Nonlinear discrete optimization in R

Question

I have a simple (indeed standard in economics) nonlinear constrained discrete maximisation problem to solve in R and am having trouble. I found solutions for pa

Answer 1

1) no packages This can be done by brute force. Using df from the question as input ensure that price is numeric (it's a factor in the df of the question) and calculate the largest number mx for each variable. Then create grid g of variable counts and compute the total price of each and the associated objective giving gg. Now sort gg in descending order of objective and take those solutions satisfying the constraint. head will show the top few solutions.

price <- as.numeric(as.character(df$price))
mx <- ceiling(20/price)
g <- expand.grid(ana = 0:mx[1], ban = 0:mx[2], cook = 0:mx[3]) 
gg <- transform(g, total = as.matrix(g) %*% price, objective = sqrt(ana * ban * cook))
best <- subset(gg[order(-gg$objective), ], total <= 20)

giving:

> head(best) # 1st row is best soln, 2nd row is next best, etc.
     ana ban cook total objective
1643   3   9    5 19.96  11.61895
1929   3   7    6 19.80  11.22497
1346   3  10    4 19.37  10.95445
1611   4   6    5 19.88  10.95445
1632   3   8    5 19.21  10.95445
1961   2  10    6 19.88  10.95445

2) dplyr This can also be nicely expressed using the dplyr package. Using g and price from above:

library(dplyr)
g %>% 
  mutate(total = c(as.matrix(g) %*% price), objective = sqrt(ana * ban * cook)) %>%
  filter(total <= 20) %>%
  arrange(desc(objective)) %>%
  top_n(6)

giving:

Selecting by objective
  ana ban cook total objective
1   3   9    5 19.96  11.61895
2   3   7    6 19.80  11.22497
3   3  10    4 19.37  10.95445
4   4   6    5 19.88  10.95445
5   3   8    5 19.21  10.95445
6   2  10    6 19.88  10.95445