This directory contains the NETLIB (http://www.netlib.org/lp/data/)
set of Linear Programming test problems.

The problems are all in MPS format, which is itself a subset of SIF.
The problems have been classified according to the CUTE classification
system (see, Bongartz, Conn, Gould and Toint, ACM Transactions on
Mathematical Software 21, 1995, pp.  123-160), and have been slightly
reformatted for consistency.


-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
-=-=-=-=-=-= Original readme from http://www.netlib.org/lp/data/ =-=-=-=-=-=-=-
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-


==== LP/DATA README (formerly index) =====

To reduce transmission times, linear programming test problems
are stored in a compressed format; issue the netlib request

    send emps.f from lp/data

to obtain a Fortran 77 Subset program for expanding the test problems
into MPS-standard input form.  The program includes comments giving
test data.  To get a (more efficient and convenient) C version of this
program (without the test data), issue the netlib request

    send emps.c from lp/data

If you are not familiar with MPS files, see Chapter 9 of "Advanced
Linear Programming" by Bruce A. Murtagh, McGraw-Hill, 1981,
or Appendix A of "Exploring Interior-Point Linear Programming"
by Ami Arbel, MIT Press, 1993.

All the material described here is now available by ftp from
netlib.bell-labs.com (login: anonymous; Password: your E-mail address;
cd /netlib/lp/data).  If you can, please use ftp to obtain the larger
problems.  Note that the *.Z files in lp/data must be copied in binary
mode and uncompressed two ways: first with uncompress, then with emps.
If you are using a Unix system and your solver reads standard input,
you can save some disk space by executing, e.g.,
    zcat pilot.Z | emps | solver
On some Unix systems and with solvers that require a named file,
you may also be able to use a named pipe, e.g.,
    /etc/mknod pilot.mps p
    zcat pilot.Z | emps >pilot.mps & solver pilot.mps
    rm pilot.mps

The "Kennington" problems, sixteen problems described in "An Empirical
Evaluation of the KORBX Algorithms for Military Airlift Applications"
by W. J. Carolan, J. E. Hill, J. L. Kennington, S. Niemi, S. J.
Wichmann (Operations Research vol. 38, no. 2 (1990), pp. 240-248),
are available only by ftp: login as above, and cd lp/data/kennington .
More details appear in lp/data/kennington/readme .

People who use EBCDIC systems may wish to issue the netlib request

    send ascii from lp/data

to get a listing of the distinct character codes that appear in the
compressed LP data files -- for the uncompression routines to work,
these distinct ASCII characters must be translated into distinct EBCDIC
characters.

The column and nonzero counts in the PROBLEM SUMMARY TABLE below exclude
slack and surplus columns and the right-hand side vector, but include
the cost row.  We have omitted other free rows and all but the first
right-hand side vector, as noted below.  The byte count is for the
compressed file; it includes a newline character at the end of each
line.  These files start with a blank initial line intended to prevent
mail programs from discarding any of the data.  The BR column indicates
whether a problem has bounds or ranges:  B stands for "has bounds", R
for "has ranges".  The BOUND-TYPE TABLE below shows the bound types
present in those problems that have bounds.

The problems below are sorted (according to the ASCII collating
sequence) on their names.  Unless problem characteristics suggest a
more rational order, we suggest using this order for reporting results.


