EXITFLAG from price computation stage = -4
xb00dx opened this issue · 9 comments
xb00dx commented
My colleagues and I are using MOST to solve lots of 24-hour SCUCs on a 2000-bus network, the error message EXITFLAG from price computation stage = -4 randomly shows up even when the primal SCUC problem is feasible (a strictly feasible solution is found). The issue was gone if we re-run the SCUC of the same day.
Initially we thought this was caused by numerical issues of GUROBI's barrier algorithm. However, after setting gurobi.method to primal-simplex or dual-simplex, the same issue kept showing up (randomly), and it is difficult to create a minimal example to reproduce this issue.
Many thanks! MOST has been super helpful for our research.
xb00dx commented
This is the complete error message from Matlab:
=============================================================================
MATPOWER Optimal Scheduling Tool -- MOST Version 1.1
A multiperiod stochastic secure OPF with unit commitment
----- Built on MATPOWER -----
by Carlos E. Murillo-Sanchez, Universidad Nacional de Colombia--Manizales
and Ray D. Zimmerman, Cornell University
(c) 2012-2020 Power Systems Engineering Research Center (PSERC)
=============================================================================
- Building indexing structures.
- Building expected storage-tracking mechanism.
- Building constraint submatrices.
- Building DC flow constraints.
- Building CCV constraints for piecewise-linear costs.
- Building contingency reserve constraints.
- Building ramping transitions and reserve constraints.
- Building unit commitment constraints.
- Building cost structures.
- Assembling full set of constraints.
- Assembling full set of variable bounds.
- Assembling full set of costs.
- Calling MILP solver.
============================================================================
Gurobi Version 9.1.0 -- automatic MILP solver
Academic license - for non-commercial use only - expires 2021-01-28
Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (linux64)
Thread count: 32 physical cores, 64 logical processors, using up to 4 threads
Optimize a model with 341850 rows, 171810 columns and 851636 nonzeros
Model fingerprint: 0xe011d3a4
Variable types: 161578 continuous, 10232 integer (10232 binary)
Coefficient statistics:
Matrix range [4e-03, 3e+03]
Objective range [1e+00, 1e+06]
Bounds range [3e-02, 3e+01]
RHS range [9e-13, 2e+03]
Presolve removed 141735 rows and 93682 columns (presolve time = 1s) ...
Presolve removed 143231 rows and 94312 columns (presolve time = 2s) ...
Presolve removed 146028 rows and 95715 columns (presolve time = 3s) ...
Presolve removed 146960 rows and 96149 columns (presolve time = 4s) ...
Presolve removed 147290 rows and 96269 columns (presolve time = 5s) ...
Presolve removed 147588 rows and 96471 columns (presolve time = 6s) ...
Presolve removed 147610 rows and 96493 columns (presolve time = 7s) ...
Presolve removed 147840 rows and 96703 columns
Presolve time: 7.94s
Presolved: 194010 rows, 75107 columns, 524222 nonzeros
Variable types: 65159 continuous, 9948 integer (9945 binary)
Deterministic concurrent LP optimizer: primal and dual simplex (primal and dual model)
Showing first log only...
Root simplex log...
Iteration Objective Primal Inf. Dual Inf. Time
0 7.1303159e+05 3.846525e+06 4.157648e+13 12s
15745 8.1027467e+05 3.806666e+04 1.073114e+11 13s
18567 8.3348362e+05 7.839911e+03 6.425818e+09 14s
Warning: Markowitz tolerance tightened to 0.03125
19191 8.4662172e+05 7.030464e+03 4.463406e+09 15s
19949 8.5772070e+05 6.149557e+03 2.912903e+09 16s
20770 8.5439631e+05 5.307759e+03 2.006707e+09 17s
21418 8.5692314e+05 4.768198e+03 1.592003e+09 18s
21946 8.6686109e+05 3.664410e+03 1.428165e+09 19s
22746 9.0502163e+05 2.638576e+03 1.033340e+09 20s
23165 9.2056674e+05 2.532551e+03 8.848475e+08 21s
23773 9.2244254e+05 2.405230e+03 7.757271e+08 22s
24175 9.2264365e+05 2.305221e+03 1.084409e+09 23s
24581 9.2563211e+05 2.179522e+03 8.227708e+08 24s
24990 9.3063040e+05 2.056802e+03 7.585868e+08 25s
25191 9.2998942e+05 1.993477e+03 5.191109e+08 26s
25794 9.3049790e+05 1.866673e+03 7.334802e+08 27s
26196 9.3211219e+05 1.779331e+03 4.824129e+08 28s
26599 9.3398322e+05 1.669250e+03 2.579899e+09 29s
27002 9.3787068e+05 1.583367e+03 6.212252e+08 30s
27404 9.4022397e+05 1.483556e+03 6.538023e+08 31s
27608 9.4016274e+05 1.435925e+03 5.066857e+08 32s
28015 9.4309339e+05 1.342245e+03 3.152944e+08 33s
28418 9.4042410e+05 1.252976e+03 5.810798e+08 34s
28822 9.3949174e+05 1.172611e+03 6.053552e+08 35s
29227 9.3696161e+05 1.093177e+03 8.879830e+08 36s
29429 9.3394421e+05 1.042934e+03 8.362371e+08 37s
29631 9.3196843e+05 9.936894e+02 8.013179e+08 38s
30035 9.2456164e+05 8.802561e+02 1.000610e+09 39s
30468 9.2058377e+05 7.191871e+02 8.594602e+08 40s
30890 9.1372140e+05 5.400489e+02 1.003337e+09 41s
31325 9.2505214e+05 4.241670e+02 7.458771e+08 42s
31551 9.2562332e+05 2.972799e+02 3.932550e+08 43s
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32760 1.0099167e+06 1.170202e+02 2.537534e+08 45s
33233 1.0437571e+06 8.227375e+01 2.486904e+08 46s
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56962 1.0069194e+06 3.322600e+00 1.615421e+07 104s
