Rcplex (version 0.2-3)

Rcplex: 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 $$min\frac{1}{2}{x}^{\prime }Qx+c^{\prime }x$$ $$\mathrm{s}.\mathrm{t}Ax\le b$$ $$lb\le x\le ub$$

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

cvec

The linear coefficient of the objective function

Amat

The constraint matrix (requires ncol(Amat)==length(cvec))

bvec

The constraints right-hand side (requires length(bvec)==nrow(Amat))

Qmat

The quadratic coefficient of the objective function. If NULL the problem is linear. If not NULL, it must be a symmetric positive semidefinite matrix of size length(cvec) by length(cvec). Default

lb

Lower bound on the problem variables. If length(lb)==1 then lb is the lower bound of all variables. Otherwise, length(lb)==length(cvec). Set lb=-Inf to have no lower bound. Default 0.

ub

Upper bound on the problem variables. See lb for further details. Default Inf.

control

A list of CPLEX parameters. See *Details*

objsense

Either "max" or "min", determines the optimization direction. Default "min"

sense

The direction of the inequality in each constraint. If length(sense)==1 then the same value is taken for each constraint. Can be one of "L" (less than or equal), "G" (reater than or equal) or "E"

vtype

Determines the type of each problem variable. Can be one of "C" (continuous), "I" (integer) or "B" (binary). If length(vtype)==1 the same value is taken for all variables. Otherwise, requires

n

Determines the maximal number of solutions the solver should return in case of an MIP with more than one solution at optimum. If CPLEX should search for "all" solutions then n has to be set to NA. In CPLEX this is als

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:
• xopt
  Values of problem variables at optimum.
• obj
  Value of objective function at optimum.
• status
  Solution status. See CPLEX documentation for meaning of status codes.
• extra
  List with extra information about solution with components [object Object],[object Object],[object Object]

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:

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

References

ILOG CPLEX User's Guide

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()