                       PROBLEM SUMMARY TABLE

Name       Rows   Cols   Nonzeros    Bytes  BR      Optimal Value

25FV47      822   1571    11127      70477        5.5018458883E+03
80BAU3B    2263   9799    29063     298952  B     9.8723216072E+05
ADLITTLE     57     97      465       3690        2.2549496316E+05
AFIRO        28     32       88        794       -4.6475314286E+02
AGG         489    163     2541      21865       -3.5991767287E+07
AGG2        517    302     4515      32552       -2.0239252356E+07
AGG3        517    302     4531      32570        1.0312115935E+07
BANDM       306    472     2659      19460       -1.5862801845E+02
BEACONFD    174    262     3476      17475        3.3592485807E+04
BLEND        75     83      521       3227       -3.0812149846E+01
BNL1        644   1175     6129      42473        1.9776292856E+03
BNL2       2325   3489    16124     127145        1.8112365404E+03
BOEING1     351    384     3865      25315  BR   -3.3521356751E+02
BOEING2     167    143     1339       8761  BR   -3.1501872802E+02
BORE3D      234    315     1525      13160  B     1.3730803942E+03
BRANDY      221    249     2150      14028        1.5185098965E+03
CAPRI       272    353     1786      15267  B     2.6900129138E+03
CYCLE      1904   2857    21322     166648  B    -5.2263930249E+00
CZPROB      930   3523    14173      92202  B     2.1851966989E+06
D2Q06C     2172   5167    35674     258038        1.2278423615E+05
D6CUBE      416   6184    43888     167633  B     3.1549166667E+02
DEGEN2      445    534     4449      24657       -1.4351780000E+03
DEGEN3     1504   1818    26230     130252       -9.8729400000E+02
DFL001     6072  12230    41873     353192  B     1.12664E+07 **
E226        224    282     2767      17749       -1.8751929066E+01
ETAMACRO    401    688     2489      21915  B    -7.5571521774E+02
FFFFF800    525    854     6235      39637        5.5567961165E+05
FINNIS      498    614     2714      23847  B     1.7279096547E+05
FIT1D        25   1026    14430      51734  B    -9.1463780924E+03
FIT1P       628   1677    10894      65116  B     9.1463780924E+03
FIT2D        26  10500   138018     482330  B    -6.8464293294E+04
FIT2P      3001  13525    60784     439794  B     6.8464293232E+04
FORPLAN     162    421     4916      25100  BR   -6.6421873953E+02
GANGES     1310   1681     7021      60191  B    -1.0958636356E+05
GFRD-PNC    617   1092     3467      24476  B     6.9022359995E+06
GREENBEA   2393   5405    31499     235711  B    -7.2462405908E+07
GREENBEB   2393   5405    31499     235739  B    -4.3021476065E+06
GROW15      301    645     5665      35041  B    -1.0687094129E+08
GROW22      441    946     8318      50789  B    -1.6083433648E+08
GROW7       141    301     2633      17043  B    -4.7787811815E+07
ISRAEL      175    142     2358      12109       -8.9664482186E+05
KB2          44     41      291       2526  B    -1.7499001299E+03
LOTFI       154    308     1086       6718       -2.5264706062E+01
MAROS       847   1443    10006      65906  B    -5.8063743701E+04
MAROS-R7   3137   9408   151120    4812587        1.4971851665E+06
MODSZK1     688   1620     4158      40908  B     3.2061972906E+02
NESM        663   2923    13988     117828  BR    1.4076073035E+07
PEROLD      626   1376     6026      47486  B    -9.3807580773E+03
PILOT      1442   3652    43220     278593  B    -5.5740430007E+02
PILOT.JA    941   1988    14706      97258  B    -6.1131344111E+03
PILOT.WE    723   2789     9218      79972  B    -2.7201027439E+06
PILOT4      411   1000     5145      40936  B    -2.5811392641E+03
PILOT87    2031   4883    73804     514192  B     3.0171072827E+02
PILOTNOV    976   2172    13129      89779  B    -4.4972761882E+03
QAP8        913   1632     8304 (see NOTES)       2.0350000000E+02
QAP12      3193   8856    44244 (see NOTES)       5.2289435056E+02
QAP15      6331  22275   110700 (see NOTES)       1.0409940410E+03
RECIPE       92    180      752       6210  B    -2.6661600000E+02
SC105       106    103      281       3307       -5.2202061212E+01
SC205       206    203      552       6380       -5.2202061212E+01
SC50A        51     48      131       1615       -6.4575077059E+01
SC50B        51     48      119       1567       -7.0000000000E+01
SCAGR25     472    500     2029      17406       -1.4753433061E+07
SCAGR7      130    140      553       4953       -2.3313892548E+06
SCFXM1      331    457     2612      19078        1.8416759028E+04
SCFXM2      661    914     5229      37079        3.6660261565E+04
SCFXM3      991   1371     7846      53828        5.4901254550E+04
SCORPION    389    358     1708      12186        1.8781248227E+03
SCRS8       491   1169     4029      36760        9.0429998619E+02
SCSD1        78    760     3148      17852        8.6666666743E+00
SCSD6       148   1350     5666      32161        5.0500000078E+01
SCSD8       398   2750    11334      65888        9.0499999993E+02
SCTAP1      301    480     2052      14970        1.4122500000E+03
SCTAP2     1091   1880     8124      57479        1.7248071429E+03
SCTAP3     1481   2480    10734      78688        1.4240000000E+03
SEBA        516   1028     4874      38627  BR    1.5711600000E+04
SHARE1B     118    225     1182       8380       -7.6589318579E+04
SHARE2B      97     79      730       4795       -4.1573224074E+02
SHELL       537   1775     4900      38049  B     1.2088253460E+09
SHIP04L     403   2118     8450      57203        1.7933245380E+06
SHIP04S     403   1458     5810      41257        1.7987147004E+06
SHIP08L     779   4283    17085     117083        1.9090552114E+06
SHIP08S     779   2387     9501      70093        1.9200982105E+06
SHIP12L    1152   5427    21597     146753        1.4701879193E+06
SHIP12S    1152   2763    10941      82527        1.4892361344E+06
SIERRA     1228   2036     9252      76627  B     1.5394362184E+07
STAIR       357    467     3857      27405  B    -2.5126695119E+02
STANDATA    360   1075     3038      26135  B     1.2576995000E+03
STANDGUB    362   1184     3147      27836  B     (see NOTES)
STANDMPS    468   1075     3686      29839  B     1.4060175000E+03
STOCFOR1    118    111      474       4247       -4.1131976219E+04
STOCFOR2   2158   2031     9492      79845       -3.9024408538E+04
STOCFOR3  16676  15695    74004 (see NOTES)      -3.9976661576E+04
TRUSS      1001   8806    36642 (see NOTES)       4.5881584719E+05
TUFF        334    587     4523      29439  B     2.9214776509E-01
VTP.BASE    199    203      914       8175  B     1.2983146246E+05
WOOD1P      245   2594    70216     328905        1.4429024116E+00
WOODW      1099   8405    37478     240063        1.3044763331E+00


