Version:	0.3-8
Title:	R Interface to CPLEX
Description:	R interface to CPLEX solvers for linear, quadratic, and (linear and quadratic) mixed integer programs. Support for quadratically constrained programming is available. See the file "INSTALL" for details on how to install the Rcplex package in Linux/Unix-like and Windows systems. Support for sparse matrices is provided by an S3-style class "simple_triplet_matrix" from package slam and by objects from the Matrix package class hierarchy.
LazyLoad:	yes
Depends:	R (≥ 2.6.0), slam
Imports:	methods
Enhances:	Matrix
SystemRequirements:	IBM ILOG CPLEX libraries and headers
License:	LGPL-2 | LGPL-2.1 | LGPL-3 [expanded from: LGPL (≥ 2.0)]
URL:	https://R-Forge.R-project.org/projects/rcplex
NeedsCompilation:	yes
Packaged:	2025-04-16 11:15:24 UTC; theussl
Author:	Hector Corrada Bravo [aut], Kurt Hornik [ctb], Stefan Theussl [aut, cre]
Maintainer:	Stefan Theussl <Stefan.Theussl@R-project.org>
Repository:	CRAN
Date/Publication:	2025-04-20 11:20:02 UTC

Solve optimization problem with CPLEX

Description

Interface to CPLEX solvers for linear quadratic and (linear or quadratic) mixed-integer programs. The general statement of the problem is

\min \frac{1}{2}x'Qx + c'x

\mathrm{s.t} Ax \leq b

lb \leq x \leq ub

If Q==NULL then the problem is linear, if any value of the vtype argument is "B" or "I" then the problem is a mixed-integer program. The control argument is used to set CPLEX's many parameters. See details. The objsense determines if the problem is a maximization or minimization problem. The sense argument is used to set the constraint directions.

Usage

Rcplex(cvec, Amat, bvec, Qmat = NULL,
       lb = 0, ub = Inf, control = list(),
       objsense = c("min", "max"), sense = "L", vtype = NULL, n = 1)

Arguments

Details

Matrices A and C may be sparse matrices from a class in the hierarchy defined by the Matrix package. In that case, the internal casting functions are used to create the proper data structures to pass to CPLEX, which is similar to the column-major storage mode defined by the dgCMatrix-class defined by the Matrix package.

We also provide a simple S3-style class for sparse matrices simple_triplet_matrix, as used in the relations package. Matrices A and C can be objects of this class. See the examples for example usage. simple_triplet_matrix objects MUST be in column-major order.

The control argument can be used to set CPLEX's many parameters, including the particular algorithm used for solving the given problem. See the ILOG CPLEX Parameters guide for further details. The following parameters are supported:

trace:

Turn CPLEX output on (1) or off(0). Default 1.

maxcalls:

Number of calls to the CPLEX optimizer before license is released. Set to 1 to get a new license on every call to Rcplex. Can be any positive number. Default 500.

method:

Algorithm to use (Default 0):

0:

Automatic: CPLEX chooses algorithm automatically

1:

Primal Simplex

2:

Dual Simplex

3:

Network Simplex

4:

Barrier

preind:

Turn presolver on (1) or off (0). Default 1.

aggind:

Limit on the number of applications of the aggregator. Possible Values: -1 (automatic), 0 (do not use), any positive integer

itlim:

Maximum number of simplex iterations. Can be any nonnegative number. Default 1e8.

epagap:

Absolute MIP optimality gap tolerance. Can be any nonnegative number. Default 1e-6.

epgap:

Relative MIP optimality gap tolerance. Can be any nonnegative number. Default 1e-4.

tilim:

Time limit in seconds of call to optimizer. Can be any nonnegative number. Default 1e75.

disjcuts:

Indicator for disjunctive cuts used in MIP solver. Must be in -1:3. Default 0 (automatic).

mipemphasis:

Indicator for MIP solver emphasis. Must be in 0:4. Default 0 (balance optimality and feasibility)

cliques:

Indicator for clique cuts in MIP solver. Must be in -1:2. Default 0 (automatic)

nodesel:

Node selection strategy in MIP solver. Must be in 0:3. Default 1 (best-bound search).

probe:

Probe level in MPI solver. Must be -1:3. Default 0 (automatic)

varsel:

Variable selection strategy in MIP solver. Must be in -1:4. Default 0 (choose best method automatically).

flowcovers:

Indicator for flowcover cuts in MIP solver. Must be in -1:2. Default 0 (automatic).

solnpoolagap:

Sets an absolute tolerance on the objective value for the solutions in the solution pool. Can be any nonnegative real number. Ignored in versions < 11.0 of CPLEX. Default 0

solnpoolgap:

Sets a relative tolerance on the objective value for the solutions in the solution pool. Can be any nonnegative real number. Ignored in versions < 11.0 of CPLEX. Default 0

solnpoolintensity:

Controls the trade-off between the number of solutions generated for the solution pool and the amount of time and memory consumed. Must be in 0:4. Ignored in versions < 11.0 of CPLEX. Default 0 (automatic).

round:

Flag indicating if integer solutions for MIPs should be rounded before returning. In some cases, CPLEX returns slightly infeasible integer solutions. Setting this option to 1 ensures that the returned solution is integral by rounding. Default 0 (no rounding).

