OMPR (Optimization Modeling Package) is a DSL to model and solve Mixed Integer Linear Programs. It is inspired by the excellent Jump project in Julia.
Here are some problems you could solve with this package:
- What is the cost minimal way to visit a set of clients and return home afterwards?
- What is the optimal conference time table subject to certain constraints (e.g.ย availability of a projector)?
- Sudokus
The Wikipedia article gives a good starting point if you would like to learn more about the topic.
I am always happy to get bug reports or feedback.
install.packages("ompr")
install.packages("ompr.roi")To install the current development version use devtools:
remotes::install_github("dirkschumacher/ompr")
remotes::install_github("dirkschumacher/ompr.roi")- ompr.roi - Bindings to ROI (GLPK, Symphony, CPLEX etc.)
suppressPackageStartupMessages(library(dplyr, quietly = TRUE))
suppressPackageStartupMessages(library(ROI))
library(ROI.plugin.glpk)
library(ompr)
library(ompr.roi)
result <- MIPModel() |>
add_variable(x, type = "integer") |>
add_variable(y, type = "continuous", lb = 0) |>
set_bounds(x, lb = 0) |>
set_objective(x + y, "max") |>
add_constraint(x + y <= 11.25) |>
solve_model(with_ROI(solver = "glpk"))
get_solution(result, x)
#> x
#> 11
get_solution(result, y)
#> y
#> 0.25These functions currently form the public API. More detailed docs can be found in the package function docs or on the website
MIPModel()create an empty mixed integer linear model (the old way)add_variable()adds variables to a modelset_objective()sets the objective function of a modelset_bounds()sets bounds of variablesadd_constraint()add constraintssolve_model()solves a model with a given solverget_solution()returns the column solution (primal or dual) of a solved model for a given variable or group of variablesget_row_duals()returns the row duals of a solution (only if it is an LP)get_column_duals()returns the column duals of a solution (only if it is an LP)
There are currently two backends. A backend is the function that initializes an empty model.
MIPModel()is the standard MILP Model.MILPModel()is another backend specifically optimized for linear models and is often faster thanMIPModel(). It has different semantics, as it is vectorized. Currently experimental and might be deprecated in the future.
Solvers are in different packages. ompr.ROI uses the ROI package which
offers support for all kinds of solvers.
with_ROI(solver = "glpk")solve the model with GLPK. InstallROI.plugin.glpkwith_ROI(solver = "symphony")solve the model with Symphony. InstallROI.plugin.symphonywith_ROI(solver = "cplex")solve the model with CPLEX. InstallROI.plugin.cplex- โฆ See the ROI package for more plugins.
Please take a look at the docs for bigger examples.
max_capacity <- 5
n <- 10
set.seed(1234)
weights <- runif(n, max = max_capacity)
MIPModel() |>
add_variable(x[i], i = 1:n, type = "binary") |>
set_objective(sum_over(weights[i] * x[i], i = 1:n), "max") |>
add_constraint(sum_over(weights[i] * x[i], i = 1:n) <= max_capacity) |>
solve_model(with_ROI(solver = "glpk")) |>
get_solution(x[i]) |>
filter(value > 0)
#> variable i value
#> 1 x 1 1
#> 2 x 6 1
#> 3 x 7 1
#> 4 x 8 1An example of a more difficult model solved by GLPK
max_bins <- 10
bin_size <- 3
n <- 10
weights <- runif(n, max = bin_size)
MIPModel() |>
add_variable(y[i], i = 1:max_bins, type = "binary") |>
add_variable(x[i, j], i = 1:max_bins, j = 1:n, type = "binary") |>
set_objective(sum_over(y[i], i = 1:max_bins), "min") |>
add_constraint(sum_over(weights[j] * x[i, j], j = 1:n) <= y[i] * bin_size, i = 1:max_bins) |>
add_constraint(sum_over(x[i, j], i = 1:max_bins) == 1, j = 1:n) |>
solve_model(with_ROI(solver = "glpk", verbose = TRUE)) |>
get_solution(x[i, j]) |>
filter(value > 0) |>
arrange(i)
#> <SOLVER MSG> ----
#> GLPK Simplex Optimizer, v4.65
#> 20 rows, 110 columns, 210 non-zeros
#> 0: obj = 0.000000000e+00 inf = 1.000e+01 (10)
#> 29: obj = 4.546337429e+00 inf = 0.000e+00 (0)
#> * 34: obj = 4.546337429e+00 inf = 0.000e+00 (0)
#> OPTIMAL LP SOLUTION FOUND
#> GLPK Integer Optimizer, v4.65
#> 20 rows, 110 columns, 210 non-zeros
#> 110 integer variables, all of which are binary
#> Integer optimization begins...
#> Long-step dual simplex will be used
#> + 34: mip = not found yet >= -inf (1; 0)
#> + 62: >>>>> 5.000000000e+00 >= 5.000000000e+00 0.0% (13; 0)
#> + 62: mip = 5.000000000e+00 >= tree is empty 0.0% (0; 25)
#> INTEGER OPTIMAL SOLUTION FOUND
#> <!SOLVER MSG> ----
#> variable i j value
#> 1 x 1 2 1
#> 2 x 1 9 1
#> 3 x 1 10 1
#> 4 x 2 5 1
#> 5 x 2 7 1
#> 6 x 2 8 1
#> 7 x 3 6 1
#> 8 x 4 4 1
#> 9 x 10 1 1
#> 10 x 10 3 1MIT
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