        BOUND-TYPE TABLE

80BAU3B    UP LO FX
BOEING1    UP LO
BOEING2    UP LO
BORE3D     UP LO FX
CAPRI      UP    FX FR
CYCLE      UP       FR
CZPROB           FX
DFL001     UP
D6CUBE        LO
ETAMACRO   UP LO FX
FINNIS     UP LO FX
FIT1D      UP
FIT1P      UP
FIT2D      UP
FIT2P      UP
FORPLAN    UP    FX
GANGES     UP LO
GFRD-PNC   UP LO
GREENBEA   UP LO FX
GREENBEB   UP LO FX FR
GROW15     UP
GROW22     UP
GROW7      UP
KB2        UP
MODSZK1             FR
NESM       UP LO FX
PEROLD     UP LO FX FR
PILOT      UP LO FX
PILOT.JA   UP LO FX FR
PILOT.WE   UP LO FX FR
PILOT4     UP    FX FR PL
PILOTNOV   UP    FX
RECIPE     UP LO FX
SEBA       UP LO
SHELL      UP LO FX
SIERRA     UP
STAIR      UP    FX FR
STANDATA   UP    FX
STANDGUB   UP    FX
STANDMPS   UP    FX
TUFF       UP LO FX FR
VTP.BASE   UP LO FX FR


Several problems have an empty RHS section:  BORE3D, CYCLE, GREENBEA,
GREENBEB, KB2, RECIPE, and TUFF.


