latte-optim {latte}

Solve an integer progam with LattE

Description

latte_max and latte_min use LattE's latte-maximize and latte-minimize functions to find the maximum or minimum of a linear objective function over the integers points in a polytope (i.e. satisfying linearity constraints). This makes use of the digging algorithm; see the LattE manual at http://www.math.ucdavis.edu/~latte for details.

Usage

latte_optim(objective, constraints, type = c("max", "min"),
  method = c("lp", "cones"), dir = tempdir(), opts = "",
  quiet = TRUE, shell = FALSE)

latte_max(objective, constraints, method = c("lp", "cones"),
  dir = tempdir(), opts = "", quiet = TRUE)

latte_min(objective, constraints, method = c("lp", "cones"),
  dir = tempdir(), opts = "", quiet = TRUE)

Arguments

objective

A linear polynomial to pass to mp(), see examples

constraints

A collection of linear polynomial (in)equalities that define the feasibility region, the integers in the polytope

type

"max" or "min"

method

Method "LP" or "cones"

dir

Directory to place the files in, without an ending /

opts

Options; see the LattE manual at http://www.math.ucdavis.edu/~latte

quiet

Show latte output

shell

Messages the shell code used to do the computation

Value

A named list with components par, a named-vector of optimizing arguments, and value, the value of the objective function at the optimial point.

Examples

if (has_latte()) {

latte_max(
  "-2 x + 3 y", 
  c("x + y <= 10", "x >= 0", "y >= 0")
)

latte_max(
  "-2 x + 3 y", 
  c("x + y <= 10", "x >= 0", "y >= 0"),
  quiet = FALSE
)


df <- expand.grid("x" = 0:10, "y" = 0:10)
df <- subset(df, x + y <= 10L)
df$objective <- with(df, -2*x + 3*y)
library("ggplot2")
ggplot(df, aes(x, y, size = objective)) +
  geom_point()

latte_min(
  "-2 x + 3 y",
  c("x + y <= 10", "x >= 0", "y >= 0"),
  method = "cones"
)



latte_min("-2 x - 3 y - 4 z", c(
  "3 x + 2 y + z <= 10",
  "2 x + 5 y + 3 z <= 15",
  "x >= 0", "y >= 0", "z >= 0"
), "cones", quiet = FALSE)





}