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58168 1.0097811e+06 2.866153e+00 1.082318e+08 107s
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109394 1.7764405e+07 0.000000e+00 7.749174e+08 273s
109610 1.7754037e+07 0.000000e+00 7.154503e+07 274s
109826 1.7744654e+07 0.000000e+00 1.035154e+09 275s
110042 1.7741410e+07 0.000000e+00 1.557136e+07 276s
110474 1.7726463e+07 0.000000e+00 6.084600e+07 278s
110690 1.7692486e+07 0.000000e+00 2.152002e+07 279s
110906 1.7676300e+07 0.000000e+00 3.353253e+07 280s
111122 1.7655922e+07 0.000000e+00 3.750095e+08 281s
111338 1.7651070e+07 0.000000e+00 4.495412e+07 283s
111554 1.7634850e+07 0.000000e+00 6.135921e+07 284s
111770 1.7617797e+07 0.000000e+00 5.425806e+07 284s
111986 1.7595013e+07 0.000000e+00 7.987432e+07 285s
112202 1.7588782e+07 0.000000e+00 2.413979e+07 286s
112418 1.7568089e+07 0.000000e+00 3.648398e+07 287s
112634 1.7542584e+07 0.000000e+00 4.224956e+07 288s
112850 1.7534245e+07 0.000000e+00 2.479945e+07 289s
113066 1.7512154e+07 0.000000e+00 4.579735e+08 290s
113498 1.7496620e+07 0.000000e+00 6.045227e+08 292s
113930 1.7485798e+07 0.000000e+00 9.957399e+07 294s
114146 1.7481695e+07 0.000000e+00 1.440133e+08 295s
114362 1.7479342e+07 0.000000e+00 1.631695e+08 296s
114578 1.7469354e+07 0.000000e+00 6.825442e+07 298s
114794 1.7462498e+07 0.000000e+00 6.478435e+07 299s
115010 1.7457737e+07 0.000000e+00 2.236442e+07 300s
115226 1.7453394e+07 0.000000e+00 6.195909e+07 300s
115442 1.7447350e+07 0.000000e+00 7.361153e+08 301s
115957 1.7434595e+07 0.000000e+00 8.210059e+08 302s
116173 1.7428300e+07 0.000000e+00 2.242420e+07 303s
116655 1.7422811e+07 0.000000e+00 2.662923e+07 305s
116871 1.7415149e+07 0.000000e+00 1.008833e+08 306s
117087 1.7396814e+07 0.000000e+00 1.228979e+07 307s
117303 1.7395093e+07 0.000000e+00 3.101173e+07 307s
117519 1.7379633e+07 0.000000e+00 1.762451e+07 308s
117735 1.7369519e+07 0.000000e+00 5.165335e+07 309s
117951 1.7356896e+07 0.000000e+00 3.667739e+07 310s
118167 1.7352192e+07 0.000000e+00 1.799886e+07 312s
118383 1.7344832e+07 0.000000e+00 8.317640e+07 312s
118599 1.7339767e+07 0.000000e+00 1.466589e+07 313s
118815 1.7324782e+07 0.000000e+00 1.275959e+08 314s
119031 1.7310385e+07 0.000000e+00 1.306398e+07 315s
119247 1.7297929e+07 0.000000e+00 1.356868e+07 316s
119463 1.7292075e+07 0.000000e+00 1.010904e+07 317s
119679 1.7280160e+07 0.000000e+00 1.461026e+07 318s
120113 1.7260642e+07 0.000000e+00 5.061195e+07 320s
120329 1.7245332e+07 0.000000e+00 1.892547e+07 321s
120545 1.7237198e+07 0.000000e+00 1.048196e+07 321s
120761 1.7232872e+07 0.000000e+00 1.058963e+07 322s
120977 1.7215995e+07 0.000000e+00 1.678218e+08 324s
121193 1.7205534e+07 0.000000e+00 6.402907e+07 325s
121409 1.7202457e+07 0.000000e+00 2.221348e+07 325s
121625 1.7192246e+07 0.000000e+00 8.659591e+06 326s
121841 1.7184408e+07 0.000000e+00 3.486963e+07 327s
122273 1.7167623e+07 0.000000e+00 1.591685e+09 328s
122489 1.7161486e+07 0.000000e+00 8.232237e+08 329s
122705 1.7153820e+07 0.000000e+00 2.377170e+08 330s
Concurrent spin time: 0.15s
Solved with dual simplex (dual model)
Root relaxation: objective 1.695716e+07, 71940 iterations, 321.37 seconds
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 1.6957e+07 0 35 - 1.6957e+07 - - 332s
0 0 1.6957e+07 0 35 - 1.6957e+07 - - 341s
0 2 1.6957e+07 0 35 - 1.6957e+07 - - 375s
1 4 1.6957e+07 1 35 - 1.6957e+07 - 27.0 376s
3 8 1.6957e+07 2 35 - 1.6957e+07 - 12.7 377s
7 12 1.6957e+07 3 35 - 1.6957e+07 - 16.7 378s
15 20 1.6957e+07 5 35 - 1.6957e+07 - 12.3 379s
23 28 1.6957e+07 7 36 - 1.6957e+07 - 10.6 380s
27 36 1.6957e+07 8 51 - 1.6957e+07 - 12.3 381s
35 49 1.6957e+07 8 34 - 1.6957e+07 - 12.6 382s
48 75 1.6957e+07 10 34 - 1.6957e+07 - 12.7 385s
74 109 1.6957e+07 20 24 - 1.6957e+07 - 13.2 390s
108 209 1.6957e+07 27 24 - 1.6957e+07 - 19.6 400s
208 425 1.6957e+07 46 8 - 1.6957e+07 - 20.1 421s
424 587 1.6958e+07 102 23 - 1.6957e+07 - 18.4 442s
586 886 1.6958e+07 141 23 - 1.6957e+07 - 20.9 471s
885 1342 1.6958e+07 182 5 - 1.6957e+07 - 26.4 488s
1341 1608 1.6958e+07 296 8 - 1.6957e+07 - 20.3 505s
1617 1754 infeasible 369 - 1.6957e+07 - 20.8 519s
1787 1852 1.7065e+07 374 18 - 1.6957e+07 - 23.3 534s
* 1870 944 548 1.695814e+07 1.6957e+07 0.01% 26.0 534s
Explored 1903 nodes (125562 simplex iterations) in 534.90 seconds
Thread count was 4 (of 64 available processors)
Solution count 1: 1.69581e+07
Optimal solution found (tolerance 1.00e-02)
Best objective 1.695814336824e+07, best bound 1.695716834532e+07, gap 0.0057%
--- Integer stage complete, starting price computation stage ---
Gurobi Version 9.1.0 -- automatic LP solver
Academic license - for non-commercial use only - expires 2021-01-28
Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (linux64)
Thread count: 32 physical cores, 64 logical processors, using up to 4 threads
Optimize a model with 341850 rows, 171810 columns and 851636 nonzeros
Model fingerprint: 0x9af2a5b6
Coefficient statistics:
Matrix range [4e-03, 3e+03]
Objective range [1e+00, 1e+06]
Bounds range [3e-02, 3e+01]
RHS range [9e-13, 2e+03]
Concurrent LP optimizer: dual simplex and barrier
Showing barrier log only...