HEARTY THANKS go to the people who supplied the above problems.
Michael Saunders provided 13 problems from the Systems Optimization
Laboratory at Stanford University:  ADLITTLE, AFIRO, BANDM, BEACONFD,
BRANDY, CAPRI, E226, ETAMACRO, ISRAEL, PILOT, SHARE1B, SHARE2B, STAIR.
Four problems are from a tape that John Reid sent me (David Gay) several
years ago:  25FV47, CZPROB, FFFFF800, SHELL.  Linus Schrage sent GANGES
and SEBA.  Bob Fourer supplied 44 problems:  80BAU3B, BORE3D, FIT1D,
FIT1P, FIT2D, FIT2P, FORPLAN, GFRD-PNC, GREENBEA, GREENBEB, GROW15,
GROW22, GROW7, NESM, PILOT.JA, PILOT.WE, PILOT4, PILOTNOV, RECIPE,
SC205, SCAGR25, SCAGR7,  SCFXM1, SCFXM2, SCFXM3, SCORPION, SCRS8, SCSD1,
SCSD6, SCSD8, SCTAP1, SCTAP2, SCTAP3, SHIP04L, SHIP04S, SHIP08L,
SHIP08S, SHIP12L, SHIP12S, SIERRA, STANDATA, STANDGUB, STANDMPS,
VTP.BASE.  Mauricio Resende provided AGG, AGG2, and AGG3, which were
formulated by R. C. Leachman. Gus Gassmann contributed STOCFOR1,
STOCFOR2, and STOCFOR3.  Nick Gould supplied BLEND, BOEING1, BOEING2,
FINNIS, PEROLD, SC105, SC50A, and SC50B from the Harwell collection of
LP test problems.  Vahid Lotfi submitted LOTFI.  With the permission of
Ketron, John Tomlin provided BNL1, BNL2, CYCLE, D2Q06C, DEGEN2, DEGEN3,
KB2, TUFF, WOOD1P, and WOODW.  At the request of Olvi Mangasarian,
Rudy Setiono supplied the generator and description (both written by
Michael Ferris) and data for TRUSS.  Istvan Maros provided MAROS,
MAROS-R7, and MODSZK1.  Irv Lustig supplied PILOT87, which he obtained
from John Stone.  Marc Meketon submitted DFL001.  Robert Hughes supplied
D6CUBE.  Problems QAP8, QAP12, and QAP15 are from a generator by Terri
Johnson (communicated by a combination of Bob Bixby, Matt Saltzman, and
Terri Johnson).
  Thanks also go to Irv Lustig for helpful comments on this index file.

NOTES:  we have omitted extra right-hand side vectors from BEACONFD,
BRANDY, FFFFF800, ISRAEL; extra bound sets from GREENBEA, GREENBEB,
GROW15, GROW22, GROW7, RECIPE; extra free rows from 80BAU3B, BOEING1,
BORE3D, E226, FFFFF800, FINNIS, FORPLAN, GANGES, GREENBEA, GREENBEB,
MAROS, PILOT, PILOT87, RECIPE, SCTAP1, SCTAP2, SCTAP3, SHARE2B, SHIP04L,
SHIP04S, SHIP08L, SHIP08S, SHIP12L, SHIP12S; and explicit zeros from
GROW15, GROW22, GROW7, NESM, SCORPION, SCRS8, SEBA, SIERRA, STAIR.  We
also negated the cost coefficients in BOEING1, BOEING2, DEGEN2, DEGEN3,
ETAMACRO, FIT1D, FIT2D, GANGES, GROW15, GROW22, GROW7, LOTFI, MAROS,
PILOT, PILOT.JA, PILOT.WE, PILOTNOV, SC105, SC50A, SC50B, STAIR.  In
their original form, these problems are usually maximized.  In their
modified form, all problems are to be minimized.  (PILOT4 appeared
to be a minimization problem already).

Problem 25FV47 is sometimes called BP or BP1, and FFFFF800 is sometimes
called POWELL.  Problems GREENBEA and GREENBEB differ only in their
BOUNDS sections.  The names shown above come mostly from the original
NAME line; the optimal values are from MINOS version 5.3 (of Sept. 1988)
running on a VAX with default options (except, as described below, for
DFL001 and the QAP problems).  [Earlier versions of this index file gave
values from earlier versions of MINOS.  Prior to 29 April 1987, this
index file gave the optimal value from maximizing rather than minimizing
PILOTNOV.]

Note that MINOS control parameters, such as SCALE, PARTIAL PRICE,
FEASIBILITY TOLERANCE, OPTIMALITY TOLERANCE, and CRASH OPTION may
affect the optimal value that MINOS reports (as may the version of
MINOS, the computer, and even the compiler used).

This directory does not provide compressed MPS files for the QAP
problems.  Instead, source for Terri Johnson's generator and input data
for producing MPS files for QAP8, QAP12, and QAP15 appear in directory
lp/generators/qap.

For discussion of some of the above test problems, including sparsity
graphs and MINOS performance with and without scaling and partial
pricing, see "An Analysis of an Available Set of Linear Programming
Test Problems" by Irvin J. Lustig [Tech. Report SOL 87-11, Systems
Optimization Laboratory, Dept. of Operations Research, Stanford Univ.,
Stanford, CA 94305-4022; a shorter version appears in Comput. Opns.
Res. vol. 16, no. 2, pp. 173-184, 1989].  Be warned that the
reproduction process may have dropped isolated nonzeros from graphs of
the larger problems.

