GLPK/GLPK 版本信息
< GLPK
此页面包含 GLPK 官方项目的版本信息。它涵盖了从 GLPK 2.0 / 2001 年 1 月 25 日到现在的版本信息，并基于以下内容：新闻文件。
注意：GLPK 更改日志 是不同的内容。
The new API routine glp_intfeas1 was added to the package.
This routine is a tentative implementation of the integer (0-1)
feasibility solver based on the CNF-SAT solver (which currently
is MiniSat). It may be used in the same way as glp_intopt to
find either any integer feasible solution or a solution, for
which the objective function is not worse than the specified
value. Detailed description of this routine can be found in the
document "CNF Satisfiability Problem", which is included in the
distribution (see doc/cnfsat.pdf).
The following two options were added to glpsol:
--minisat translate 0-1 feasibility problem to CNF-SAT
problem and solve it with glp_intfeas1/MiniSat
(if the problem instance is already in CNF-SAT
format, no translation is performed)
--objbnd bound add inequality obj <= bound (minimization) or
obj >= bound (maximization) to 0-1 feasibility
problem (this option assumes --minisat)
The paint-by-numbers puzzle model (pbn.mod) included in the
distribution is a nice example of the 0-1 feasibility problem,
which can be efficiently solved with glp_intfeas1/MiniSat. This
model along with a brief instruction (pbn.pdf) and benchmark
examples from <webpbn.com> encoded in GNU MathProg (*.dat) can
be found in subdirectory examples/pbn/.
The glpsol lp/mip solver was modified to bypass postprocessing
of MathProg models if the solution reported is neither optimal
nor feasible.
A minor bug in examples/Makefile.am was fixed to correctly
build glpk in a separate directory. Thanks to Marco Atzeri
<address@hidden> for bug report and patch.
The following new API routines were added:
glp_read_cnfsat read CNF-SAT problem data in DIMACS format
glp_check_cnfsat check for CNF-SAT problem instance
glp_write_cnfsat write CNF-SAT problem data in DIMACS format
glp_minisat1 solve CNF-SAT problem instance with MiniSat
The routine glp_minisat1 is a driver to MiniSat, a CNF-SAT
solver developed by Niklas Een and Niklas Sorensson, Chalmers
University of Technology, Sweden. This routine is similar to
the routine glp_intopt, however, it is intended to solve a 0-1
programming problem instance, which is the MIP translation of
a CNF-SAT problem instance.
Detailed description of these new API routines can be found in
the document "CNF Satisfiability Problem", which is included in
the distribution (see files doc/cnfsat.tex and doc/cnfsat.pdf).
The following new glpsol command-line options were added:
--cnf filename read CNF-SAT problem instance in DIMACS
format from filename and translate it to MIP
--wcnf filename write CNF-SAT problem instance in DIMACS
format to filename
--minisat solve CNF-SAT problem instance with MiniSat
solver
The zlib compression library (version 1.2.5) was ANSIfied,
modified according to GLPK requirements and included in the
distribution as an external software module. Thus, now this
feature is platform independent.
Some bugs were fixed in the SQL table driver. Thanks to Xypron
<address@hidden>.
This is a bug-fix release.
Several bugs/typos were fixed. Thanks to
Xypron <[email protected]>,
Robbie Morrison <[email protected]>, and
Ali Baharev <[email protected]> for reports.
Some glpk documents was re-formatted and merged into a single
document. Now the glpk documentation consists of the following
three main documents (all included in the distribution):
GLPK: Reference Manual
GLPK: Graph and Network Routines
Modeling Language GNU MathProg: Language Reference
The following suffixes for variables and constraints were
implemented in the MathProg language:
.lb (lower bound),
.ub (upper bound),
.status (status in the solution),
.val (primal value), and
.dual (dual value).
Thanks to Xypron <[email protected]> for draft implementation
and testing.
Now the MathProg language allows comment records (marked by
'#' in the very first position) in CSV data files read with the
table statements. Note that the comment records may appear only
in the beginning of a CSV data file.
The API routine glp_cpp to solve the Critical Path Problem was
added and documented.
This is a maintainer release.
`configure.ac' was changed to allow building the package under
Mac OS and Darwin with ODBC support.
Thanks to Xypron <[email protected]> for suggestions and Noli
Sicad <[email protected]> for testing.
The SQL table driver was improved to process NULL data. Thanks
to Xypron <[email protected]>.
Some bugs were fixed in the LP/MIP preprocessor.
The following new API routines were added:
glp_check_dup check for duplicate elements in sparse
matrix
glp_sort_matrix sort elements of the constraint matrix
glp_read_prob read problem data in GLPK format
glp_write_prob write problem data in GLPK format
glp_analyze_bound analyze active bound of non-basic variable
glp_analyze_coef analyze objective coefficient at basic
variable
glp_print_ranges print sensitivity analysis report (this
routine replaces lpx_print_sens_bnds and
makes it deprecated)
For description of these new routines and the GLPK LP/MIP
format see a new edition of the reference manual included in
the distribution. (Chapter "Graph and network API routines" was
carried out from the main reference manual and included in the
distribution as a separate document.)
The following new command-line options were added to the stand-
alone solver glpsol:
--glp filename read problem data in GLPK format
--wglp filename write problem data in GLPK format
--ranges filename print sensitivity analysis report (this
option replaces --bounds)
Now all GLPK routines performing file I/O support special
filenames "/dev/stdin", "/dev/stdout", and "/dev/stderr", which
can be specified in the same way as regular filenames. This
feature is platform-independent.
The following new API routies were added:
glp_transform_row transform explicitly specified row
glp_transform_col transform explicitly specified column
glp_prim_rtest perform primal ratio test
glp_dual_rtest perform dual ratio test
For description of these new routines see a new edition of the
reference manual included in the distribution.
The following API routines are deprecated: lpx_transform_row,
lpx_transform_col, lpx_prim_ratio_test, lpx_dual_ratio_test.
Some improvements were made in the MIP solver (glp_intopt).
The SQL table driver used to read/write data in MathProg models
was changed to allow multiple arguments separated by semicolon
in SQL statements. Thanks to Xypron <[email protected]>.
Two new options were added to the glpsol stand-alone solver:
--seed value (to initialize the pseudo-random number generator
used in MathProg models with specified value), and
--ini filename (to use a basis previously saved with -w option
as an initial basis on solving similar LP's).
Two new MathProg example models were included. Thanks to
Nigel Galloway <[email protected]> and Noli Sicad
<[email protected]> for contribution.