Value

Returns a list with the following components, or, if n > 1 a list of length equal to the number of optimal solutions containing the following components for each solution:

Author(s)

Hector Corrada Bravo and Stefan Theussl

References

IBM ILOG CPLEX Optimization Studio documentation

See Also

Rcplex.close, optim

Examples

## A linear program (this is lpex1.c in the CPLEX examples)
cvec <- c(1,2,3)
Amat <- matrix(c(-1,1,1,-1,3,-1),byrow=TRUE,nc=3)
bvec <- c(20,-30)
ub <- c(40,Inf,Inf)

res <- Rcplex(cvec,Amat,bvec,ub=ub,objsense="max",sense=c('L','G'))
print(res)

## A linear program with random data
## use the barrier method
n = 20; m = 25
nnz <- trunc(.2 * m * n)

## entries in simple_triplet_matrix clas
##  *must* be in column major order
nnz <- sort(sample(m*n,nnz,replace=FALSE)-1)
Amat <- simple_triplet_matrix(
             i = (nnz %% m) + 1,
             j = trunc(nnz/m) + 1,
             v = rnorm(nnz),
             nrow=m,ncol=n)

x0 <- runif(n)
b <- as.matrix(Amat) %*% x0
cvec <- rnorm(n)

res <- Rcplex(cvec,Amat,b,sense='E',control=list(method=4))
print(res)

## A quadratic problem (this is qpex1.c in the CPLEX examples)
cvec <- c(1,2,3)
Qmat <- matrix(c(-33,6,0,
                  6,-22,11.5,
                  0,11.5,-11),
                byrow=TRUE,
                nc=3)
Amat <- matrix(c(-1,1,1,
                  1,-3,1),
               byrow=TRUE,nc=3)
bvec <- c(20,30)
ub <- c(40,Inf,Inf)

res <- Rcplex(cvec,Amat,bvec,Qmat,ub=ub,objsense="max")
print(res)

## A mixed integer linear program (mipex1.c in the CPLEX examples)
cvec <- c(1,2,3,1)
Amat <- matrix(c(-1,1,1,10,
                  1,-3,1,0,
                  0,1,0,-3.5),
               byrow=TRUE, nc=4)
bvec <- c(20,30,0)
lb <- c(0,0,0,2)
ub <- c(40,Inf,Inf,3)
vtype <- c(rep("C",3),"I")

res <- Rcplex(cvec,Amat,bvec,lb=lb,ub=ub,sense=c("L","L","E"),
              objsense="max",vtype=vtype)
print(res)

## A mixed integer quadratic program
cvec <- c(1,2,3,1)
Qmat <- matrix(c(-33,6,0,0,
                  6,-22,11.5,0,
                  0,11.5,-11,0,
                  0,0,0,0),
               byrow=TRUE, nc=4)
Amat <- matrix(c(-1,1,1,10,
                  1,-3,1,0,
                  0,1,0,-3.5),
               byrow=TRUE, nc=4)
bvec <- c(20,30,0)
ub <- c(40,Inf,Inf,3)
vtype <- c(rep("C",3),"I")

res <- Rcplex(cvec,Amat,bvec,Qmat=Qmat,ub=ub,sense=c("L","L","E"),
              objsense="max",vtype=vtype)
print(res)
Rcplex.close()

Release CPLEX license

Description

This function releases the currently held CPLEX license.

Usage

Rcplex.close()

Author(s)

Hector Corrada Bravo

See Also

Rcplex

Solve quadratically constrained optimization problem with CPLEX

Description

Interface to CPLEX solvers for quadratically constrained linear, quadratic, and mixed-integer programs. The general statement of the problem is

\min \frac{1}{2}x'Qx + c'x

\mathrm{s.t} Ax \leq b

\mathrm{and} a_i'x + x'Q_ix \leq r_i for i=1,\ldots,q

lb \leq x \leq ub

If Q==NULL then the problem is linear, if any value of the vtype argument is "B" or "I" then the problem is a mixed-integer program. The control argument is used to set CPLEX's many parameters. See details. The objsense determines if the problem is a maximization or minimization problem. The sense argument is used to set the constraint directions.

Usage

Rcplex_solve_QCP(cvec, Amat, bvec, Qmat = NULL, QC,
       lb = 0, ub = Inf, sense = "L", objsense = c("min", "max"), vtype
  = NULL, n = 1, control = list())

Arguments

Details

See function link[Rcplex]{Rcplex}() for more information about sparse matrix representation and control arguments.

Value

Returns a list with the following components, or, if n > 1 a list of length equal to the number of optimal solutions containing the following components for each solution:

Author(s)

Hector Corrada Bravo and Stefan Theussl

References

IBM ILOG CPLEX Optimization Studio documentation

See Also

Rcplex.close, optim

Examples

## objective function
c <- c(1, 2, 3)
Q <- matrix(c(-33, 6, 0, 6, -22, 11.5, 0, 11.5, -11), nrow = 3)

## constraints

## linear part
A <- matrix(c(-1, 1, 1, -3, 1, 1), nrow = 2)
dir <- c("L", "L")
b <- c(20, 30)

## quadratic part
QC <- list(QC = list(Q = list(diag(1, nrow = 3)), L = NULL), dir = "L", b = 1)

## bounds
ub <- c(40, Inf, Inf)

## solve
res <- Rcplex_solve_QCP(c,A, b, Q, ub = ub, QC = QC, sense = dir, objsense = "max")
print(res)

## solve MIQCP
res <- Rcplex_solve_QCP(c, A, b, Q, ub = ub, QC = QC,
                        sense = dir, objsense = "max", vtype = c("C", "I", "C"))

## quadratic and linear part
QC <- list(QC = list(Q = list(diag(1, nrow = 3)), L = list(c(3,4,-3))), dir = "L", b = 1)

## solve
res <- Rcplex_solve_QCP(c,A, b, Q, ub = ub, QC = QC, sense = dir, objsense = "max")
print(res)


Rcplex.close()