Bob Bixby reports that the CPLEX solver (running on a Sparc station)
finds slightly different optimal values for some of the problems.
On a MIPS processor, MINOS version 5.3 (with crash and scaling of
December 1989) also finds different optimal values for some of the
problems.  The following table shows the values that differ from those
shown above.  (Whether CPLEX finds different values on the recently
added problems remains to be seen.)

Problem        CPLEX(Sparc)          MINOS(MIPS)

25FV47                            5.5018467791E+03
80BAU3B      9.8722419241E+05     9.8722952818E+05
BNL1         1.9776295615E+03     1.9776293385E+03
D2Q06C                            1.2278423521E+05
DFL001       1.1266396047E+07            **
ETAMACRO    -7.5571523337E+02    -7.5571522100E+02
FIT2D                            -6.8464293232E+04
FFFFF800     5.5567956482E+05     5.5567958085E+05
FORPLAN     -6.6421896127E+02
GANGES      -1.0958573613E+05    -1.0958577038E+05
GREENBEA    -7.2555248130E+07
GREENBEB    -4.3022602612E+06    -4.3021537702E+06
NESM         1.4076036488E+07     1.4076065292E+07
PEROLD      -9.3807552782E+03    -9.3807553661E+03
PILOT       -5.5748972928E+02    -5.5741215293E+02
PILOT.JA    -6.1131364656E+03    -6.1131349867E+03
PILOT.WE    -2.7201075328E+06    -2.7201042967E+06
PILOT4      -2.5811392589E+03    -2.5811392624E+03
PILOT87                           3.0171074161E+02
SCAGR7      -2.3313898243E+06    -2.3313897524E+06
SCRS8        9.0429695380E+02     9.0429695380E+02
SCSD6        5.0500000077E+01
SIERRA                            1.5394364186E+07
STOCFOR3    -3.9976785944E+04    -3.9976776417E+04

The above CPLEX and MINOS results were both obtained using double-
precision IEEE (binary) arithmetic, i.e., arithmetic of precision
similar to the VAX double precision with which the MINOS 5.3 results
in the PROBLEM SUMMARY TABLE were computed.

The old problem GUB was the same as CZPROB (except for the NAME line)
and hence is withdrawn.

STANDGUB includes GUB markers; with these lines removed (lines in
the expanded MPS file that contain primes, i.e., that mention the rows
'EGROUP' and 'ENDX'), STANDGUB becomes the same as problem STANDATA;
MINOS does not understand the GUB markers, so we cannot report an
optimal value from MINOS for STANDGUB.  STANDMPS amounts to STANDGUB
with the GUB constraints as explicit constraints.

STOCFOR1,2,3 are stochastic forestry problems from Gus Gassmann.  To
quote Gus, "All of them are seven-period descriptions of a forestry
problem with a random occurrence of forest fires, and the size varies
according to the number of realizations you use in each period."
STOCFOR1 "is the deterministic version, STOCFOR2 has 2 realizations
each in periods 2 to 7, and the monster STOCFOR3 has 4,4,4,2,2, and 2
realizations, respectively."  The compressed form of STOCFOR3 would be
652846 bytes long, so requesting STOCFOR3 will instead get you a bundle
of about 174 kilobytes that includes source for Gus's program, the
data files for generating STOCFOR3 and a summary of "A Standard
Input Format for Multistage Stochastic Linear Programs" by J.R. Birge,
M.A.H. Dempster, H.I. Gassmann, E.A. Gunn, A.J. King, and S.W. Wallace
[COAL Newsletter No. 17 (Dec. 1987), pp. 1-19].  Data files are also
included for generating versions of STOCFOR1,2 that have more decimal
places than the versions in lp/data.

Concerning the problems he supplied, Nick Gould says that BLEND "is
is a variant of the [oil refinery] problem in Murtagh's book (the
coefficients are different) which I understand John Reid obtained
from the people at NPL (Gill and Murray?); they were also the original
sources for the SC problems"; BOEING1 and BOEING2 "have to do with
flap settings on aircraft for economical operations"; PEROLD "is
another Pilot model (Pilot1)"; and FINNIS "is from Mike Finnis at
Harwell, a model for the selection of alternative fuel types."