Scripts to build GLPK with Microsoft Visual Studio 2010 for
both 32-bit and 64-bit Windows were included. Thanks to Xypron
<[email protected]> for contribution and testing.
The following new API routines were added:
glp_del_vertices remove vertices from graph
glp_del_arc remove arc from graph
glp_wclique_exact find maximum weight clique with the exact
algorithm developed by Prof. P. Ostergard
glp_read_ccdata read graph in DIMACS clique/coloring
format
glp_write_ccdata write graph in DIMACS clique/coloring
format
For description of these new routines see a new edition of the
reference manual included in the distribution.
The hybrid pseudocost branching heuristic was included in the
MIP solver. It is available on API level (iocp.br_tech should
be set to GLP_BR_PCH) and in the stand-alone solver glpsol
(via the command-line option --pcost). This heuristic may be
useful on solving hard MIP instances.
The branching heuristic by Driebeck and Tomlin (used in the
MIP solver by default) was changed to switch to branching on
most fractional variable if an lower bound of degradation of
the objective is close to zero for all branching candidates.
A bug was fixed in the LP preprocessor (routine npp_empty_col).
Thanks to Stefan Vigerske <[email protected]> for the
bug report.
A bug was fixed and some improvements were made in the FPUMP
heuristic module. Thanks to Xypron <[email protected]>.
A bug was fixed in the API routine glp_warm_up (dual
feasibility test was incorrect in maximization case). Thanks to
Uday Venkatadri <[email protected]> for the bug report.
The following new API routines were added:
glp_warm_up "warm up" LP basis
glp_set_vertex_name assign (change) vertex name
glp_create_v_index create vertex name index
glp_find_vertex find vertex by its name
glp_delete_v_index delete vertex name index
glp_read_asnprob read assignment problem data in DIMACS
format
glp_write_asnprob write assignment problem data in DIMACS
format
glp_check_asnprob check correctness of assignment problem
data
glp_asnprob_lp convert assignment problem to LP
glp_asnprob_okalg solve assignment problem with the
out-of-kilter algorithm
glp_asnprob_hall find bipartite matching of maxumum
cardinality with Hall's algorithm
Also were added some API routines to read plain data files.
The API routines glp_read_lp and glp_write_lp to read/write
files in CPLEX LP format were re-implemented. Now glp_write_lp
correctly writes double-bounded (ranged) rows by introducing
slack variables rather than by duplicating the rows.
For description of these new routines see a new edition of the
reference manual included in the distribution.
The 'xfree(NULL)' bug was fixed in the AMD routines. Thanks to
Niels Klitgord <[email protected]> for bug report.
The message "Crashing..." was changed to "Constructing initial
basis..." due to suggestion by Thomas Kahle <[email protected]>.
Some typos were corrected in glpsol output messages. Thanks to
Xypron <[email protected]> for patch.
API routines glp_read_mps and glp_write_mps were improved.
Some improvements were made in the dual simplex routines.
Two external software modules AMD and COLAMD were included in
the distribution (for more details please see src/amd/README
and src/colamd/README). Now they are used in the interior-point
solver to reorder the matrix prior to Cholesky factorization.
API routine glp_ipt_status may return two new statuses due to
changes in the routine glp_interior. For details please see the
reference manual included in the distribution.
A minor bug was fixed in the graph/network routines. Thanks to
Nelson H. F. Beebe <[email protected]> for bug report.
The 0-1 Feasibility Pump heuristic was included in the GLPK
integer optimizer glp_intopt. On API level the heuristic can be
enabled by setting the parameter fp_heur in glp_iocp to GLP_ON.
This feature is also available in the solver glpsol through
command-line option '--fpump'. For more details please see the
reference manual included in the distribution.
The following new API routines were added:
glp_print_sol write basic solution in printable format
glp_print_ipt write interior-point solution in printable
format
glp_print_mip write MIP solution in printable format
glp_read_graph read (di)graph from plain text file
glp_write_graph write (di)graph to plain text file
glp_weak_comp find all weakly connected components
glp_strong_comp find all strongly connected components
The following API routines are deprecated: lpx_print_sol,
lpx_print_ips, lpx_print_mip, lpx_print_prob (the latter is
equivalent to glp_write_lp).
A bug was fixed in the interior-point solver (glp_interior) to
correctly compute dual solution components when the problem is
scaled.
The files configure.ac and Makefile.am were changed:
(a) to allow using autoreconf/autoheader;
(b) to allow building the package in a directory other than its
source directory.
Thanks to Marco Atzeri <[email protected]> for bug report.
An example model in the GNU MathProg language was added.
Thanks to Larry D'Agostino <Larry.D'[email protected]> for
contribution.
The following new API routines were added to the package:
glp_mincost_okalg find minimum-cost flow with out-of-kilter
algorithm
glp_maxflow_ffalg find maximal flow with Ford-Fulkerson
algorithm
For detailed description of these new routines and related data
structures see chapter "Graph and Network API Routines" in a new
edition of the reference manual included in the distribution.
The following two new command-line options were added to the
solver glpsol:
--mincost read min-cost flow data in DIMACS format
--maxflow read maximum flow data in DIMACS format
Duplicate symbols in the header glpk.h were removed to allow
using swig.
Thanks to Kelly Westbrooks <[email protected]> and
Nigel Galloway <[email protected]> for suggestion.
A minor defect was fixed in the routine glp_write_lp.
Thanks to Sebastien Briais <[email protected]> for bug report.
A minor bug was fixed in the SQL module.
Thanks to Xypron <[email protected]> for patch.
Some new example models in the GNU MathProg modeling language
were added. Thanks to Sebastian Nowozin <[email protected]> and
Nigel Galloway <[email protected]> for contribution.
The following new API routines were added to the package:
glp_create_graph create graph
glp_set_graph_name assign (change) graph name
glp_add_vertices add new vertices to graph
glp_add_arc add new arc to graph
glp_erase_graph erase graph content
glp_delete_graph delete graph
glp_read_mincost read minimum cost flow problem data in
DIMACS format
glp_write_mincost write minimum cost flow problem data in
DIMACS format
glp_mincost_lp convert minimum cost flow problem to LP
glp_netgen Klingman's network problem generator
glp_gridgen grid-like network problem generator
glp_read_maxflow read maximum flow problem data in DIMACS
format
glp_write_maxflow write maximum flow problem data in DIMACS
format
glp_maxflow_lp convert maximum flow problem to LP
glp_rmfgen Goldfarb's maximum flow problem generator
For detailed description of these new routines and related data
structures see chapter "Graph and Network API Routines" in a new
edition of the reference manual included in the distribution.
