lp: Linear and Integer Programming

In lpSolve: Interface to 'Lp_solve' v. 5.5 to Solve Linear/Integer Programs

Linear and Integer Programming

Description

Interface to lp_solve linear/integer programming system

Usage

lp (direction = "min", objective.in, const.mat, const.dir, const.rhs,
	transpose.constraints = TRUE, int.vec, presolve=0, compute.sens=0,
        binary.vec, all.int=FALSE, all.bin=FALSE, scale = 196, dense.const, 
        num.bin.solns=1, use.rw=FALSE, timeout = 0L)

Arguments

direction	Character string giving direction of optimization: "min" (default) or "max."
objective.in	Numeric vector of coefficients of objective function
const.mat	Matrix of numeric constraint coefficients, one row per constraint, one column per variable (unless transpose.constraints = FALSE; see below).
const.dir	Vector of character strings giving the direction of the constraint: each value should be one of "<," "<=," "=," "==," ">," or ">=". (In each pair the two values are identical.)
const.rhs	Vector of numeric values for the right-hand sides of the constraints.
transpose.constraints	By default each constraint occupies a row of const.mat, and that matrix needs to be transposed before being passed to the optimizing code. For very large constraint matrices it may be wiser to construct the constraints in a matrix column-by-column. In that case set transpose.constraints to FALSE.
int.vec	Numeric vector giving the indices of variables that are required to be integer. The length of this vector will therefore be the number of integer variables.
presolve	Numeric: presolve? Default 0 (no); any non-zero value means "yes." Currently ignored.
compute.sens	Numeric: compute sensitivity? Default 0 (no); any non-zero value means "yes."
binary.vec	Numeric vector like int.vec giving the indices of variables that are required to be binary.
all.int	Logical: should all variables be integer? Default: FALSE.
all.bin	Logical: should all variables be binary? Default: FALSE.
scale	Integer: value for lpSolve scaling. Details can be found in the lpSolve documentation. Set to 0 for no scaling. Default: 196
dense.const	Three column dense constraint array. This is ignored if const.mat is supplied. Otherwise the columns are constraint number, column number, and value; there should be one row for each non-zero entry in the constraint matrix.
num.bin.solns	Integer: if all.bin=TRUE, the user can request up to num.bin.solns optimal solutions to be returned.
use.rw	Logical: if TRUE and num.bin.solns > 1, write the lp out to a file and read it back in for each solution after the first. This is just to defeat a bug somewhere. Although the default is FALSE, we recommend you set this to TRUE if you need num.bin.solns > 1, until the bug is found.
timeout	Integer: timeout variable in seconds, defaults to 0L which means no limit is set.

Details

This function calls the lp_solve 5.5 solver. That system has many options not supported here. The current version is maintained at https://lpsolve.sourceforge.net/5.5/

Note that every variable is assumed to be >= 0!

Value

An lp object. See lp.object for details.

Author(s)

Sam Buttrey, [e-mail]

See Also

lp.assign, lp.transport

Examples

#
# Set up problem: maximize
#   x1 + 9 x2 +   x3 subject to
#   x1 + 2 x2 + 3 x3  <= 9
# 3 x1 + 2 x2 + 2 x3 <= 15
#
f.obj <- c(1, 9, 1)
f.con <- matrix (c(1, 2, 3, 3, 2, 2), nrow=2, byrow=TRUE)
f.dir <- c("<=", "<=")
f.rhs <- c(9, 15)
#
# Now run.
#
lp ("max", f.obj, f.con, f.dir, f.rhs)
## Not run: Success: the objective function is 40.5
lp ("max", f.obj, f.con, f.dir, f.rhs)$solution
## Not run: [1] 0.0 4.5 0.0
#
# The same problem using the dense constraint approach:
#
f.con.d <- matrix (c(rep (1:2,each=3), rep (1:3, 2), t(f.con)), ncol=3)
lp ("max", f.obj, , f.dir, f.rhs, dense.const=f.con.d)
## Not run: Success: the objective function is 40.5
#
# Get sensitivities
#
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$sens.coef.from
## Not run: [1] -1e+30  2e+00 -1e+30
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$sens.coef.to  
## Not run: [1] 4.50e+00 1.00e+30 1.35e+01
#
# Right now the dual values for the constraints and the variables are
# combined, constraints coming first. So in this example...
#
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$duals     
## Not run: [1]   4.5   0.0  -3.5   0.0 -10.5
#
# ...the duals of the constraints are 4.5 and 0, and of the variables,
# -3.5, 0.0, -10.5. Here are the lower and upper limits on these:
#
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$duals.from
## Not run: [1]  0e+00 -1e+30 -1e+30 -1e+30 -6e+00
lp ("max", f.obj, f.con, f.dir, f.rhs, compute.sens=TRUE)$duals.to  
## Not run: [1] 1.5e+01 1.0e+30 3.0e+00 1.0e+30 3.0e+00
#
# Run again, this time requiring that all three variables be integer
#
lp ("max", f.obj, f.con, f.dir, f.rhs, int.vec=1:3)
## Not run: Success: the objective function is 37
lp ("max", f.obj, f.con, f.dir, f.rhs, int.vec=1:3)$solution
## Not run: [1] 1 4 0
#
# You can get sensitivities in the integer case, but they're harder to
# interpret.
#
lp ("max", f.obj, f.con, f.dir, f.rhs, int.vec=1:3, compute.sens=TRUE)$duals
## Not run: [1] 1 0 0 7 0
#
# Here's an example in which we want more than one solution to a problem
# in which all variables are binary: the 8-queens problem, 
# with dense constraints.
#
chess.obj <- rep (1, 64)
q8 <- make.q8 ()
chess.dir <- rep (c("=", "<"), c(16, 26))
chess.rhs <- rep (1, 42)
lp ('max', chess.obj, , chess.dir, chess.rhs, dense.const = q8, 
    all.bin=TRUE, num.bin.solns=3)

lpSolve documentation built on Sept. 13, 2024, 1:11 a.m.