This appendix presents a few examples of the output produced by the problem analyzer described in Section 10.1. The first two problems are taken from the MIPLIB 2003 collection, http://miplib.zib.de/.
Analyzing the problem
Constraints Bounds Variables
fixed : all ranged : all bin : all
-------------------------------------------------------------------------------
Objective, min cx
range: min |c|: 31.0000 max |c|: 2258.00
distrib: |c| vars
[31, 100) 176
[100, 1e+03) 8084
[1e+03, 2.26e+03] 644
-------------------------------------------------------------------------------
Constraint matrix A has
823 rows (constraints)
8904 columns (variables)
72965 (0.995703%) nonzero entries (coefficients)
Row nonzeros, A_i
range: min A_i: 2 (0.0224618%) max A_i: 368 (4.13297%)
distrib: A_i rows rows% acc%
2 2 0.24 0.24
[3, 7] 4 0.49 0.73
[8, 15] 19 2.31 3.04
[16, 31] 80 9.72 12.76
[32, 63] 236 28.68 41.43
[64, 127] 289 35.12 76.55
[128, 255] 186 22.60 99.15
[256, 368] 7 0.85 100.00
Column nonzeros, A|j
range: min A|j: 2 (0.243013%) max A|j: 15 (1.8226%)
distrib: A|j cols cols% acc%
2 118 1.33 1.33
[3, 7] 2853 32.04 33.37
[8, 15] 5933 66.63 100.00
A nonzeros, A(ij)
range: all |A(ij)| = 1.00000
-------------------------------------------------------------------------------
Constraint bounds, lb <= Ax <= ub
distrib: |b| lbs ubs
[1, 10] 823 823
Variable bounds, lb <= x <= ub
distrib: |b| lbs ubs
0 8904
[1, 10] 8904
-------------------------------------------------------------------------------
Analyzing the problem
Constraints Bounds Variables
lower bd: 82 lower bd: 38 cont: 850
upper bd: 946 fixed : 353 bin : 415
fixed : 20 free : 1 int : 123
ranged : 996
-------------------------------------------------------------------------------
Objective, min cx
range: all |c| in {0.00000, 1.00000}
distrib: |c| vars
0 1387
1 1
-------------------------------------------------------------------------------
Constraint matrix A has
1048 rows (constraints)
1388 columns (variables)
20439 (1.40511%) nonzero entries (coefficients)
Row nonzeros, A_i
range: min A_i: 1 (0.0720461%) max A_i: 1046 (75.3602%)
distrib: A_i rows rows% acc%
1 29 2.77 2.77
2 476 45.42 48.19
[3, 7] 49 4.68 52.86
[8, 15] 56 5.34 58.21
[16, 31] 64 6.11 64.31
[32, 63] 373 35.59 99.90
[1024, 1046] 1 0.10 100.00
Column nonzeros, A|j
range: min A|j: 1 (0.0954198%) max A|j: 29 (2.76718%)
distrib: A|j cols cols% acc%
1 381 27.45 27.45
2 19 1.37 28.82
[3, 7] 38 2.74 31.56
[8, 15] 233 16.79 48.34
[16, 29] 717 51.66 100.00
A nonzeros, A(ij)
range: min |A(ij)|: 0.000200000 max |A(ij)|: 2.33067e+07
distrib: A(ij) coeffs
[0.0002, 0.001) 167
[0.001, 0.01) 1049
[0.01, 0.1) 4553
[0.1, 1) 8840
[1, 10) 3822
[10, 100) 630
[100, 1e+03) 267
[1e+03, 1e+04) 699
[1e+04, 1e+05) 291
[1e+05, 1e+06) 83
[1e+06, 1e+07) 19
[1e+07, 2.33e+07] 19
-------------------------------------------------------------------------------
Constraint bounds, lb <= Ax <= ub
distrib: |b| lbs ubs
[0.1, 1) 386
[1, 10) 74
[10, 100) 101 456
[100, 1000) 34
[1000, 10000) 15
[100000, 1e+06] 1 1
Variable bounds, lb <= x <= ub
distrib: |b| lbs ubs
0 974 323
[0.001, 0.01) 19
[0.1, 1) 370 57
[1, 10) 41 704
[10, 100] 2 246
-------------------------------------------------------------------------------
Analyzing the problem
Constraints Bounds Variables
lower bd: 40 upper bd: 1 cont: all
upper bd: 121 fixed : 204
fixed : 5480 free : 5600