Presolve removed 273450 rows and 143383 columns
Presolve time: 1.69s
Presolved: 68400 rows, 64918 columns, 232866 nonzeros
Ordering time: 0.05s
Barrier statistics:
Free vars : 17780
AA' NZ : 5.221e+05
Factor NZ : 3.195e+06 (roughly 80 MBytes of memory)
Factor Ops : 2.559e+08 (less than 1 second per iteration)
Threads : 3
Objective Residual
Iter Primal Dual Primal Dual Compl Time
0 8.01031436e+09 -5.99283816e+08 9.52e+03 2.24e+04 4.94e+06 3s
1 4.63886989e+09 -5.59914664e+08 5.55e+03 5.57e+03 2.69e+06 3s
2 1.93209958e+09 -4.58161742e+08 2.33e+03 1.09e+03 1.02e+06 3s
3 6.56615793e+08 -2.76660955e+08 6.76e+02 1.10e+02 2.92e+05 3s
4 4.18034284e+08 -2.11903826e+08 3.76e+02 4.73e+01 1.62e+05 3s
5 2.36406767e+08 -2.02157373e+08 1.63e+02 3.76e+01 7.29e+04 4s
6 1.06232114e+08 -1.26516549e+08 3.82e+01 2.87e+00 1.87e+04 4s
7 5.30649088e+07 -7.62273778e+07 1.18e+01 2.89e-02 5.94e+03 4s
8 3.74595646e+07 -4.79622786e+07 6.58e+00 3.77e-03 3.11e+03 4s
9 2.86859325e+07 -2.95206315e+07 3.20e+00 1.31e-03 1.53e+03 4s
10 2.08400175e+07 -1.54725742e+07 9.02e-01 4.42e-04 5.91e+02 4s
11 1.74224568e+07 9.10260122e+06 7.79e-02 3.27e-05 9.37e+01 4s
12 1.70619222e+07 1.38480830e+07 1.20e-02 1.43e-05 3.43e+01 5s
13 1.70348204e+07 1.44602029e+07 8.60e-03 1.26e-05 2.74e+01 5s
14 1.70169960e+07 1.49027712e+07 6.17e-03 1.11e-05 2.25e+01 5s
15 1.70056119e+07 1.51104051e+07 4.67e-03 1.02e-05 2.01e+01 5s
16 1.69936672e+07 1.59439067e+07 3.28e-03 6.96e-06 1.11e+01 5s
17 1.69782071e+07 1.61712940e+07 1.87e-03 5.99e-06 8.54e+00 5s
18 1.69714328e+07 1.64348565e+07 1.15e-03 4.98e-06 5.68e+00 5s
19 1.69660578e+07 1.66537528e+07 6.28e-04 4.41e-06 3.30e+00 6s
20 1.69625737e+07 1.68443233e+07 3.34e-04 3.72e-06 1.25e+00 6s
21 1.69607767e+07 1.69112399e+07 1.28e-03 3.16e-06 5.23e-01 6s
22 1.69586439e+07 1.69397878e+07 2.97e-03 1.37e-06 1.99e-01 6s
23 1.69582918e+07 1.69493819e+07 4.37e-04 6.22e-07 9.32e-02 6s
24 1.69582052e+07 1.69571610e+07 2.56e-04 2.00e-07 1.01e-02 6s
25 1.69581709e+07 1.69580242e+07 3.69e-04 9.94e-09 5.53e-04 6s
26 1.69581648e+07 1.69580678e+07 4.05e-04 2.40e-08 5.38e-06 7s
27 1.69581644e+07 1.69580679e+07 3.99e-04 1.16e-10 1.31e-06 7s
28 1.69581644e+07 1.69580679e+07 3.69e-04 1.75e-10 6.88e-07 7s
29 1.69581643e+07 1.69580679e+07 3.11e-04 1.72e-10 4.55e-07 7s
30 1.69581643e+07 1.69580679e+07 5.59e-04 2.91e-10 4.56e-10 7s
31 1.69581643e+07 1.69580679e+07 7.03e-04 1.75e-10 1.80e-10 7s
32 1.69581643e+07 1.69580679e+07 5.15e-04 1.16e-10 1.31e-10 7s
33 1.69581643e+07 1.69580679e+07 5.09e-04 1.75e-10 7.32e-11 8s
34 1.69581643e+07 1.69580679e+07 3.26e-04 1.24e-10 1.58e-13 8s
35 1.69581643e+07 1.69580679e+07 8.53e-05 1.75e-10 2.84e-15 8s
36 1.69581643e+07 1.69580679e+07 7.72e-05 1.16e-10 2.12e-16 8s
37 1.69581643e+07 1.69580679e+07 8.04e-05 1.16e-10 6.54e-18 8s
38 1.69581643e+07 1.69580679e+07 6.88e-05 1.24e-10 5.47e-20 8s
39 1.69581643e+07 1.69580679e+07 8.18e-05 1.16e-10 5.47e-23 9s
40 1.69581643e+07 1.69580679e+07 9.05e-05 1.46e-10 5.47e-26 9s
Barrier solved model in 40 iterations and 8.73 seconds
Optimal objective 1.69581643e+07
Crossover log...