A minor change were made in the internal routine xputc. Thanks
to Luiz Bettoni <[email protected]> for suggestion.
A minor bug was fixed in the internal routine mpl_fn_time2str.
Thanks to Stefan Vigerske <[email protected]> for bug report.
The GNU MathProg modeling language was supplemented with three
new built-in functions:
gmtime obtaining current calendar time
str2time converting character string to calendar time
time2str converting calendar time to character string
(Thanks to Xypron <[email protected]>.)
For detailed description of these functions see Appendix A in
the document "Modeling Language GNU MathProg", a new edition of
which was included in the distribution.
A bug was fixed in the MIP solver. Thanks to Nigel Galloway
<[email protected]> for bug report.
A new makefile was added to build the GLPK DLL with Microsoft
Visual Studio Express 2008 for 64-bit Windows. Thanks to Xypron
<[email protected]> for contribution and testing.
The following new API routines were added to the package:
glp_copy_prob copy problem object content
glp_exact solve LP in exact arithmetic
(makes lpx_exact deprecated)
glp_get_unbnd_ray determine variable causing unboundedness
(makes lpx_get_ray_info deprecated)
glp_interior solve LP with interior-point method
(makes lpx_interior deprecated)
The following new API routines for processing models written in
the GNU Mathprog language were added to the package:
glp_mpl_alloc_wksp allocate the translator workspace
glp_mpl_read_model read and translate model section
glp_mpl_read_data read and translate data section
glp_mpl_generate generate the model
glp_mpl_build_prob build LP/MIP instance from the model
glp_mpl_postsolve postsolve the model
glp_mpl_free_wksp deallocate the translator workspace
(These routines make lpx_read_model deprecated.)
For description of all these new API routines see the reference
manual included in the distribution.
A crude implementation of CPLEX-like interface to GLPK API was
added to the package. Currently it allows using GLPK as a core
LP solver for Concorde, a well known computer code for solving
the symmetric TSP. For details see examples/cplex/README.
Some bugs were fixed in the SQL table driver. Thanks to Xypron
<[email protected]>.
The following new features were included in the MIP solver
(the API routine glp_intopt):
* MIP presolver
* mixed cover cut generator
* clique cut generator
* Euclidean reduction of the objective value
Due to changes the routine glp_intopt may additionally return
GLP_ENOPFS, GLP_ENODFS, and GLP_EMIPGAP.
The API routines lpx_integer are lpx_intopt are deprecated,
since they are completely superseded by glp_intopt.
The following new branch-and-cut API routines were added:
glp_ios_row_attr determine additional row attributes
glp_ios_pool_size determine current size of the cut pool
glp_ios_add_row add constraint to the cut pool
glp_ios_del_row delete constraint from the cut pool
glp_ios_clear_pool delete all constraints from the cut pool
For description of these new routines see the reference manual
included in the distribution.
The stand-alone solver glpsol was changed to allow multiple
data files.
A new edition of the supplement "Using Data Tables in the GNU
MathProg Modeling Language" was included.
As usual, some bugs were fixed (in the MathProg translator).
Thanks to Xypron <[email protected]>.
The core LP solver based on the dual simplex method was
re-implemented and now it provides both phases I and II.
The following new API routines were added:
glp_scale_prob automatic scaling of problem data
glp_std_basis construct standard initial LP basis
glp_adv_basis construct advanced initial LP basis
glp_cpx_basis construct Bixby's initial LP basis
For description of these new routines see the reference manual
included in the distribution.
The following API routines are deprecated:
lpx_scale_prob, lpx_std_basis, lpx_adv_basis, lpx_cpx_basis.
Necessary changes were made in memory allocation routines to
resolve portability issues for 64-bit platforms.
New version of the routine lpx_write_pb to write problem data
in OPB (pseudo boolean format) was added to the package. Thanks
to Oscar Gustafsson <[email protected]> for the contribution.
Two new makefiles were added to build the package for 32- and
64-bit Windows with Microsoft Visual Studio Express 2008.
Thanks to Heinrich Schuchardt <[email protected]> (aka
Xypron) for the contribution and testing.
Two new makefiles were added to build the package with Digital
Mars C/C++ 8.50 and Open Watcom C/C++ 1.6 (for 32-bit Windows).
The core LP solver based on the primal simplex method was
re-implemented to allow its further improvements. Currently the
new version provides the same features as the old one, however,
it is a bit faster and more numerically stable.
Some changes were made in the MathProg translator to allow <,
<=, >=, and > on comparing symbolic values. Thanks to Heinrich
Schuchardt <[email protected]> for patches.
Internal routine set_d_eps in the exact LP solver was changed
to prevent approximation errors in case of integral data.
Thanks to Markus Pilz <[email protected]> for bug report.
The configure script was changed to disable all optional
features by default. For details please see file INSTALL.
The following new API routines were added:
glp_erase_prob erase problem object content
glp_read_mps read problem data in MPS format
glp_write_mps write problem data in MPS format
glp_read_lp read problem data in CPLEX LP format
glp_write_lp write problem data in CPLEX LP format
For description of these new routines see the reference manual
included in the distribution.
The following API routines are deprecated:
lpx_read_mps, lpx_read_freemps, lpx_write_mps,
lpx_write_freemps, lpx_read_cpxlp, and lpx_write_cpxlp.
Two bugs were fixed. Thanks to
Anne-Laurence Putz <[email protected]> and
Xypron <[email protected]> for bug report.
The iODBC and MySQL table drivers, which allows transmitting
data between MathProg model objects and relational databases,
were re-implemented to replace a static linking by a dynamic
linking to corresponding shared libraries.
Many thanks to Heinrich Schuchardt <[email protected]>
for the contribution, Rafael Laboissiere <[email protected]>
for useful advices concerning the shared library support under
GNU/Linux, and Vijay Patil <[email protected]> for testing
this feature under Windows XP.
A new optional feature was added to the package. This feature
is based on the zlib data compression library and allows GLPK
API routines and the stand-alone solver to read and write
compressed data files performing compression/decompression "on
the fly" (compressed data files are recognized by suffix `.gz'
in the file name). It may be useful in case of large MPS files
to save the disk space (up to ten times).