BOEING1 and BOEING2 were originally mixed-integer programming problems.
The COLUMNS section of BOEING1 had
    INTBEG    'MARKER'                 'INTORG'
between the coefficients for columns GRDTIMN6 and N1001AC1, and that
BOEING2 had such a line between columns GRDTIMN4 and N1003AC1.  Both had
    INTFIN    'MARKER'                 'INTEND'
just before the start of the ROWS section.  These 'MARKER' lines have
been removed.  These problems also had a few rows defined as linear
combinations of other rows.  These rows are now given explicitly, since
the compression/expansion programs do not understand D lines in the ROWS
section.

LOTFI, says Vahid Lotfi, "involves audit staff scheduling.  This problem
is semi real world and we have used it in a study, the results of which
are to appear in Decision Sciences (Fall 1990).  The detailed
description of the problem is also in the paper.  The problem is
actually an MOLP with seven objectives, the first is maximization and
the other six are minimization.  The version that I am sending has the
aggregated objective (i.e., z1-z2-z3-z4-z5-z6-z7)."

On the problems supplied by John Tomlin, MINOS 5.3 reports that about
10% to 57% of its steps are degenerate:
     Name     Steps  Degen  Percent
     BNL1      1614    169   10.47
     BNL2      4914    906   18.44
     CYCLE     3156   1485   47.05
     D2Q06C   42417   4223    9.96
     DEGEN2    1075    610   56.74
     DEGEN3    6283   3299   52.51
     KB2         82     29   35.37
     TUFF       745    345   46.31
     WOOD1P    1059    471   44.48
     WOODW     4147   1604   38.68

Concerning PILOT87, Irv Lustig says, "PILOT87 is considered (by John
Stone, at least) to be harder than PILOT because of the bad scaling in
the numerics."

Requesting TRUSS will get you a bundle of Fortran source and data for
generating an MPS file for TRUSS, a problem of minimizing the weight
of a certain structure.  The bundle also includes a description of the
problem.

DFL001, says Marc Meketon, "is a 'real-world' airline schedule planning
(fleet assignment) problem.  This LP was preprocessed by a modified
version of the KORBX(r) System preprocessor.  The problem reduced in
size (rows, columns, non-zeros) significantly.  The row and columns were
randomly sorted and renamed, and a fixed adjustment to the objective
function was eliminated.  The name of the problem is derived from the
initials of the person who created it."

Of D6CUBE, Robert Hughes says, "Mike Anderson and I are working on the
problem of finding the minimum cardinality of triangulations of the
6-dimensional cube.  The optimal objective value of the problem I sent
you provides a lower bound for the cardinalities of all triangulations
which contain a certain simplex of volume 8/6! and which contains the
centroid of the 6-cube in its interior.  The linear programming
problem is not easily described."

Concerning the problems he submitted, Istvan Maros says that MAROS is
an industrial production/allocation model about which "the customer does
not want to reveal the exact meaning".   MAROS-R7 is "an interesting
real-life LP problem which appeared hard to some solvers."  It "is an
image restoration problem done via a goal programming approach.  It is
structured, namely, its first section is a band matrix with the
dominating number of nonzeros, while the second section is also a band
matrix with bandwidth equals 2 and coefficients +1, -1.  The problem is
a representative of a family of problems in which the number of rows and
the bandwidth of the first section can vary.  This one is a medium size
problem from the family.  MAROS-R7 became available in cooperation with
Roni Levkovitz and Carison Tong."  MODSZK1 is a "real-life problem" that
is "very degenerate" and on which a dual simplex algorithm "may require
up to 10 times" fewer iterations than a primal simplex algorithm.  It
"is a multi-sector economic planning model (a kind of an input/output
model in economy)" and "is an old problem of mine and it is not easy to
recall more."

** On an IEEE-arithmetic machine (an SGI 4D/380S), I (dmg) succeeded in
getting MINOS 5.3 to report optimal objective values, 1.1261702419E+07
and 1.1249281428E+07, for DFL001 only by starting with LOAD files
derived from the solution obtained on the same machine by Bob
Vanderbei's ALPO (an interior-point code); starting from one of the
resulting "optimal" bases, MINOS ran 23914 iterations on a VAX before
reporting an optimal value of 1.1253287141E+07.  When started from the
same LOAD file used on the SGI machine, MINOS on the VAX reported an
optimal value of 1.1255107696E+07.  Changing the FEASIBILITY TOLERANCE
to 1.E-10 (from its default of 1.E-6) led MINOS on the SGI machine to
report "optimal" values of 1.1266408461E+07 and 1.1266402835E+07.  This
clearly is a problem where the FEASIBILITY TOLERANCE, initial basis, and
floating-point arithmetic strongly affect the "optimal" solution that
MINOS reports.  On the SGI machine, ALPO with SPLIT 3 found
 primal:  obj value =  1.126639607e+07      FEASIBLE   ( 2.79e-09 )
 dual:    obj value =  1.126639604e+07      FEASIBLE   ( 1.39e-16 )