46833 variables added to crossover basis 9s
163 DPushes remaining with DInf 0.0000000e+00 10s
0 DPushes remaining with DInf 0.0000000e+00 10s
26 PPushes remaining with PInf 8.3156557e-04 10s
0 PPushes remaining with PInf 8.3156659e-04 10s
Push phase complete: Pinf 8.3156659e-04, Dinf 1.6704658e-06 11s
Iteration Objective Primal Inf. Dual Inf. Time
148 1.6958143e+07 8.315620e-04 0.000000e+00 11s
Solved with barrier
Solved in 148 iterations and 11.26 seconds
Infeasible or unbounded model
Error using miqps_gurobi (line 395)
miqps_gurobi: EXITFLAG from price computation stage = -4
Error in miqps_master (line 213)
miqps_gurobi(H, c, A, l, u, xmin, xmax, x0, vtype, opt);
Error in opt_model/solve (line 190)
miqps_master(HH, CC, A, l, u, xmin, xmax, x0, vtype, opt);
Error in most (line 2015)
mdo.om.solve(mdo.QP.opt);
Error in run_SCUC_net (line 233)
mdo = most(mdi, mpopt);
rdzman commented
It looks to me like it may still be related to the barrier method. At least in the output you included, it appears the algorithm is set to "automatic MILP solver", which I believe probably does a concurrent run of barrier and possibly multiple simplex algorithms. In this case, it appears the initial integer stage is solved successfully by dual simplex, while in the price computation stage the barrier method completed first (claiming infeasibility).
In order to select the dual simplex method, you have to set the gurobi.method option to 1 (not the string 'dual-simplex'). Can you confirm that you see this error with the gurobi.method option set to 1?
Also, I assume you are familiar with what the two stages (integer and price computation) are doing ... depending on your application, the price computation stage may be completely unnecessary.
xb00dx commented
Thanks for the fast response! Sorry I posted the error messages the first time I encountered this issue, where I used default MILP algorithm.
In my recent simulations, I included the following line
mpopt = mpoption(mpopt,'gurobi.method',1); % use dual simplex algorithm
The same issue still happened. I will post the error message using dual-simplex algorithm in the comments below
xb00dx commented
running SCUC for day 161
Warning: the original case does not have consecutive bus numbers
> In daily_SCED (line 18)
In run_SCUC (line 100)
Warning: DONE: renumber everything
> In daily_SCED (line 37)
In run_SCUC (line 100)
creating load profiles
creating wind profiles
creating solar profiles
creating hydro profiles
=============================================================================
MATPOWER Optimal Scheduling Tool -- MOST Version 1.1
A multiperiod stochastic secure OPF with unit commitment
----- Built on MATPOWER -----
by Carlos E. Murillo-Sanchez, Universidad Nacional de Colombia--Manizales
and Ray D. Zimmerman, Cornell University
(c) 2012-2020 Power Systems Engineering Research Center (PSERC)
=============================================================================
- Building indexing structures.
- Building expected storage-tracking mechanism.
- Building constraint submatrices.
- Building DC flow constraints.
- Building CCV constraints for piecewise-linear costs.
- Building contingency reserve constraints.
- Building ramping transitions and reserve constraints.
- Building unit commitment constraints.
- Building cost structures.
- Assembling full set of constraints.
- Assembling full set of variable bounds.
- Assembling full set of costs.
- Calling MILP solver.
============================================================================
Gurobi Version 9.1.0 -- dual simplex MILP solver
Academic license - for non-commercial use only - expires 2021-03-17
Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (linux64)
Thread count: 32 physical cores, 64 logical processors, using up to 32 threads
Optimize a model with 384820 rows, 214828 columns and 959973 nonzeros
Model fingerprint: 0x60ef6a22
Variable types: 200897 continuous, 13931 integer (13931 binary)
Coefficient statistics:
Matrix range [9e-04, 4e+03]
Objective range [1e+00, 1e+06]
Bounds range [3e-02, 3e+01]
RHS range [9e-13, 2e+03]
Presolve removed 121828 rows and 119835 columns (presolve time = 1s) ...
Presolve removed 153662 rows and 119835 columns (presolve time = 2s) ...
Presolve removed 164233 rows and 120000 columns (presolve time = 3s) ...
Presolve removed 165347 rows and 120385 columns (presolve time = 4s) ...
Presolve removed 166562 rows and 121600 columns (presolve time = 5s) ...
Presolve removed 168014 rows and 121600 columns (presolve time = 6s) ...
Presolve removed 169051 rows and 122209 columns (presolve time = 7s) ...
Presolve removed 169051 rows and 122209 columns (presolve time = 8s) ...
Presolve removed 169406 rows and 122508 columns (presolve time = 9s) ...
Presolve removed 169644 rows and 122540 columns (presolve time = 10s) ...
Presolve removed 169644 rows and 122540 columns (presolve time = 11s) ...
Presolve removed 169827 rows and 122723 columns (presolve time = 12s) ...
Presolve removed 169858 rows and 122754 columns (presolve time = 13s) ...
Presolve removed 169858 rows and 122754 columns (presolve time = 14s) ...
Presolve removed 169895 rows and 122769 columns (presolve time = 15s) ...
Presolve removed 171794 rows and 124680 columns (presolve time = 16s) ...
Presolve removed 171794 rows and 124680 columns
Presolve time: 16.37s
Presolved: 213026 rows, 90148 columns, 570510 nonzeros
Variable types: 76680 continuous, 13468 integer (13468 binary)
Root simplex log...