The `configure' script was re-implemented. Now it supports the
following specific options:
--with-gmp Enable using the GNU MP bignum library
--without-gmp Disable using the GNU MP bignum library
--with-zlib Enable using the zlib data compression
library
--without-zlib Disable using the zlib data compression
library
--enable-dl Enable shared library support (auto check)
--enable-dl=ltdl Enable shared library support (GNU)
--enable-dl=dlfcn Enable shared library support (POSIX)
--disable-dl Disable shared library support
--enable-odbc Enable using ODBC table driver
--disable-odbc Disable using ODBC table driver
--enable-mysql Enable using MySQL table driver
--disable-mysql Disable using MySQL table driver
For more details please see file INSTALL.
Three new table drivers were added to the MathProg translator:
xBASE built-in table driver, which allows reading and writing
data in .dbf format (only C and N fields are supported);
MySQL table driver, which provides connection to a MySQL
database;
iODBC table driver, which provides connection to a database
through ODBC.
The MySQL and iODBC table drivers were contributed to GLPK by
Heinrich Schuchardt <[email protected]>.
The table driver is a program module which allows transmitting
data between MathProg model objects and external data tables.
For detailed description of the table statement and table
drivers see the document "Using Data Tables in the GNU MathProg
Modeling Language" (file doc/tables.txt) included in the
distribution. Some examples which demonstrate using MySQL and
iODBC table drivers can be found in subdirectory examples/sql.
The table statement was implemented in the GNU MathProg
modeling language. This new feature allows reading data from
external tables into model objects such as sets and parameters
as well as writing results of computations to external tables.
A table is a (unordered) set of records, where each record
consists of the same number of fields, and each field is
provided with a unique symbolic name called the field name.
Currently the GLPK package has the only built-in table driver,
which supports tables in the CSV (comma-separated values) file
format. This format is very simple and supported by almost all
spreadsheets and database management systems.
Detailed description of the table statement and CSV format can
be found in file doc/tables.txt, included in the distribution.
A tentative implementation of Gomory's mixed integer cuts was
included in the branch-and-cut solver. To enable generating
Gomory's cuts the control parameter gmi_cuts passed to the
routine glp_intopt should be set to GLP_ON. This feature is
also available in the solver glpsol through command-line option
'--gomory'. For more details please see the reference manual
included in the distribution.
A tentative implementation of MIR (mixed integer rounding) cuts
was included in the MIP solver. To enable generating MIR cuts
the control parameter mir_cuts passed to the routine glp_intopt
should be set to GLP_ON. This feature is also available in the
stand-alone solver glpsol via command-line option '--mir'. For
more details please see the reference manual included in the
distribution.
The implementation is mainly based on the following two papers:
1. H. Marchand and L. A. Wolsey. Aggregation and mixed integer
rounding to solve MIPs. CORE discussion paper 9839, CORE,
Universite catholique de Louvain, June 1998.
2. G. Andreello, A. Caprara, and M. Fischetti. Embedding cuts
in a Branch&Cut framework. Preliminary draft, October 2003.
MIR cuts can be generated on any level of the search tree that
makes the GLPK MIP solver to be a real branch-and-cut solver.
A bug was fixed in the routine lpx_write_cpxlp. If a variable
x has upper bound and no lower bound, it should appear in the
bounds section as "-inf <= x <= u", not as "x <= u". Thanks to
Enric Rodriguez <[email protected]> for the bug report.
The following new API routines were added:
glp_read_sol read basic solution from text file
glp_write_sol write basic solution to text file
glp_read_ipt read interior-point solution from text file
glp_write_ipt write interior-point solution to text file
glp_read_mip read MIP solution from text file
glp_write_mip write MIP solution to text file
For description of these routines and corresponding file
formats see Chapter "API Routines", Section "Utility routines"
in the reference manual included in the distribution.
Advanced API routine glp_free_env was added. It may be used by
the application program to free all resources allocated by GLPK
routines.
The following three new command-line options were added to the
solver glpsol:
--mipgap tol set relative MIP gap tolerance
-r filename read solution from filename
-w filename write solution to filename
This is a maintainer release.
A bug was fixed in the MIP preprocessor (ios_preprocess_node).
Thanks to Roberto Bagnara <[email protected]> (Department of
Mathematics, University of Parma, Italy) for the bug report.
A bug was fixed in the MIP preprocessor (col_implied_bounds),
due to which constraint coefficients with small magnitude could
lead to wrong implied bounds of structural variables.
A similar bug was fixed in the routine reduce_bounds.
A bug was fixed in the routines glp_set_mat_row and
glp_set_mat_col. (The bug appeared due to incorrect removing
zero elements from the row/column lists.)
A bug was fixed in the API routines lpx_read_mps and
lpx_read_freemps, due to which bounds of type LI specified in
BOUNDS section were incorrectly processed.
A call to standard function vsprintf was replaced by a call to
vsnprintf for security reasons. Many thanks to Peter T. Breuer
<[email protected]> and Rafael Laboissiere <[email protected]>.
Additional reasons for calling the callback routine used in the
MIP solver (glp_intopt) were introduced. Currently the following
reasons are supported:
* request for subproblem selection
* request for preprocessing
* request for row generation
* request for heuristic solution
* request for cut generation
* request for branching
* better integer solution found
A basic preprocessing component used to improve subproblem
formulations by tightening bounds of variables was included in
the MIP solver. Depending on the control parameter pp_tech
passed to the routine glp_intopt the preprocessing can be
performed either on the root level or on all levels (default)
or can be disabled.
Backtracking heuristic used by default in the MIP solver was
changed to the "best local bound".
For more details see Chapter "Advanced API routines", Section
"Branch-and-bound interface routines" in a new edition of the
reference manual included in the distribution.
API routine lpx_integer was replaced by API routine glp_intopt,
which provides equivalent functionality and additionally allows
the application to control the solution process by means of the
user-written callback routine, which is called by the solver at
various points of the branch-and-bound algorithm. Besides, the
new MIP solver allows generating "lazy" constraints and cutting
planes on all levels of the branch-and-bound tree, not only on
the root level. The routine lpx_integer is also still available
for the backward compatibility.
The following new advanced API routines, which may be called
from the B&B callback routine, were included in the package:
glp_ios_reason determine reason for calling callback
routine
glp_ios_get_prob access the problem object
glp_ios_tree_size determine size of the branch-and-bound tree
glp_ios_curr_node determine current active subproblem
glp_ios_next_node determine next active subproblem
glp_ios_prev_node determine previous active subproblem
glp_ios_up_node determine parent subproblem
glp_ios_node_level determine subproblem level
glp_ios_node_bound determine subproblem local bound
glp_ios_mip_gap compute relative MIP gap
glp_ios_heur_sol provide solution found by heuristic
glp_ios_terminate terminate the solution process
For description of these routines see Chapter "Advanced API
routines", Section "Branch-and-bound interface routines" in a
new edition of the reference manual, which was included in the
distribution.