Bob Bixby reports the following about his experience solving DFL001
with CPLEX:
  First, the value for the objective function that I get running
  defaults is 1.1266396047e+07, with the following residuals:

  Max. unscaled (scaled) bound        infeas.: 4.61853e-14 (2.30926e-14)
  Max. unscaled (scaled) reduced-cost infeas.: 6.40748e-08 (6.40748e-08)
  Max. unscaled (scaled) Ax-b          resid.: 4.28546e-14 (4.28546e-14)
  Max. unscaled (scaled) c_B-B'pi      resid.: 8.00937e-08 (8.00937e-08)

  The L_infinity condition number of the (scaled) optimal basis is
  213737.  I got exactly the same objective value solving the problem in
  several different ways.  I played a bit trying to get a better
  reduced-cost infeasibility, but that seems hopeless (if not pointless)
  given the c-Bpi residuals.

  Just as an aside, this problem exhibits very interesting behavior when
  solved using a simplex method.  I ran reduced-cost pricing on it in
  phase I, with the result that it took 465810 iterations to get
  feasible.  Running the default CPLEX pricing scheme, the entire
  problem solved in 94337 iterations (33059 in phase I) on a
  Sparcstation.  Steepest-edge pricing (and a different scaling) took
  25803 iterations.  This is a nasty problem.


Notes from Michael Saunders describing experience with MINOS on the
problems he provided are available via the netlib request

    send minos from lp/data

Sources for the problems from Bob Fourer:
  BORE3D, RECIPE, SHIP04L, SHIP04S, SHIP08L, SHIP08S, SHIP12L,
SHIP12S, STANDATA, STANDGUB, STANDMPS, VTP.BASE: consulting.
  80BAU3B: W. Kurator and Harvey Greenberg, Energy Information
Administration (Greenberg is now at the Univ. of Colorado - Denver).
  GREENBEA, GREENBEB: a large refinery model; see the book
"A Model-Management Framework for Mathematical Programming" by Kenneth
H. Palmer et al. (John Wiley & Sons, New York, 1984).
  GROW15, GROW22, GROW7: R. Fourer, "Solving Staircase Linear Programs
by the Simplex Method, 2: Pricing", Math. Prog. 25 (1983), pp. 251-292.
  PILOT.JA, PILOT.WE, PILOT4, PILOTNOV: SOL, Stanford University.
  GFRD-PNC, SIERRA: R. Helgason, J. Kennington, and P. Wong,
"An Application of Network Programming for National Forest Planning",
Technical Report OR 81006, Dept. of Operations Research, Southern
Methodist University.
  SC205, SCAGR25, SCAGR7, SCFXM1, SCFXM2, SCFXM3, SCORPION, SCRS8,
SCSD1, SCSD6, SCSD8, SCTAP1, SCTAP2, SCTAP3: J.K. Ho and E. Loute,
"A Set of Staircase Linear Programming Test Problems",
Math. Prog. 20 (1981), pp. 245-250.
  NESM: Gerald Brown, Naval Postgraduate School.
  FORPLAN: John Mulvey, Princeton.
  FIT1D, FIT1P, FIT2D, FIT2P: Bob Fourer himself.

Concerning FIT1D, FIT1P, FIT2D, FIT2P, Bob Fourer says
    The pairs FIT1P/FIT1D and FIT2P/FIT2D are primal and
    dual versions of the same two problems [except that we
    have negated the cost coefficients of the dual problems
    so all are minimization problems].  They originate from
    a model for fitting linear inequalities to data, by
    minimization of a sum of piecewise-linear penalties.
    The FIT1 problems are based on 627 data points and 2-3
    pieces per primal pl penalty term.  The FIT2 problems
    are based on 3000 data points (from a different sample
    altogether) and 4-5 pieces per pl term.