Iteration Objective Primal Inf. Dual Inf. Time
0 1.7618325e+06 1.330642e+05 0.000000e+00 18s
2931 2.6688951e+06 6.546809e+05 0.000000e+00 19s
7659 2.7077141e+06 1.376905e+05 0.000000e+00 20s
10258 2.7077173e+06 9.729232e+04 0.000000e+00 21s
12375 2.7077194e+06 1.396232e+05 0.000000e+00 22s
14472 2.7077213e+06 1.190876e+05 0.000000e+00 23s
16083 2.7077225e+06 1.209776e+05 0.000000e+00 24s
17767 2.7077238e+06 1.009681e+05 0.000000e+00 25s
19377 2.7077251e+06 7.883726e+04 0.000000e+00 26s
21021 2.7077263e+06 1.283601e+05 0.000000e+00 27s
22666 2.7077275e+06 1.346826e+05 0.000000e+00 28s
24039 2.7247806e+06 8.257410e+04 0.000000e+00 29s
25389 2.7322209e+06 8.538645e+04 0.000000e+00 30s
26389 2.7322219e+06 2.489279e+05 0.000000e+00 31s
27389 2.7322231e+06 8.176272e+05 0.000000e+00 32s
28376 2.7322243e+06 1.326416e+06 0.000000e+00 33s
30126 2.7322262e+06 7.877573e+05 0.000000e+00 34s
31376 2.7322274e+06 1.271134e+06 0.000000e+00 35s
32626 2.7322286e+06 1.168266e+06 0.000000e+00 36s
34126 2.7322300e+06 1.307243e+06 0.000000e+00 37s
35376 2.7322311e+06 1.179000e+06 0.000000e+00 38s
36376 2.7322320e+06 1.304296e+06 0.000000e+00 39s
37376 2.7322328e+06 1.147549e+05 0.000000e+00 40s
38376 2.7322335e+06 2.624817e+05 0.000000e+00 41s
39376 2.7322342e+06 3.685077e+05 0.000000e+00 42s
40626 2.7322351e+06 6.302395e+05 0.000000e+00 43s
41626 2.7322358e+06 1.178970e+06 0.000000e+00 44s
42626 2.7322366e+06 2.596832e+05 0.000000e+00 45s
43376 2.7322374e+06 2.264671e+05 0.000000e+00 46s
44376 2.7322382e+06 1.001514e+06 0.000000e+00 47s
45376 2.7322389e+06 5.401778e+05 0.000000e+00 48s
46376 2.7322397e+06 3.251146e+06 0.000000e+00 49s
47126 2.7322405e+06 1.085039e+06 0.000000e+00 50s
48126 2.7322414e+06 1.530027e+06 0.000000e+00 51s
48876 2.7322420e+06 8.830234e+05 0.000000e+00 52s
49876 2.7322429e+06 4.707355e+05 0.000000e+00 53s
50876 2.7322438e+06 6.745890e+05 0.000000e+00 54s
51626 2.7322449e+06 4.220676e+05 0.000000e+00 55s
52376 2.7322457e+06 1.086825e+06 0.000000e+00 56s
53376 2.7322471e+06 1.344693e+06 0.000000e+00 57s
Warning: Markowitz tolerance tightened to 0.03125
54126 2.7322479e+06 3.469251e+05 0.000000e+00 58s
54876 2.7322486e+06 5.025600e+05 0.000000e+00 59s
55876 2.7322495e+06 8.592988e+05 0.000000e+00 60s
56626 2.7322505e+06 4.776123e+05 0.000000e+00 61s
57376 2.7322513e+06 3.102283e+05 0.000000e+00 62s
58376 2.7322522e+06 1.296912e+06 0.000000e+00 63s
59126 2.7322529e+06 3.313611e+05 0.000000e+00 64s
59876 2.7322537e+06 6.947460e+05 0.000000e+00 65s
60626 2.7322546e+06 2.498150e+05 0.000000e+00 66s
61376 2.7322553e+06 4.237545e+05 0.000000e+00 67s
62126 2.7322564e+06 1.480442e+05 0.000000e+00 68s
62876 2.7322572e+06 4.008720e+05 0.000000e+00 69s
63876 2.7322583e+06 5.797794e+05 0.000000e+00 70s
64626 2.7322592e+06 2.252017e+06 0.000000e+00 71s
65376 2.7322601e+06 3.623325e+06 0.000000e+00 72s
66126 2.7322609e+06 1.838864e+05 0.000000e+00 73s
66876 2.7322622e+06 7.451918e+05 0.000000e+00 74s
67626 2.7322631e+06 4.818809e+05 0.000000e+00 75s
68376 2.7322645e+06 3.679325e+05 0.000000e+00 76s
69126 2.7322655e+06 1.534483e+05 0.000000e+00 77s
69626 2.7322660e+06 8.826319e+04 0.000000e+00 78s
70376 2.7322671e+06 1.124166e+05 0.000000e+00 79s
71126 2.7322678e+06 2.740791e+04 0.000000e+00 80s
71876 2.7322689e+06 1.958078e+04 0.000000e+00 82s
72126 2.7322691e+06 2.257323e+05 0.000000e+00 82s
72876 2.7322703e+06 1.349934e+05 0.000000e+00 83s
73626 2.7322718e+06 6.857481e+05 0.000000e+00 84s
74126 2.7322732e+06 2.504236e+04 0.000000e+00 85s
74876 2.7322743e+06 1.070825e+05 0.000000e+00 86s
Warning: Markowitz tolerance tightened to 0.0625
75376 2.7322750e+06 3.075718e+05 0.000000e+00 87s
75876 2.7322762e+06 1.210053e+05 0.000000e+00 88s
76626 2.7322778e+06 8.503890e+04 0.000000e+00 89s
77126 2.7322792e+06 4.992115e+05 0.000000e+00 90s
77879 2.7322805e+06 8.128360e+05 0.000000e+00 91s
78379 2.7322815e+06 7.676338e+05 0.000000e+00 92s
79129 2.7322834e+06 7.457786e+04 0.000000e+00 93s
79629 2.7322839e+06 2.103272e+05 0.000000e+00 94s
80379 2.7322862e+06 4.963677e+05 0.000000e+00 95s
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237471 1.9670948e+07 7.088430e+03 0.000000e+00 1065s
237721 1.9680469e+07 2.064704e+03 0.000000e+00 1067s
237971 1.9684434e+07 7.527975e+04 0.000000e+00 1069s
238221 1.9771396e+07 5.296179e+03 0.000000e+00 1071s
238471 1.9775560e+07 2.219118e+06 0.000000e+00 1072s
238721 1.9782938e+07 1.336817e+04 0.000000e+00 1074s