Old version of the integer optimization suite (IOS) as well as
TSP solver tspsol based on it are no longer supported and were
removed from the package.
A minor error in the MIP presolver was fixed; thanks to Graham
Rockwell <[email protected]> for the bug report.
The principal change is upgrading to GPLv3.
A serious bug in the routine glp_del_cols was fixed; thanks to
Cedric[FR] <[email protected]> for the bug report. The bug
appeared because on deleting non-basic columns the basis header
remained valid, however, contained invalid (old) column ordinal
numbers.
A new advanced API routine glp_mem_limit was added.
The case GLP_EBOUND was added to the routine lpx_simplex.
Thanks to Cameron Kellough <[email protected]> for the
bug report.
An API routine lpx_write_pb to write the problem instance in
OPB (pseudo boolean) format format was added. Thanks to Oscar
Gustafsson <[email protected]> for the contribution.
Two new options --wpb and --wnpb were added to glpsol to write
the problem instance in OPB format.
The following new API routines were added:
glp_set_rii set (change) row scale factor
glp_set_sjj set (change) column scale factor
glp_get_rii retrieve row scale factor
glp_get_sjj retrieve column scale factor
glp_simplex solve LP problem with the simplex method
(this routine replaces lpx_simplex, which is
also available for backward compatibility)
glp_init_smcp initialize simplex method control params
glp_bf_exists check if the basis factorization exists
glp_factorize compute the basis factorization
glp_bf_updated check if the basis factorization has been
updated
glp_get_bfcp retrieve basis factorization control params
glp_set_bfcp change basis factorization control params
glp_get_bhead retrieve the basis header information
glp_get_row_bind retrieve row index in the basis header
glp_get_col_bind retrieve column index in the basis header
glp_ftran perform forward transformation
glp_btran perform backward transformation
For description of all these routines see a new edition of the
reference manual included in the distribution.
Type names ulong_t and uldiv_t were changed to glp_ulong and
glp_uldiv to avoid conflicts with standard type names on some
platforms. Thanks to Boris Wirtz <[email protected]>
for the bug report.
Some new examples in the MathProg language were added. Thanks
to Sebastian Nowozin <[email protected]>.
API routines glp_set_mat_row, glp_set_mat_col, and glp_load_mat
were modified to allow zero constraint coefficients (which are
not stored in the constraint matrix). Note that constraint
coefficients with duplicate row/column indices are not allowed.
Another form of LP basis factorization was implemented in the
package. It is based on LU-factorization of an initial basis
and Schur complement to reflect changes in the basis. Currently
the implementation is incomplete and provides only updating the
factorization on replacing a column of the basis matrix. On API
level the user can set the control parameter LPX_K_BFTYPE to
choose between the following forms of LP basis factorization to
be used in the simplex method routines:
1) LU + Forrest-Tomlin update;
2) LU + Schur complement + Bartels-Golub update;
3) LU + Schur complement + Givens rotation update.
The GLPK implementation is similar to LUSOL/LUMOD developed by
Michael A. Saunders.
The user can choose the form of LP basis factorization used by
the simplex method routines by specifying the following options
of glpsol: --luf, --cbg, --cgr.
A number of basic GLPK API routines, which now are in the
stable stable, were renamed to be prefixed with 'glp_'. Note
that all these routines are available via their old names
prefixed with 'lpx_' that keeps the downward compatibility with
older versions of the package.
Three new GLPK API routines were added to the package:
glp_version, glp_term_hook, and glp_mem_usage; for more details
see a new edition of the GLPK reference manual included in the
distribution. The routine glp_version reports the actual version
of the GLPK library and also can be used (along with the header
glpk.h) in Autotools specification files to check if the GLPK
library has been installed.
The header glpk.h was changed to conform to C++ environment.
Autotools specification files (configure.ac, Makefile.am) were
changed to use GNU Libtool. This allows building the static as
well as shared GLPK library.
Now GLPK conforms to ILP32, LLP64, and LP64 programming models
(the latter seems to be the ultimate choice regarding 64-bit
architectures). Note that GLPK itself is a 32-bit application,
and the conformity only means that the package works correctly
on all these arenae. Nevertheless, on 64-bit platforms it is
possible to use more than 4GB of memory, if necessary.
A tentative implementation of the "exact" simplex method based
on bignum (rational) arithmetic was included in the package.
On API level this new feature is available through the routine
lpx_exact, which is similar to the routine lpx_simplex.
In the solver glpsol this feature is available through two new
command-line options: --exact and --xcheck. If the '--exact'
option is specified, glpsol solves LP instance using the exact
simplex method; in case of MIP it is used to obtain optimal
solution of LP relaxation. If the --xcheck option is specified,
LP instance (or LP relaxation) is solved using the standard
(floating-point) simplex method, however, then glpsol calls the
exact simplex routine to make sure that the final LP basis is
exactly optimal, and if it is not, to perform some additional
simplex iterations in exact arithmetic.
A tentative implementation of some simplex method routines
based on exact (bignum) arithmetic was included in the package.
Currently these routines provide computing LU-factorization of
the basis matrix and computing components of basic solution.
These routines were used to implement a routine, which checks
primal and dual feasibility of basic solution exactly, i.e. in
rational numbers, without round-off errors. In glpsol this
feature is available through the command-line option --xcheck.
GLPK has its own low-level routines implementing operations on
integer and rational numbers that makes it independent on other
software packages. However, to attain a much better performance
it is highly recommended to install (before configuring GLPK)
the GNU Multiple Precision Arithmetic Library (GMP). Using GMP
makes computations 100-200 times faster.
Three new built-in functions in the modeling language were
implemented: card (cardinality of set), length (length of
character string), and substr (substring of character string).
Another improvement concerns the printf statement which now
allows redirecting its output to a specified file. These new
features are illustrated in example models crypto.mod and
graph.mod included in the distribution. For more details see
the document "Modeling Language GNU MathProg".
Four batch files (along with corresponding makefiles) were
included in the distribution to simplify building GLPK under
MS Windows; see them in subdirectory 'w32'.
Cutting planes of two new classes were implemented: mixed cover
cuts and clique cuts. On API level this feature can be enabled
by setting control parameter LPX_K_USECUTS passed to the routine
lpx_intopt. In glpsol this feature is available through the
command-line options --cover and --clique. For more details see
the reference manual.
