lpsymphony_solve_LP {lpsymphony} | R Documentation

## 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

    lpsymphony_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 lpsymphony 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, 2, 2), nrow = 3)
    dir <- c("<=", "<=", "<=")
    rhs <- c(60, 40, 80)
    max <- TRUE

    lpsymphony_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")

    lpsymphony_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)))

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

[Package lpsymphony version 1.12.0 Index]