create_MIQP: Internal functions that support the export of (mixed) integer...

In DoE.MIParray: Creation of Arrays by Mixed Integer Programming

Internal functions that support the export of (mixed) integer quadratic or linear problems in MPS format

Description

create_MIQP creates an MPS format character object, write_MPSILP saves a single integer linear problem in MPS format (used in the user-visible write_MSPILPlist). The functions work, if neither Mosek nor Gurobi is available.

Usage

create_MIQP(nruns, nlevels, resolution=3, distinct=TRUE,
              start=NULL, forced=NULL, forMosek=FALSE)
write_MPSILP(file, qco=NULL, qcoinfo=NULL,
              cvec=NULL, bvec=NULL, Amat=NULL, bsense=NULL, boundmat=NULL,
              name = "EnforceResolution", commentline="* no comment")

Arguments

nruns	positive integer; number of runs
nlevels	vector of integers (>=2); numbers of factor levels
resolution	positive integer; the minimum resolution requested
distinct	logical; if TRUE (default), restricts counting vector to 0/1 entries, which means that the resulting array is requested to have distinct rows; otherwise, duplicate rows are permitted, i.e. the counting vector can have arbitrary non-negative integers. Designs with distinct runs are usually better; in addition, binary variables are easier to handle by the optimization algorithm. Nevertheless, there are occasions where a better array is found faster with option distinct=FALSE, even if it has distinct rows.
start	a starting value for the algorithm: can be a array matrix with entries 1 to number of levels for each column, or a counting vector for the full factorial in lexicographic order; if specified, start must specify an array with the appropriate number of rows and columns, the requested resolution and, if distinct = TRUE, also contain distinct rows (matrix) or 0/1 elements only. start cannot be combined with search.orders=TRUE.
forced	for resolution > 1 only; runs to force into the solution design; can be given as an array matrix with the appropriate number of columns and less than nruns rows or a counting vector for the full factorial in lexicographic order with sum smaller than nruns; if distinct=TRUE, forced must have distinct rows (matrix) or 0/1 elements only.
forMosek	logical
file	character string that provides the path to the save file
qco	an object of class qco that can be used as input for function Rmosek::mosek
qcoinfo	contains information on the qco object (keeping that information in qco itself hinders execution of Rmosek::mosek)
cvec	coefficients of linear objective function
bvec	RHS of the constraints
Amat	matrix of coefficients for the LHS of the constraints
bsense	directions of constraints (character vector with elements "E" for equal, "G" for greater, "L" for less or "N" for not restricted.
boundmat	matrix of lower (first row) and upper (second row) bounds for the variables
name	name to be written into the name field of the mps file
commentline	comment to be written directly underneath the name (comments have to start with a *)

Details

The functions do not do any problem solving, they serve the sole purpose of exporting problems so that they can be addressed by solvers other than Mosek or Gurobi. The target solver must be able to process the MPS format.

write_MPSILP writes a single problem to an MPS file. The function is used by function write_MPSILPlist.

create_MIQP creates a quadratic problem in MPS format, using a general quadratic representation (section Q) for external solvers (default) or Mosek format with conic quadratic constraints (forMosek=TRUE); the function is used by function write_MPSMIQP.

The start array for create_MIQP can be made available from a previous linear optimization (though this is not enforced). If an admissible start array is provided, write_MPSMIQP initially prints the GWLP of that start array. Otherwise, it warns of inadmissibility. The start value cannot be stored in the MPS file. Instead, for a non-NULL start array, a separate file (suffix .start) is created, and users have to work out how they can make their solver use that start solution. Note that the availability of a start array can improve the ability of a solver to find an optimum solution. However, this is not always the case, there are also instances for which a better solution is found without providing a start solution.

Note that it can take a long time to write the problems, if the problem has many variables (the number of variables is prod(nlevels)).

Value

Function create_MIPQ creates a list object of class qco, see also section "Details".

Function write_MPSILP does not return a value.

Note

The functions are not meant for situations, for which a full factorial design would be huge. Even though the functions do not solve anything, MPS files will be very large and writing them will be quite slow for such cases.

Author(s)

Ulrike Groemping

References

Groemping, U. and Fontana, R. (2019). An Algorithm for Generating Good Mixed Level Factorial Designs. Computational Statistics & Data Analysis 137, 101-114. doi:10.1016/j.csda.2019.01.020.

Mosek ApS (2017a). MOSEK version w.x.y.z documentation. Accessible at: https://www.mosek.com/documentation/. This package has been developed using version 8.1.0.23 (accessed August 29 2017).

Mosek ApS (2017b). MOSEK Rmosek Package 8.1.y.z. https://docs.mosek.com/8.1/rmosek/index.html. !!! In normal R speak, this is the documentation of the Rmosek package version 8.0.69 (or whatever comes next), when applied on top of the Mosek version 8.1.y.z (this package has been devoloped with Mosek version 8.1.0.23 and will likely not work for Mosek versions before 8.1). !!! (accessed August 29 2017)

See Also

See also write_MPSILPlist and write_MPSMIQP.

Examples

## Not run: 
## can also be run with gurobi_MIParray instead of mosek_MIParray
## there are of course better ways to obtain good arrays for these parameters
## (e.g. function FrF2 from package FrF2)
problemlist <- create_ILPlist(16, c(2,2,4,8), resolution=2, kmax=4)
feld
names(attributes(feld))
attr(feld, "MIPinfo")$info

## using a start value
start <- DoE.base::L16.2.8.8.1[,1:5]
feld <- mosek_MIParray(16, rep(2,5), resolution=4, start=start)

## counting vector representation of the start value could also be used
DoE.MIParray:::dToCount(start-1)
   ## "-1", because the function requires values starting with 0
   ## 32 elements for the full factorial in lexicographic order, 16 ones for the runs

## extending an existing array
force <- matrix(as.numeric(as.matrix(DoE.base::undesign(DoE.base::oa.design(L8.2.7)))), nrow=8)
feld <- mosek_MIParray(16, rep(2,7), resolution=3, kmax=4, forced=force)
attr(feld, "MIPinfo")$info

## End(Not run)

DoE.MIParray documentation built on Aug. 21, 2023, 5:08 p.m.