Now the routines lpx_read_mps and lpx_read_freemps support LI
bound type. It is similar to LO, however, indicates the column
as of integer kind.
An advanced MIP solver was implemented. It includes:
- basic presolving technique (removing free, singleton and
redundant rows, improving bounds of columns, removing fixed
columns, reducing constraint coefficents);
- generating cutting planes to improve LP relaxation (currently
only Gomory's mixed integer cuts are implemented);
- using the branch-and-bound method to solve resultant MIP;
- recovering solution of the original MIP.
The solver is available on API level via the routine lpx_intopt
(see the reference manual). It is similar to the routine
lpx_integer, however, does not require initial solution of LP
relaxation.
The solver is also available in the command-line utility glpsol
via two options: --intopt (only presolving) and --cuts (assumes
--intopt plus generating cuts).
Note that efficiency of the MIP solver strongly depends on the
internal structure of the problem to be solved. For some hard
instances it is very efficient, but for other instances it may
be significantly worse than the standard branch-and-bound.
For some comparative benchmarks see doc/bench1.txt.
Well, what else...
Three built-in functions were added to MathProg: sin, cos, and
atan (the latter allows one or two arguments).
Some bugs were fixed.
Several new examples in MathProg were included: color.mod
(graph coloring problem), tsp.mod (traveling salesman problem),
and pbn.mod (paint-by-numbers puzzle).
Core simplex method and interior-point method routines were
re-implemented and now they use a new, "storage-by-rows" sparse
matrix format (unlike previous versions where linked lists were
used to represent sparse matrices). For details see ChangeLog.
Also a minor bug was fixed in API routine lpx_read_cpxlp.
Now GLPK supports free MPS format. Two new API routines
lpx_read_freemps (to read problem data in free MPS format) and
lpx_write_freemps (to write problem data in free MPS format)
were added. This feature is also available in the solver glpsol
via new command-line options --freemps and --wfreemps. For more
details see the GLPK reference manual.
API routines lpx_read_cpxlp and lpx_write_cpxlp for reading and
writing problem data in CPLEX LP format were re-implemented to
allow long symbolic names (up to 255 characters).
The following three modules were temporarily removed from the
GLPK distribution due to licensing problems: DELI (an interface
module to Delphi), GLPKMEX (an interface module to Matlab), and
JNI (an interface module to Java).
Three new statements were implemented in the GNU MathProg
language: solve, printf, and for. Their detailed description can
be found in the GLPK documentation included in the distribution.
(See also a sample model, examples/queens.mod, which illustrates
using these new statements.)
Two new API routines were added to the package: lpx_read_prob
and lpx_write_prob. They allow reading/writing problem data in
GNU LP low-level text format.
Three new command-line options were implemented in the LP/MIP
solver glpsol: --glp (to read problem data in GNU LP format),
--wglp (to write problem data in GNU LP format), and --name (to
change problem name). Now glpsol also supports processing models
where the new statements (see above) are used.
A new version of GLPKMEX, a Matlab MEX interface to GLPK, was
included. For more details see contrib/glpkmex/ChangeLog.
The branch-and-bound solver was completely re-implemented.
Some modifications were made in memory allocation routines that
allows using the package on 64-bit platforms.
For more details see ChangeLog.
All API routines were re-implemented using new data structures.
The new implementation provides the same specifications and
functionality of API routines as the old one, however, it has
some important advantages, in particular:
* linked lists are used everywhere that allows creating and
modifying the problem object as efficiently as possible
* all data stored in the problem object are non-scaled (even if
the internal scaling is used) that prevents distortion of the
original problem data
* solution components obtained by the solver remain available
even if the problem object has been modified
* no solver-specific data are used in the new data structures
that allows attaching any external lp/mip solver using GLPK
API as an uniform interface
Note that some API routines became obsolete being replaced by
new, more convenient routines. These obsolete routines are kept
for backward compatibility, however, they will be removed in
the future. For more details please see ChangeLog and the GLPK
Reference Manual.
New edition of the GLPK Reference Manual was included in the
distribution.
GLPKMEX, a Matlab MEX interface to GLPK package, contributed by
Nicolo Giorgetti <[email protected]> was included in the
distribution.
GLPK FAQ contributed by Harley Mackenzie <[email protected]> was
included in the distribution.
The bug, due to which the standard math library is not linked
on building the package on some platforms, was fixed.
The following new built-in functions were added to the MathProg
language: round, trunc, Irand224, Uniform01, Uniform, Normal01,
Normal. For details see the language description.
The MathProg syntax was changed to allow writing 'subj to' that
means 'subject to'.
The new api routine lpx_get_ray_info was added. It is intended
to determine which (non-basic) variable causes unboundness. For
details see the reference manual.
The module glpmps.c was changed to avoid compilation errors on
building the package on Mac OS X.
Several typos was fixed and some new material was added to the
GLPK documentation.
A preliminary implementation of the Integer Optimization Suite
(IOS) was included in the package. The Branch-and-Cut Framework
being completely superseded by IOS was removed from the package.
New API routine lpx_print_sens_bnds intended for bounds
sensitivity analysis was contributed to GLPK by Brady Hunsaker
<[email protected]>. This function is also available in
the solver glpsol (via command-line option --bounds).
An improved version of GLPK JNI (Java Native Interface) was
contributed by Chris Rosebrugh <[email protected]>.
GLPK DELI (Delphi Interface) was contributed by Ivo van Baren
<[email protected]>.
Several makefiles were added to allow compiling GLPK on some
non-GNU 32-bit platforms:
* Windows single-threaded static library, Visual C++ 6.0
* Windows multi-threaded dynamic library, Visual C++ 6.0
* Windows single-threaded static library, Borland C++ 5.2
* DOS single-threaded static library, Digital Mars C++ 7.50
And, of course, some bugs were fixed.
For more details see ChangeLog.
Some improvements were made in the lp/mip solver routines and
several bugs were fixed in the model translator.
For more details see ChangeLog.
Now GLPK supports the GNU MathProg modeling language, which is
a subset of the AMPL modeling language.
The document "GLPK: Modeling Language GNU MathProg" included in
the distribution is a complete description of GNU MathProg. (See
the files lang.latex, lang.dvi, and lang.ps in the subdirectory
'doc'. See also some examples in the subdirectory 'sample'.)
New version of the solver glpsol, which supports models written
in GNU MathProg, was implemented. (Brief instructions how to use
glpsol can be found in the GNU MathProg documentation.)
