e+00 6.933568e+03 400s
744253 2.2499681e+06 0.000000e+00 1.856548e+04 405s
749752 2.2497610e+06 0.000000e+00 3.462994e+04 410s
755392 2.2484234e+06 0.000000e+00 2.022091e+04 415s
760751 2.2462999e+06 0.000000e+00 7.603167e+03 420s
766391 2.2452210e+06 0.000000e+00 8.434201e+03 425s
772031 2.2427808e+06 0.000000e+00 5.097947e+05 430s
Warning: 1 variables dropped from basis
778856 2.2030285e+06 0.000000e+00 3.167473e+05 435s
793478 1.2478573e+06 0.000000e+00 1.781553e+06 440s
805009 2.8786660e+05 0.000000e+00 1.482391e+07 445s
811247 6.4946147e+03 0.000000e+00 1.663538e+05 450s
815341 4.0270196e+03 0.000000e+00 1.803596e+05 455s
819016 3.1061212e+03 0.000000e+00 1.287679e+04 460s
822413 2.7174554e+03 0.000000e+00 1.819462e+03 465s
825800 2.5330401e+03 0.000000e+00 6.112820e+02 470s
829331 2.4365688e+03 0.000000e+00 1.101857e+02 475s
832020 2.5056048e+03 0.000000e+00 0.000000e+00 477s

Root relaxation: objective 2.505605e+03, 832020 iterations, 476.52 seconds

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

H 0 0 2599.2977801 - - - 477s
H 0 0 2586.7374746 - - - 477s
H 0 0 2544.8485470 - - - 477s
H 0 0 2544.7372682 - - - 477s
H 0 0 2520.6028416 - - - 477s
H 0 0 2505.8920714 - - - 477s
0 0 2505.60481 0 1813 2505.89207 2505.60481 0.01% - 477s

Explored 0 nodes (832020 simplex iterations) in 477.51 seconds
Thread count was 16 (of 16 available processors)

Solution count 7: 2505.89 2520.6 2544.74 ... 4.51976e+06

Optimal solution found (tolerance 1.00e-03)
Best objective 2.505892071376e+03, best bound 2.505604814249e+03, gap 0.0115%

479.302623 s