ranged : 161 ranged : 40
-------------------------------------------------------------------------------
Objective, maximize cx
range: all |c| in {0.00000, 15.4737}
distrib: |c| vars
0 5844
15.4737 1
-------------------------------------------------------------------------------
Constraint matrix A has
5802 rows (constraints)
5845 columns (variables)
6480 (0.0191079%) nonzero entries (coefficients)
Row nonzeros, A_i
range: min A_i: 0 (0%) max A_i: 3 (0.0513259%)
distrib: A_i rows rows% acc%
0 80 1.38 1.38
1 5003 86.23 87.61
2 680 11.72 99.33
3 39 0.67 100.00
0/80 empty rows have quadratic terms
Column nonzeros, A|j
range: min A|j: 0 (0%) max A|j: 15 (0.258532%)
distrib: A|j cols cols% acc%
0 204 3.49 3.49
1 5521 94.46 97.95
2 40 0.68 98.63
[3, 7] 40 0.68 99.32
[8, 15] 40 0.68 100.00
0/204 empty columns correspond to variables used in conic
and/or quadratic expressions only
A nonzeros, A(ij)
range: min |A(ij)|: 2.02410e-05 max |A(ij)|: 35.8400
distrib: A(ij) coeffs
[2.02e-05, 0.0001) 40
[0.0001, 0.001) 118
[0.001, 0.01) 305
[0.01, 0.1) 176
[0.1, 1) 40
[1, 10) 5721
[10, 35.8] 80
-------------------------------------------------------------------------------
Constraint bounds, lb <= Ax <= ub
distrib: |b| lbs ubs
0 5481 5600
[1000, 10000) 1
[10000, 100000) 2 1
[1e+06, 1e+07) 78 40
[1e+08, 1e+09] 120 120
Variable bounds, lb <= x <= ub
distrib: |b| lbs ubs
0 243 203
[0.1, 1) 1 1
[1e+06, 1e+07) 40
[1e+11, 1e+12] 1
-------------------------------------------------------------------------------
Quadratic constraints: 121
Gradient nonzeros, Qx
range: min Qx: 1 (0.0171086%) max Qx: 2720 (46.5355%)
distrib: Qx cons cons% acc%
1 40 33.06 33.06
[64, 127] 80 66.12 99.17
[2048, 2720] 1 0.83 100.00
-------------------------------------------------------------------------------
Analyzing the problem
Constraints Bounds Variables
upper bd: 3600 fixed : 3601 cont: all
fixed : 21760 free : 28802
-------------------------------------------------------------------------------
Objective, minimize cx
range: all |c| in {0.00000, 1.00000}
distrib: |c| vars
0 32402
1 1
-------------------------------------------------------------------------------
Constraint matrix A has
25360 rows (constraints)
32403 columns (variables)
93339 (0.0113587%) nonzero entries (coefficients)
Row nonzeros, A_i
range: min A_i: 1 (0.00308613%) max A_i: 8 (0.0246891%)
distrib: A_i rows rows% acc%
1 3600 14.20 14.20
2 10803 42.60 56.79
[3, 7] 3995 15.75 72.55
8 6962 27.45 100.00
Column nonzeros, A|j
range: min A|j: 0 (0%) max A|j: 61 (0.240536%)
distrib: A|j cols cols% acc%
0 3602 11.12 11.12
1 10800 33.33 44.45
2 7200 22.22 66.67
[3, 7] 7279 22.46 89.13
[8, 15] 3521 10.87 100.00
[32, 61] 1 0.00 100.00
3600/3602 empty columns correspond to variables used in conic
and/or quadratic constraints only
A nonzeros, A(ij)
range: min |A(ij)|: 0.00833333 max |A(ij)|: 1.00000
distrib: A(ij) coeffs
[0.00833, 0.01) 57280
[0.01, 0.1) 59
[0.1, 1] 36000
-------------------------------------------------------------------------------
Constraint bounds, lb <= Ax <= ub
distrib: |b| lbs ubs
0 21760 21760
[0.1, 1] 3600
Variable bounds, lb <= x <= ub
distrib: |b| lbs ubs
[1, 10] 3601 3601
-------------------------------------------------------------------------------
-------------------------------------------------------------------------------
Rotated quadratic cones: 3600
dim RQCs
4 3600