The GLPK/L modeling language is no more supported. The reason is
that GNU MathProg being much more powerful completely supersedes
all features of GLPK/L.
LP PRESOLVER
------------
Now the routine lpx_simplex (which is a driver to the simplex
method for solving LP) is provided with the built-in LP
presolver, which is a program that transforms the original LP
problem to an equivalent LP problem, which may be easier for
solving with the simplex method than the original one. Once the
transformed LP has been solver, the presolver transforms its
basic solution back to a corresponding basic solution of the
original problem. For details about this feature please see the
GLPK reference manual.
Currently the LP presolver implements the following features:
* removing empty rows;
* removing empty columns;
* removing free rows;
* removing fixed columns;
* removing row singletons, which have the form of equations;
* removing row singletons, which have the form of inequalities;
* removing column singletons, which are implied slack variables;
* fixing and removing column singletons, which are implied free
variables;
* removing forcing rows that involves fixing and removing the
corresponding columns;
* checking for primal and dual infeasibilities.
The LP presolver is also used by default in the stand-alone
program glpsol. In order *not* to use it, the option --nopresol
should be specified in the command-line.
CHANGES IN GLPK/L
-----------------
The syntax and semantics of the GLPK/L modeling language was
changed to allow declaration of "interval" sets. This means that
now the user can declare a set, for example, as:
set task = [8:11];
that is exactly equivalent to the following declaration:
set task = (task_8, task_9, task_10, task_11);
For details see the language description.
JAVA INTERFACE
--------------
Now GLPK includes the package GLPK JNI (Java Native Interface)
that implements Java binding for GLPK. It allows Java programs
to utilize GLPK in solving LP and MIP problems. For details see
a brief user's guide in the subdirectory contrib/java-binding.
This package was developed and programmed by Yuri Victorovich
<[email protected]>, who contributed it to GLPK.
This is a bug-fix release. For details see ChangeLog.
A new implementation of the api routine lpx_integer which now
is based on the b&b driver (which is based on the implicit
enumeration suite) was included in the package. This new
implementation has exactly the same functionality as the old
version, so all changes are transparent to the api user.
Four new api routines were included in the package:
lpx_check_kkt checks Karush-Kuhn-Tucker optmality conditions;
lpx_read_bas reads predefined basis in MPS format;
lpx_write_bas writes current basis in MPS format;
lpx_write_lpt writes problem data in CPLEX LP format.
Also other minor improvements were made (for details see the
file 'ChangeLog').
The api routine lpx_read_lpt was included in the package. It
is similar to the routine lpx_read_mps and intended to read
LP/MIP data prepared in CPLEX LP format. Description of this
format is given in the GLPK reference manual, a new edition of
which was also included in the distribution (see the files
'refman.latex', 'refman.dvi', 'refman.ps' in the subdirectory
'doc'). In order to use data files in CPLEX LP format with the
solver glpsol the option '--lpt' should be specified in the
command line.
Several bugs were fixed and some minor improvements were made
(for details see the file 'ChangeLog').
Now GLPK includes a preliminary implementation of the
branch-and-cut framework, which is a set of data structures and
routines intended for developing branch-and-cut methods for
solving mixed-integer and combinatorial optimization problems.
Detailed description of the branch-and-cut framework is given in
the document "GLPK: A Preliminary Implementation of the
Branch-And-Cut Framework" included in the distribution (see the
file 'brcut.txt' in the subdirectory 'doc').
In order to illustrate how the GLPK branch-and-cut framework
can be used for solving a particular optimization problem there
is an example included in the package. This is a stand-alone
program, TSPSOL, which is intended for solving to optimality the
symmetric Traveling Salesman Problem (TSP), a classical problem
of the combinatorial optimization (see the file 'tspsol.c' in
the subdirectory 'sample').
New edition of the document "GLPK: Reference Manual" was
included (see the files 'refman.latex', 'refman.dvi', and
'refman.ps' in the subdirectory 'doc').
New edition of the document "GLPK: Modeling Language GLPK/L" was
included (see the files 'lang.latex', 'lang.dvi', and 'lang.ps'
in the subdirectory 'doc').
The following new API routines were added to the package:
lpx_transform_row (transform explicitly specified row);
lpx_transform_col (transform explicitly specified column);
lpx_prim_ratio_test (perform primal ratio test);
lpx_dual_ratio_test (perform dual ratio test);
lpx_interior (solve LP problem using interior point method);
lpx_get_ips_stat (query status of interior point solution);
lpx_get_ips_row (obtain row interior point solution);
lpx_get_ips_col (obtain column interior point solution);
lpx_get_ips_obj (obtain interior point value of obj.func.);
lpx_read_lpm (read LP/MIP model written in GLPK/L);
lpx_write_mps (write problem data using MPS format);
lpx_print_ips (print interior point solution).
Detailed description of all these new API routines are given in
the new edition of the reference manual.
New version of the stand-alone solver glpsol (which is based on
the new API) was implemented.
So long as the new API (introduced in glpk 3.0) now provides
all the functions, which were provided by the old API, the old
API routines were removed from the package at all.
A preliminary implementation of new API routines was completed
and included in the package.
These new API routines provide much more flexible interaction
between the application program, LP/MIP problem instances, and
solver routines. Based on completely changed data structures
they are, however, similar to the API routines and provide the
same functionality. Please note that three routines, namely,
solving LPs using interior point method, reading model written
in the GLPK/L modeling language, and writing problem data in
the MPS format, are not implemented in the new API, however,
these routines are planned to be implemented in the next version
of the package.
A description of the new API routines is given in the document
"GLPK Reference Manual", a draft edition of which is included
in the package (see the files 'refman.latex', 'refman.dvi', and
'refman.ps' in the subdirectory 'doc').
Although the old API routines are kept in the package, they are
no longer supported and will be removed in the future.
A preliminary implementation of new API routines was included
in the package. These new API routines are intended to provide
much more flexible interaction between the application program,
LP/MIP problem and solver routines. See the document "New GLPK
API Routines" (the file 'newapi.txt' in the subdirectory 'doc')
also included in the package.
The api routines glp_simplex2, glp_call_ipm1, glp_call_bbm1 were
renamed, respectively, to glp_simplex, glp_interior, glp_integer
in order to reflect changes in implementation. The api routines
glp_call_rsm1, glp_simplex1, glp_pivot_in, glp_pivout_out were
removed from the package since they are completely superseded by
the new API routines (however, these routines still can be found
in the subdirectory 'oldsrc'). Please consult a new edition of
the document "GLPK User's Guide" about all these changes in the
existing api routines.
