B. Problem analyzer examples


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/.

B.1. air04

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

-------------------------------------------------------------------------------

B.2. arki001

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

-------------------------------------------------------------------------------

B.3. Problem with both linear and quadratic constraints

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

-------------------------------------------------------------------------------

B.4. Problem with both linear and conic constraints

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

Wed Feb 29 16:08:54 2012