To get C source for the compression program, issue the netlib request

    send mpc.src from lp/data

Contributions are welcome, either problems in MPS format or source code
for problem generators.  Send questions, comments, contributions to
    David M. Gay
    AT&T Bell Laboratories
    600 Mountain Avenue, room 2C-463
    Murray Hill, NJ 07974-2070
    U.S.A.
 phone (908) 582-5623; FAX (908) 582-5857
 E-mail research!dmg or dmg@research.bell-labs.com

Cross reference: Eberhard Kranich's extensive bibliography on interior-
point methods is available from netlib.  For details, ask netlib to

        send index from bib

Change log...
  1 June 1987:   mpc.src added.
  6 May 1988:    GREENBEA, GREENBEB, AGG, AGG2, AGG3 added.
  25 June 1988:  STOCFOR1,2 added
  16 Jan. 1989:  STOCFOR3 added; bound and range information added to
index file; MINOS 5.3 optimal values inserted.
  23 Jan. 1989:  correction to bound-handling portion of STOCFOR3 source
code.  This does not affect STOCFOR3 itself, but is relevant to other
uses of this Fortran code.
  6 April 1989: BLEND BOEING1 BOEING2 FINNIS PEROLD SC105 SC50A SC50B
added.
  27 June 1989: CYCLE KB2 LOTFI TUFF WOOD1P WOODW added.
  30 Oct. 1989: BNL1 BNL2 D2Q06C DEGEN2 DEGEN3 added.
  30 Nov. 1989: options -s and -S added to emps.c so you can request
several problems at once and split them into files named by the
problem name (in upper case with -S or in lower case with -s).  For
use with these new options, the NAME line of several problems has now
been modified so that the first word after "NAME" gives the name
specified above for the problem.  Now all compressed MPS files have
this property.  The problems whose NAME line was thus modified are
BLEND, BOEING1, FINNIS, FORPLAN, PEROLD, PILOT, PILOTNOV, STANDGUB,
STANDMPS, STOCFOR1, and STOCFOR2.
  22 Jan. 1990: all material described here made available by
anonymous ftp from research.att.com .
  31 Jan. 1990: FIT1D, FIT1P, FIT2D, FIT2P added.
  8 Feb. 1990: emps.c, emps.f modified to quietly ignore extra lines at
the end of a compressed MPS file (e.g., those that mailers add).
  15 Feb. 1990: added table of optimal values reported by Bob Bixby.
  26 Feb. 1990: TRUSS added.
  30 Apr. 1990: ascii (table of ASCII codes) added; MINOS(MIPS)
optimal values added to this index file.
  15 June 1990: MAROS and PILOT87 added.
  11 Oct. 1990: DFL001 added.
  9 Jan. 1991: Bixby's remarks about DFL001 added to index.
  6 June 1991: emps.c and emps.f adjusted to pass "mystery lines"
through, for possible use in conveying other problem information
(in connection with mpc -m).  [For years emps.c has had this ability;
today's change fixes a bug with mystery lines just before ENDATA.]
  4 Sept. 1991: "Kennington" problems made available by ftp from netlib.
  21 Oct. 1991: minor cleanups...
1. BOEING1: remove duplicate upper bounds for columns N1019AC3 and
N1019AC4.
2. PILOT: remove 8 duplicate right-hand side values for row BTRB01.
3. PILOT87: remove lower bound of 49.5 on U[OG]ST0[12], which are
subsequently fixed at 99 (UOST[12]) or 65.4.
  2 May 1992: emps.c ANSIfied (with #ifdef KR_headers lines for
old-style C compilers); new option -b changes blanks within names
to underscores (and changes blank RHS names to RHS, etc.) -- for
awk scripts and other programs that assume no blanks in names.
  4 Feb. 1993: STOCFOR3 updated.  STOCFOR3 and the other problems
you can generate with the data in the stocfor3 bundle are the same
numerically as before (but with different row and column labels).
The update (courtesy of Gus Gassmann) fixes some bugs in other uses
of the generator and expands your options in using the generator.
The previous version is now stocfor3.old.
  26 March 1993: D6CUBE added.
  17 Jan. 1994: MAROS-R7 and MODSZK1 added.
  12 April 1996: QAP8, QAP12, QAP15 added to result table; directory
lp/generators/qap added for generating these problems.