The document "GLPK Library Reference" was removed from the
package (into the subdirectory 'oldsrc') since it describes the
obsolete library routines, most of which are no longer used.
A new, more efficient implementation of the primal/dual simplex
method was included in the package. Due to some improvements the
simplex-based solver allows solving many LP problems faster and
provides more reliable results. Note that the new implementation
is currently incomplete and available only via the api routine
glp_simplex2.
All the changes are transparent on API level.
New version of LU-factorization and basis maintenance routines
(based on Forrest-Tomlin updating technique) was implemented.
Since these new routines functionally supersede some routines
(which implement other forms of the basis matrix) and make them
obsolete, the latter were removed from the package (they still
can be found in the subdirectory 'oldsrc').
All the changes are transparent on API level.
New edition of the document "GLPK User's Guide" was included in
the distribution. Now it describes all additional API routines,
which were recently added to the package.
Structure of the package was re-organized in order to make its
maintenance easier (all small files in the subdurectory 'source'
were merged in bigger units). These changes are transparent for
the user.
A new, more efficient implementation of the two-phase primal
simplex method was included in the package. Due to some new
features (an advanced initial basis, projected steepest edge,
recursive updating values and reduced costs) the new LP solver
is faster and numerically more stable than the old one.
The new LP solver is available as API routine glp_simplex2 and
has the same purpose as API routine glp_call_rsm1. For detailed
specification see the file 'newapi.txt' in the directory 'doc'.
Now the new LP solver is also used by default to solve an
initial LP problem in the branch-and-bound routine glp_call_bbm1
instead the routine rsm1_driver. Note that the branch-and-bound
procedure itself is still based on rsm1_driver.
The new LP solver is also used as default solver in GLPSOL for
solving LP and MIP problems. In order to choose the old solver
the option '--old-sim' can be specified in the command line.
Some minor changes were made in the simplex method routines in
order to improve numerical stability of the method.
A new implementation of the basis maintaining routines was
included in the package. These routines, which are based on so
called FHV-factorization (a variety of LU-factorization) of the
basis matrix and Gustavson's data structures, allows performing
the main operations faster at the expense of some worsening
numerical accuracy.
AFI (Advanced Form of the Inverse), which is the form of the
basis matrix based on FHV-factorization, is available via the
parameter form = 3 (on API level) or via the option --afi (in
GLPSOL solver).
Old GLPK API routines have been removed from the package.
New GLPK API routines were added:
- scaling routines;
- a routine for writing problem data in MPS format;
- a comprehensive driver to the simplex method;
- basis maintaining routines.
A description of the new API routines is given in the document
"Additional GLPK API Routines". This document is included into
the distribution in plain text format (see the file 'newapi.txt'
in the subdirectory 'doc').
Now the distribution includes a non-trivial example of using
GLPK as a base LP solver for Concorde, a well known program that
solves Traveling Salesman Problem (TSP). For further details see
comments in the file 'sample/lpglpk30.c'.
Now GLPK is provided with new API, which being more flexible
can be used in more complex algorithmic schemes.
New edition of the document "GLPK User's Guide" is included in
the distribution. Now it completely corresponds to the new GLPK
API routines.
Old API routines are not removed yet from the package, however
they became obsolete and therefore should not be used. Since now
the header glpk.h corresponds to new API, in order to compile
existing programs that use old GLPK API routines the statement
#define GLP_OLD_API
should be inserted before the statement
#include "glpk.h"
The document "Modeling language GLPK/L" is included into the
distribution in texinfo format.
New edition of the document "GLPK User's Guide" is included in
the distribution. Now it describes all additional API routines
which were recently added to the package.
Now GLPK includes an implementation of a preliminary version
of the GLPK/L modeling language. This language is intended for
writing mathematical programming models. The name GLPK/L is
derived from GNU Linear Programming Kit Language.
A brief description of the GLPK/L language is given in the
document "GLPK/L Modeling Language: A Brief Description". This
document is included into the distribution in plain text format
(see the file 'language.txt' in the subdirectory 'doc').
The language processor (which is a program that analyzes model
description written in GLPK/L and translates it to internal data
structures) is available as the GLPK API routine.
The stand-alone solver GLPSOL now is able: a) to process model
descriptions written in the GLPK/L language; b) to solve pure LP
problems using the interior point method (therefore the program
GLPIPM was removed from the package).
New edition of the document "GLPK User's Guide" is included in
the distribution. Now it describes all additional API routines
which were recently added to the package.
The MIP solver was fully re-programmed in order to improve its
robustness and performance. In particular, a basis recovering
procedure was implemented (this procedure allows switching to
the primal simplex method in case when the dual simplex method
fails).
Now GLPK includes a tentative implementation of the
branch-and-bound procedure based on the dual simplex method for
mixed integer linear programming (MIP).
Complete description of this new feature of the package is given
in the preliminary document "Mixed Integer Linear Programming
Using GLPK Version 2.2 (Supplement to GLPK User's Guide)". This
document is included into the distribution in plain text format
(see the file 'mip.txt' in the subdirectory 'doc').
The MIP solver (glp_integer) can be used as GLPK API routine in
the same way as the pure LP solver (glp_simplex).
The stand-alone program 'glpsol' is now able to solve LP as well
as MIP problems.
Note that the current version of GLPK MIP solver is based on
easiest heuristics for branching and backtracking. Therefore the
solver is fit mainly for MIP problems which are not very hard
and have few integer variables.
The document "GLPK Implementation of the Revised Simplex Method"
is included into the distribution. This document describes most
of routines related to the revised simplex method.
Now GLPK includes a tentative implementation of the primal-dual
interior point method for large-scale linear programming.
The interior point solver can be used as GLPK API routine in the
same manner as the simplex method solver (glp_simplex):
ret = glp_interior();
Note that currently the interior point solver implemented in
GLPK doesn't include many important features, in particular:
* it can't process dense columns; therefore if the problem has
dense columns, the solving will be extremely inefficient;
* it has no special features against numerical unstability;
some problems may cause premature termination of the solving
when the matrix A*D*A' becomes ill-conditioned;
* it computes only values of primal (auxiliary and structural)
variables and doesn't compute values of dual variables (i.e.
reduced costs) which are just set to zero;
* it doesn't identify optimal basis corresponding to the found
interior point solution; all variables in the found solution
are just marked as basic variables.
GLPK also includes a stand-alone program 'glpipm' which is a
demo based on the interior point method. It may be used in the
same way as the program 'glpsol' that is based on the simplex
method.