# lpsymphony_solve: COIN-OR SYMPHONY Linear and Mixed Integer Programming Solver In lpsymphony: Symphony integer linear programming solver in R

## Description

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

## Usage

 ```1 2 3 4``` ```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

`lp` in package lpSolve; `Rglpk_solve_LP` in package Rglpk.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42``` ```## 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) ```