238971 1.9787548e+07 9.646034e+03 0.000000e+00 1076s
239221 1.9800768e+07 7.967938e+04 0.000000e+00 1077s
239471 1.9871179e+07 1.287791e+03 0.000000e+00 1080s
239721 1.9883432e+07 5.787151e+04 0.000000e+00 1081s
239971 1.9889451e+07 2.117696e+03 0.000000e+00 1083s
240221 1.9899555e+07 2.025077e+03 0.000000e+00 1085s
240471 1.9923956e+07 2.397878e+05 0.000000e+00 1087s
240721 1.9952704e+07 3.861618e+02 0.000000e+00 1089s
240971 2.0064319e+07 2.286193e+03 0.000000e+00 1092s
241221 2.0086473e+07 1.107155e+05 0.000000e+00 1094s
241471 2.0097958e+07 2.935005e+02 0.000000e+00 1095s
241721 2.0170279e+07 3.742208e+03 0.000000e+00 1097s
241971 2.0272140e+07 1.053023e+03 0.000000e+00 1099s
242221 2.0277531e+07 1.740025e+03 0.000000e+00 1100s
242471 2.0293538e+07 1.183596e+05 0.000000e+00 1102s
242721 2.0348020e+07 5.081762e+03 0.000000e+00 1104s
242971 2.0351122e+07 2.065422e+05 0.000000e+00 1105s
243221 2.0426135e+07 2.296257e+03 0.000000e+00 1107s
243471 2.0528597e+07 3.188630e+03 0.000000e+00 1108s
243721 2.0529716e+07 1.456579e+03 0.000000e+00 1110s
243971 2.0551524e+07 9.830001e+03 0.000000e+00 1112s
244221 2.0563531e+07 2.709688e+04 0.000000e+00 1113s
244471 2.0681664e+07 1.866864e+04 0.000000e+00 1115s
244721 2.0687195e+07 9.398725e+04 0.000000e+00 1116s
244971 2.0689163e+07 1.021952e+04 0.000000e+00 1118s
245221 2.0693062e+07 4.216852e+02 0.000000e+00 1120s
245471 2.0794747e+07 9.311414e+03 0.000000e+00 1121s
245721 2.0948236e+07 1.723679e+04 0.000000e+00 1122s
245971 2.0957221e+07 4.454216e+03 0.000000e+00 1123s
246221 2.0993513e+07 2.611237e+02 0.000000e+00 1124s
246471 2.1056899e+07 4.639497e+03 0.000000e+00 1126s
246721 2.1060446e+07 2.500612e+03 0.000000e+00 1128s
246971 2.1062559e+07 7.565151e+03 0.000000e+00 1129s
247221 2.1106470e+07 1.300442e+04 0.000000e+00 1131s
247471 2.1108140e+07 1.065785e+03 0.000000e+00 1133s
247971 2.1262714e+07 3.954785e+03 0.000000e+00 1135s
248221 2.1291553e+07 3.483086e+05 0.000000e+00 1136s
248471 2.1417905e+07 5.347943e+04 0.000000e+00 1137s
248721 2.1421292e+07 7.981764e+03 0.000000e+00 1138s
248971 2.1456670e+07 4.723888e+03 0.000000e+00 1140s
249221 2.1469972e+07 8.044097e+03 0.000000e+00 1141s
249471 2.1511738e+07 1.316515e+05 0.000000e+00 1142s
249721 2.1555635e+07 4.107095e+06 0.000000e+00 1143s
249971 2.1622805e+07 4.024730e+03 0.000000e+00 1144s
250221 2.1626417e+07 7.082784e+05 0.000000e+00 1146s
250471 2.1734804e+07 3.596519e+04 0.000000e+00 1147s
250721 2.1738083e+07 9.761903e+03 0.000000e+00 1149s
250971 2.1742196e+07 9.332351e+02 0.000000e+00 1150s
251221 2.1752334e+07 4.440256e+04 0.000000e+00 1152s
251471 2.1861924e+07 7.109006e+04 0.000000e+00 1153s
251721 2.1870208e+07 1.428789e+03 0.000000e+00 1154s
251971 2.1883215e+07 2.636190e+03 0.000000e+00 1156s
252227 2.2005662e+07 1.404146e+06 0.000000e+00 1157s
252477 2.2093224e+07 5.018753e+02 0.000000e+00 1158s
252727 2.2097171e+07 7.449617e+03 0.000000e+00 1160s
252977 2.2099849e+07 5.127606e+03 0.000000e+00 1161s
253227 2.2112382e+07 5.912989e+03 0.000000e+00 1162s
253477 2.2172462e+07 5.197590e+04 0.000000e+00 1164s
253727 2.2214977e+07 3.651734e+05 0.000000e+00 1166s
253977 2.2233696e+07 1.088232e+06 0.000000e+00 1168s
254227 2.2331233e+07 4.295890e+04 0.000000e+00 1169s
254477 2.2338709e+07 1.164563e+05 0.000000e+00 1171s
254727 2.2345742e+07 9.796890e+04 0.000000e+00 1172s
254977 2.2360089e+07 4.012055e+03 0.000000e+00 1173s
255227 2.2466747e+07 2.585345e+07 0.000000e+00 1174s
255477 2.2545984e+07 2.083807e+03 0.000000e+00 1175s
255727 2.2550648e+07 2.254197e+04 0.000000e+00 1176s
255977 2.2555412e+07 1.585829e+04 0.000000e+00 1178s
256227 2.2568816e+07 1.688798e+04 0.000000e+00 1179s
256477 2.2606703e+07 2.105273e+03 0.000000e+00 1181s
256727 2.2610014e+07 1.331891e+03 0.000000e+00 1182s
256977 2.2613219e+07 5.049610e+03 0.000000e+00 1183s
257227 2.2627431e+07 7.775215e+06 0.000000e+00 1185s
257477 2.2721154e+07 2.208978e+05 0.000000e+00 1186s
257727 2.2792096e+07 1.812025e+06 0.000000e+00 1187s
257977 2.2893125e+07 7.037776e+03 0.000000e+00 1188s
258227 2.2897766e+07 1.804226e+03 0.000000e+00 1190s
258477 2.2901126e+07 2.787446e+03 0.000000e+00 1191s
258727 2.2917362e+07 7.298804e+02 0.000000e+00 1192s
258977 2.2922571e+07 1.270025e+03 0.000000e+00 1193s
259227 2.2960794e+07 1.206492e+03 0.000000e+00 1195s
259477 2.3031912e+07 5.027949e+03 0.000000e+00 1196s
259727 2.3034565e+07 1.370381e+03 0.000000e+00 1197s
259977 2.3069749e+07 7.563333e+01 0.000000e+00 1198s
