Rsymphony_solve_LP {Rsymphony}

COIN-OR SYMPHONY Linear and Mixed Integer Programming Solver

Description

High level R interface to the COIN-OR SYMPHONY solver for linear as well as mixed integer linear programming problems (MILPs).

Usage

Rsymphony_solve_LP(obj, mat, dir, rhs, bounds = NULL, types = NULL,
                   max = FALSE, verbosity = -2, time_limit = -1,
                   node_limit = -1, gap_limit = -1, first_feasible = FALSE,
                   write_lp = FALSE, write_mps = FALSE)

Arguments

obj

a vector with the objective coefficients

mat

a vector or a matrix of the constraint coefficients

dir

a character vector with the directions of the constraints. Each element must be one of "<=", "==" or ">=".

rhs

the right hand side of the constraints

bounds

NULL (default) or a list with elements upper and lower containing the indices and corresponding bounds of the objective variables. The default for each variable is a bound between 0 and Inf.

types

a character vector giving the types of the objective variables, with "C", "I", and "B" corresponding to continuous, integer, and binary, respectively, or NULL (default), taken as all-continuous. Recycled as needed.

max

a logical giving the direction of the optimization. TRUE means that the objective is to maximize the objective function, FALSE (default) means to minimize it.

verbosity

an integer defining the level of verbosity, -2 (default) means no output.

time_limit

an integer defining the time limit in seconds, -1 (default) means no time limit.

node_limit

an integer defining the limit in number of iterations, -1 (default) means no node limit.

gap_limit

when the gap between the lower and the upper bound reaches this point, the solution process will stop and the best solution found to that point will be returned, -1 (default) means no gap limit.

first_feasible

a logical defining if the solution process should stop after the first feasible solution has been found, FALSE (default) means that the solution process does not stop after the first feasible solution has been found.

write_lp

a logical value indicating if an LP representation of the problem should be written for debugging purposes, FALSE (default) means no LP file is written.

write_mps

a logical value indicating if an MPS representation of the problem should be written for debugging purposes, FALSE (default) means no MPS file is written.

Details

SYMPHONY is an open source solver for solving mixed integer linear programs (MILPs). The current version can be found at https://projects.coin-or.org/SYMPHONY. Package Rsymphony uses the C interface of the callable library provided by SYMPHONY, and supplies a high level solver function in R using the low level C interface.

Value

A list containing the optimal solution, with the following components.

solution

the vector of optimal coefficients

objval

the value of the objective function at the optimum

status

an integer with status information about the solution returned: 0 if the optimal solution was found, a non-zero value otherwise.

Author(s)

Reinhard Harter, Kurt Hornik and Stefan Theussl

References

SYMPHONY development home page (https://projects.coin-or.org/SYMPHONY/wiki).

See Also

lp in package lpSolve; Rglpk_solve_LP in package Rglpk.

Examples

## Simple linear program.
## maximize:   2 x_1 + 4 x_2 + 3 x_3
## subject to: 3 x_1 + 4 x_2 + 2 x_3 <= 60
##             2 x_1 +   x_2 +   x_3 <= 40
##               x_1 + 3 x_2 + 2 x_3 <= 80
##               x_1, x_2, x_3 are non-negative real numbers

obj <- c(2, 4, 3)
mat <- matrix(c(3, 2, 1, 4, 1, 3, 2, 1, 2), nrow = 3)
dir <- c("<=", "<=", "<=")
rhs <- c(60, 40, 80)
max <- TRUE

Rsymphony_solve_LP(obj, mat, dir, rhs, max = max)

## Simple mixed integer linear program.
## maximize:    3 x_1 + 1 x_2 + 3 x_3
## subject to: -1 x_1 + 2 x_2 +   x_3 <= 4
##                      4 x_2 - 3 x_3 <= 2
##                x_1 - 3 x_2 + 2 x_3 <= 3
##                x_1, x_3 are non-negative integers
##                x_2 is a non-negative real number

obj <- c(3, 1, 3)
mat <- matrix(c(-1, 0, 1, 2, 4, -3, 1, -3, 2), nrow = 3)
dir <- c("<=", "<=", "<=")
rhs <- c(4, 2, 3)
max <- TRUE
types <- c("I", "C", "I")

Rsymphony_solve_LP(obj, mat, dir, rhs, types = types, max = max)

## Same as before but with bounds replaced by
## -Inf <  x_1 <= 4
##    0 <= x_2 <= 100
##    2 <= x_3 <  Inf

bounds <- list(lower = list(ind = c(1L, 3L), val = c(-Inf, 2)),
               upper = list(ind = c(1L, 2L), val = c(4, 100)))

Rsymphony_solve_LP(obj, mat, dir, rhs, types = types, max = max,
                   bounds = bounds)