I'm trying to solve a MIP using GLPK and CBC, and neither solver can efficiently find the solution. The GLPK solver log shows that it quickly finds a solution that is within 0.1% of the true optimum, but then takes forever trying to find that true optimum.
I know I can use the miptol arg to set a tolerance -- my question is, what about this problem causes the solver to be so inefficient finding the true optimum? I routinely solve versions of this problem with slightly different inputs and they solve in less than a second.
Here is a file with my problem specification which can be run in GLPK with glpsol --cpxlp anonymizedlp.lp.
And below is some of the GLPK log -- you'll see that a near optimal MIP solution is found within 54K iterations, and then the branch tree just starts growing and growing:
GLPSOL: GLPK LP/MIP Solver, v4.61
Parameter(s) specified in the command line:
--cpxlp /var/folders/g6/fs71g8j575v4_whqythqw7h40000gn/T/11446-pulp.lp -o
/var/folders/g6/fs71g8j575v4_whqythqw7h40000gn/T/11446-pulp.sol
Reading problem data from '/var/folders/g6/fs71g8j575v4_whqythqw7h40000gn/T/11446-pulp.lp'...
664 rows, 781 columns, 2576 non-zeros
443 integer variables, 338 of which are binary
3195 lines were read
GLPK Integer Optimizer, v4.61
664 rows, 781 columns, 2576 non-zeros
443 integer variables, 338 of which are binary
Preprocessing...
213 constraint coefficient(s) were reduced
524 rows, 652 columns, 2246 non-zeros
318 integer variables, 213 of which are binary
Scaling...
A: min|aij| = 1.282e-01 max|aij| = 1.060e+07 ratio = 8.267e+07
GM: min|aij| = 7.573e-01 max|aij| = 1.320e+00 ratio = 1.744e+00
EQ: min|aij| = 6.108e-01 max|aij| = 1.000e+00 ratio = 1.637e+00
2N: min|aij| = 3.881e-01 max|aij| = 1.355e+00 ratio = 3.491e+00
Constructing initial basis...
Size of triangular part is 524
Solving LP relaxation...
GLPK Simplex Optimizer, v4.61
524 rows, 652 columns, 2246 non-zeros
0: obj = -0.000000000e+00 inf = 2.507e+02 (195)
238: obj = -5.821025664e+06 inf = 0.000e+00 (0)
* 363: obj = -7.015287886e+04 inf = 0.000e+00 (0) 1
OPTIMAL LP SOLUTION FOUND
Integer optimization begins...
+ 363: mip = not found yet <= +inf (1; 0)
+ 8606: mip = not found yet <= -7.015289436e+04 (8239; 0)
+ 13027: mip = not found yet <= -7.015289436e+04 (12660; 0)
+ 16367: mip = not found yet <= -7.015289436e+04 (16000; 0)
+ 19135: mip = not found yet <= -7.015289436e+04 (18768; 0)
+ 21523: mip = not found yet <= -7.015289436e+04 (21156; 0)
+ 23667: mip = not found yet <= -7.015289436e+04 (23300; 0)
+ 25415: mip = not found yet <= -7.015289436e+04 (25048; 0)
+ 27260: mip = not found yet <= -7.015289436e+04 (26893; 0)
+ 29055: mip = not found yet <= -7.015289436e+04 (28688; 0)
+ 30770: mip = not found yet <= -7.015289436e+04 (30403; 0)
+ 32362: mip = not found yet <= -7.015289436e+04 (31995; 0)
Time used: 60.0 secs. Memory used: 14.1 Mb.
+ 33876: mip = not found yet <= -7.015289436e+04 (33509; 0)
+ 35338: mip = not found yet <= -7.015289436e+04 (34971; 0)
+ 36721: mip = not found yet <= -7.015289436e+04 (36354; 0)
+ 38080: mip = not found yet <= -7.015289436e+04 (37713; 0)
+ 39372: mip = not found yet <= -7.015289436e+04 (39005; 0)
+ 40601: mip = not found yet <= -7.015289436e+04 (40234; 0)
+ 41837: mip = not found yet <= -7.015289436e+04 (41470; 0)
+ 43036: mip = not found yet <= -7.015289436e+04 (42669; 0)
+ 44192: mip = not found yet <= -7.015289436e+04 (43825; 0)
+ 45350: mip = not found yet <= -7.015289436e+04 (44983; 0)
+ 46374: mip = not found yet <= -7.015289436e+04 (46007; 0)
+ 47281: mip = not found yet <= -7.015289436e+04 (46914; 0)
Time used: 120.0 secs. Memory used: 20.4 Mb.
+ 48220: mip = not found yet <= -7.015289436e+04 (47853; 0)
+ 49195: mip = not found yet <= -7.015289436e+04 (48828; 0)
+ 50131: mip = not found yet <= -7.015289436e+04 (49764; 0)
+ 51110: mip = not found yet <= -7.015289436e+04 (50743; 0)
+ 52131: mip = not found yet <= -7.015289436e+04 (51764; 0)
+ 53092: mip = not found yet <= -7.015289436e+04 (52725; 0)
+ 53901: >>>>> -7.015398607e+04 <= -7.015289436e+04 < 0.1% (53532; 0)
+ 61014: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (57365; 3302)
+ 64785: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (61136; 3302)
+ 67671: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (64022; 3302)
+ 70330: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (66681; 3302)
+ 72613: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (68964; 3302)
+ 74731: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (71082; 3302)
Time used: 180.0 secs. Memory used: 29.9 Mb.
+ 76685: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (73036; 3302)
+ 78508: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (74859; 3302)
+ 80220: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (76571; 3302)
+ 81852: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (78203; 3302)
+ 83368: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (79719; 3302)
+ 84815: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (81166; 3302)
+ 86126: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (82477; 3302)
+ 87358: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (83709; 3302)
+ 88612: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (84963; 3302)
+ 89821: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (86172; 3302)
+ 90989: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (87340; 3302)
+ 92031: mip = -7.015398607e+04 <= -7.015290061e+04 < 0.1% (88382; 3302)