260227 2.3112916e+07 5.735980e+03 0.000000e+00 1200s
260477 2.3134057e+07 2.313676e+04 0.000000e+00 1201s
260727 2.3173203e+07 3.335834e+02 0.000000e+00 1202s
261227 2.3267079e+07 2.644696e+03 0.000000e+00 1204s
261477 2.3288604e+07 1.008385e+07 0.000000e+00 1205s
261727 2.3350832e+07 6.146104e+04 0.000000e+00 1206s
261977 2.3356158e+07 2.684700e+03 0.000000e+00 1207s
262227 2.3398476e+07 2.521963e+04 0.000000e+00 1208s
262477 2.3460947e+07 2.134253e+03 0.000000e+00 1209s
262727 2.3466070e+07 5.625645e+01 0.000000e+00 1210s
262977 2.3509752e+07 5.033943e+06 0.000000e+00 1211s
263227 2.3585807e+07 1.528286e+04 0.000000e+00 1212s
263477 2.3594473e+07 7.441876e+03 0.000000e+00 1214s
263727 2.3648181e+07 3.307045e+03 0.000000e+00 1215s
263977 2.3651563e+07 3.111766e+03 0.000000e+00 1216s
264227 2.3662587e+07 2.398204e+02 0.000000e+00 1217s
264477 2.3683666e+07 9.521677e+04 0.000000e+00 1218s
264727 2.3723038e+07 1.276300e+03 0.000000e+00 1219s
264977 2.3726480e+07 3.142216e+04 0.000000e+00 1220s
265227 2.3794504e+07 1.672959e+03 0.000000e+00 1221s
265477 2.3800880e+07 2.206119e+04 0.000000e+00 1222s
265727 2.3820268e+07 1.970245e+03 0.000000e+00 1224s
265977 2.3868784e+07 2.261351e+07 0.000000e+00 1226s
266227 2.3881521e+07 8.568627e+03 0.000000e+00 1228s
266477 2.3892759e+07 2.151166e+03 0.000000e+00 1229s
266727 2.3894439e+07 3.267296e+03 0.000000e+00 1231s
266977 2.3911671e+07 1.391605e+03 0.000000e+00 1232s
267227 2.3945560e+07 6.088376e+05 0.000000e+00 1233s
267477 2.3981447e+07 8.342222e+01 0.000000e+00 1235s
267727 2.4010259e+07 1.340537e+04 0.000000e+00 1236s
267977 2.4049364e+07 3.563667e+04 0.000000e+00 1238s
268227 2.4076965e+07 1.509217e+03 0.000000e+00 1239s
268477 2.4103952e+07 1.040616e+05 0.000000e+00 1240s
268757 2.4108789e+07 1.009601e+02 0.000000e+00 1241s
269007 2.4141113e+07 4.792583e+04 0.000000e+00 1242s
269257 2.4155449e+07 6.441207e+02 0.000000e+00 1244s
269507 2.4186500e+07 3.771411e+04 0.000000e+00 1245s
269757 2.4194606e+07 3.581487e+03 0.000000e+00 1246s
270111 2.4203025e+07 4.345654e+03 0.000000e+00 1247s
270372 2.4206657e+07 7.357365e+04 0.000000e+00 1247s
270622 2.4211948e+07 2.099791e+04 0.000000e+00 1249s
270872 2.4213639e+07 2.329264e+03 0.000000e+00 1251s
271185 2.4215801e+07 1.133843e+03 0.000000e+00 1252s
271435 2.4217095e+07 7.879358e+03 0.000000e+00 1252s
271685 2.4218535e+07 1.057778e+03 0.000000e+00 1253s
271790 2.4218456e+07 0.000000e+00 0.000000e+00 1254s
Root relaxation: objective 2.421846e+07, 271790 iterations, 1236.04 seconds
Total elapsed time = 1257.80s
Total elapsed time = 1259.24s
Nodes | Current Node | Objective Bounds | Work
Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
0 0 2.4218e+07 0 116 - 2.4218e+07 - - 1261s
0 0 2.4218e+07 0 99 - 2.4218e+07 - - 1268s
0 0 2.4218e+07 0 86 - 2.4218e+07 - - 1284s
0 2 2.4218e+07 0 84 - 2.4218e+07 - - 1337s
1 4 2.4218e+07 1 76 - 2.4218e+07 - 37.0 1338s
3 8 2.4219e+07 2 75 - 2.4218e+07 - 31.0 1340s
7 16 2.4219e+07 3 75 - 2.4219e+07 - 24.4 1342s
15 32 2.4219e+07 4 75 - 2.4219e+07 - 21.2 1345s
18 32 2.4219e+07 4 70 - 2.4219e+07 - 25.3 1346s
31 64 2.4219e+07 5 75 - 2.4219e+07 - 24.2 1352s
63 96 2.4219e+07 6 74 - 2.4219e+07 - 38.4 1360s
95 128 2.4219e+07 7 68 - 2.4219e+07 - 59.5 1398s
127 160 2.4224e+07 8 69 - 2.4219e+07 - 73.7 1404s
159 192 2.4219e+07 8 69 - 2.4219e+07 - 73.3 1411s
191 226 2.4220e+07 9 71 - 2.4219e+07 - 73.9 1415s
225 263 2.4221e+07 10 64 - 2.4219e+07 - 69.4 1420s
262 392 2.4221e+07 11 63 - 2.4219e+07 - 64.7 1448s
391 663 2.4222e+07 14 72 - 2.4219e+07 - 61.3 1469s
397 663 2.4223e+07 16 72 - 2.4219e+07 - 60.9 1470s
662 1144 2.4223e+07 20 64 - 2.4219e+07 - 45.0 1508s
1143 1919 2.4223e+07 34 63 - 2.4219e+07 - 36.9 1560s
1918 2984 2.4224e+07 50 41 - 2.4219e+07 - 30.2 1627s
2983 4511 2.4224e+07 84 32 - 2.4219e+07 - 25.0 1698s
4510 5656 2.4225e+07 144 25 - 2.4219e+07 - 22.7 1767s
5655 6812 2.4225e+07 175 24 - 2.4219e+07 - 24.8 1840s
6811 8324 2.4225e+07 208 19 - 2.4219e+07 - 26.7 1911s
8323 9814 2.4225e+07 237 24 - 2.4219e+07 - 26.7 1979s
* 9700 8252 293 2.422468e+07 2.4219e+07 0.02% 26.4 1979s
Cutting planes:
Gomory: 16
Flow cover: 12
Explored 9825 nodes (534800 simplex iterations) in 1981.36 seconds
Thread count was 32 (of 64 available processors)
Solution count 1: 2.42247e+07
Optimal solution found (tolerance 1.00e-02)
Best objective 2.422468401458e+07, best bound 2.421884781807e+07, gap 0.0241%
--- Integer stage complete, starting price computation stage ---
