dirkschumacher

library(armacmp)

# taken from https://gallery.rcpp.org/articles/black-scholes-three-ways/
put_option_pricer_arma <- armacmp(function(s = type_colvec(),
                                           k = type_scalar_numeric(),
                                           r = type_scalar_numeric(),
                                           y = type_scalar_numeric(),
                                           t = type_scalar_numeric(),
                                           sigma = type_scalar_numeric()) {

dirkschumacher

a <- Matrix::sparseVector(1:2, i = 1:2, length = 2)
b <- Matrix::sparseVector(1:2, i = 1:2, length = 2)
class(a * b)
#> [1] "dsparseVector"
#> attr(,"package")
#> [1] "Matrix"
class(a / b) # bug? numeric instead of sparseVector
#> [1] "numeric"

dirkschumacher

splice_df <- function(x, ...) {
  expr <- rlang::enquo(x)
  cols <- lapply(rlang::ensyms(..., .named = TRUE), as.character)
  lapply(cols, function(col_name) {
    rlang::quo(`[[`(!!expr, !!col_name))
  })
}

dirkschumacher

# this is just a script to test the rhxl package, I just quickly looked at the data

# Ethiopia Who is doing What Where - 3W December 2017 
# source: https://data.humdata.org/dataset/3w-december-2017
url <- "https://data.humdata.org/dataset/615416d2-457b-461a-8155-090f0ced0bf8/resource/f71bf111-8706-42f4-ba46-4ce3c8c949dc/download/3w_hxl.xlsx"

# load the rhxl package
# https://github.com/dirkschumacher/rhxl
library(rhxl)
download.file(url, "file.xlsx")

dirkschumacher

# Linear regression with tensorflow and R

library(tensorflow)

# Y = X * beta + epsilon
# =>
# beta = (X'X)^-1X'y

# first we build the computational graph
X <- tf$placeholder(tf$float64, name = "X")

dirkschumacher

# There are essential two prominent ways to model a TSP as a MILP. One is to formulate the full model using the Miller–Tucker–Zemlin (MTZ) formulation and the other option is to use the so-called sub-tour elimination constraints .[1](https://www.unc.edu/~pataki/papers/teachtsp.pdf)
# 
# The first formulation is fairly compact (quadratic many constraints and variables) but is not suitable anymore when n gets larger. The second formulation has exponential many constraints at most, but can solve larger TSPs due to the better LP relaxation. The idea of the latter approach is add constraints to the model *during* the solution process as soon as a solution was found that contains a sub-tour. For solution strategies like this solvers usually offer callbacks that let's you modify the model during the the branch-and-cut process - this is however not currently supported by `ompr`.
# 
# Therefor we will use the MTZ formulation and solve a fairly small TSP.


library(ompr)
library(magrittr)

dirkschumacher

# based on a article from here https://dirkschumacher.github.io/ompr/articles/problem-graph-coloring.html

library(maptools)
library(dplyr)

# devtools::install_github("dirkschumacher/ompr@milp")

# CC by
map_data <- rgdal::readOGR("https://raw.githubusercontent.com/nvkelso/natural-earth-vector/master/geojson/ne_50m_admin_0_countries.geojson", "OGRGeoJSON")

dirkschumacher

This vignettes discribes the modelling techniques available in ompr to make your life easier when developing a mixed integer programming model.

A MILP Model

You can think of a MIP Model as a big constraint maxtrix and a set of vectors. But you can also think of it as a set of decision variables, an objective function and a number of constraints as equations/inequalities. ompr implements the latter approach.

dirkschumacher

# based on the formulation from here
# http://wwwhome.math.utwente.nl/~uetzm/do/IP-FKS.pdf
library(magrittr)
# devtools::install_github("dirkschumacher/ompr@milp")
library(ompr)

max_colors <- 10
n <- 100

# variables n * max_colors

dirkschumacher

# based on a article from here https://dirkschumacher.github.io/ompr/articles/problem-graph-coloring.html

library(maptools)
library(dplyr)

# CC by
# license here https://github.com/berlinermorgenpost/Berlin-Geodaten
map_data <- rgdal::readOGR("https://github.com/berlinermorgenpost/Berlin-Geodaten/raw/master/berlin_bezirke.geojson", "OGRGeoJSON")

# this gives as an adjancy list