Gurobi Version 9.1.0 -- dual simplex LP solver
Academic license - for non-commercial use only - expires 2021-03-17
Gurobi Optimizer version 9.1.0 build v9.1.0rc0 (linux64)
Thread count: 32 physical cores, 64 logical processors, using up to 32 threads
Optimize a model with 384820 rows, 214828 columns and 959973 nonzeros
Model fingerprint: 0x24a3d482
Coefficient statistics:
Matrix range [9e-04, 4e+03]
Objective range [1e+00, 1e+06]
Bounds range [3e-02, 3e+01]
RHS range [9e-13, 2e+03]
Presolve removed 313102 rows and 182912 columns
Presolve time: 4.11s
Presolved: 71718 rows, 70976 columns, 245465 nonzeros
Iteration Objective Primal Inf. Dual Inf. Time
0 handle free variables 4s
4589 handle free variables 5s
10707 handle free variables 6s
18462 handle free variables 7s
21553 1.1391136e+07 1.314806e+04 0.000000e+00 10s
Warning: Markowitz tolerance tightened to 0.125
21765 1.1391136e+07 1.113417e+04 0.000000e+00 10s
22463 1.1391136e+07 5.198002e+03 0.000000e+00 11s
23302 1.1391136e+07 4.426838e+03 0.000000e+00 12s
24819 1.1391136e+07 4.166450e+03 0.000000e+00 14s
25424 1.1391136e+07 2.136283e+03 0.000000e+00 14s
26892 1.1668269e+07 5.925378e+04 0.000000e+00 16s
27882 1.2299130e+07 1.407371e+05 0.000000e+00 16s
30524 1.4000445e+07 1.683071e+05 0.000000e+00 18s
31957 1.4720988e+07 1.468787e+05 0.000000e+00 19s
33362 1.5471243e+07 1.594428e+05 0.000000e+00 19s
34651 1.5935867e+07 4.787914e+04 0.000000e+00 20s
36010 1.6558513e+07 4.877104e+04 0.000000e+00 21s
38838 1.8025264e+07 6.103413e+05 0.000000e+00 22s
40271 1.8564394e+07 3.932230e+05 0.000000e+00 23s
41664 1.9207057e+07 3.689915e+05 0.000000e+00 24s
43097 1.9943878e+07 3.454983e+05 0.000000e+00 25s
45963 2.1058458e+07 1.122702e+05 0.000000e+00 27s
47396 2.1733444e+07 1.251915e+05 0.000000e+00 28s
48829 2.2283260e+07 1.493312e+05 0.000000e+00 29s
50262 2.2847785e+07 5.880740e+04 0.000000e+00 29s
51695 2.3568288e+07 1.477289e+05 0.000000e+00 30s
53128 2.4129469e+07 1.058929e+04 0.000000e+00 31s
Solved in 54179 iterations and 31.79 seconds
Infeasible or unbounded model
Error using miqps_gurobi (line 395)
miqps_gurobi: EXITFLAG from price computation stage = -4
Error in miqps_master (line 213)
miqps_gurobi(H, c, A, l, u, xmin, xmax, x0, vtype, opt);
Error in opt_model/solve (line 190)
miqps_master(HH, CC, A, l, u, xmin, xmax, x0, vtype, opt);
Error in most (line 2015)
mdo.om.solve(mdo.QP.opt);
Error in daily_SCED (line 126)
mdo = most(mdi, mpopt);
Error in run_SCUC (line 100)
[mdo, ms] = daily_SCED(mpc_day, xgd, area_load, wind_pen, solar_pen, hydro_pen,
init, mpopt);
xb00dx commented
Also, I assume you are familiar with what the two stages (integer and price computation) are doing ... depending on your application, the price computation stage may be completely unnecessary.
- I really need the price information, especially the multipliers for transmission constraints and (day-ahead) LMPs
- I read through MOST manual, and the pricing stage is done by fixing the integer variables then solving the LP/QP. If the MILP is feasible, then there must be a feasible solution to the pricing stage (LP). This really looks like a weird error to me
- Also another note: this issue happens usually when the SCUC problem is close to being infeasible. For example, if I increase all the loads by 3% in the cases above, GUROBI will tell me the MILP is infeasible. That's why I guess this might be a numerical issue with solvers..
rdzman commented
Hmmm ... I suspect it is a numerical issue with the solvers ... the question is what to do about it. Have you tried playing with some of the Gurobi tolerances? Maybe decreasing gurobi.opts.IntFeasTol?
It might actually be more fruitful to ask about this on a Gurobi forum. I'd be very interested in following the response.
And, yes, you are correct about the pricing stage. You can see here how I fix the integer variables before solving the LP.
xb00dx commented
I haven't tried to change the tolerance settings yet, will do so tonight.
Thanks for your help!
xb00dx commented
tried
mpopt = mpoption(mpopt,'gurobi.opts.OptimalityTol',1e-5); % default value is 1e-9
mpopt = mpoption(mpopt,'gurobi.opts.BarConvTol',1e-5); % default value is 1e-9
mpopt = mpoption(mpopt,'gurobi.opts.IntFeasTol',1e-5); % default value is 1e-9
and this issue seems gone
thanks for the suggestions!
rdzman commented
Great! That's helpful to know, in case I or others encounter this in the future.