How to avoid multiple for loops in this optimization problem

Question

I am trying to find the combination of columns "a" and "b" in table "brand_1" and "brand_2" that maximize my objective function "obj." How can I accomplish this without writing 4 for-loops?

Here is a simple code to illustrate my question. I also need to generalize it so that it works for any number of tables (not just "brand_1" and "brand_2") with each table will always have two columns ("a" and "b"). Thanks so much!

brand_1 <- data.frame(a = c(1, 3),  b = c(5, 2))
brand_2 <- data.frame(a = c(5, 4),  b = c(2, 1))

num_row <- nrow(brand_1) # where nrow(brand_1) = nrow(brand_2)

all_a1 <- vector()
all_b1 <- vector()
all_a2 <- vector()
all_b2 <- vector()
all_obj <- vector()

for (a1 in 1:num_row) {
  for (b1 in 1:num_row) {
    for (a2 in 1:num_row) {
      for (b2 in 1:num_row) {
        obj <- brand_1[a1, "a"] + brand_1[b1, "b"] + brand_2[a2, "a"] + brand_2[b2, "b"]
        all_a1  <- c(all_a1, brand_1[a1, "a"])
        all_b1  <- c(all_b1, brand_1[b1, "b"])
        all_a2  <- c(all_a2, brand_2[a2, "a"])
        all_b2  <- c(all_b2, brand_2[b2, "b"])
        
        all_obj <- c(all_obj, obj)
      }
    }
  }
}

out <- data.frame(all_a1, all_b1, all_a2, all_b2, all_obj)

Here line 9 shows the solution that maximizes "obj".

Answer 1

For a general solution with any number of dataframes we can use ls to get all the objects with "brand" in it, get them in list using mget, rename the column names based on there object name and use crossing to generate their all possible combinations. Finally, you can use rowSums to sum the rows.

library(tidyverse)

mget(ls(pattern = 'brand')) %>%
  imap_dfc(~setNames(., paste0(names(.x), sub('.*_', '', .y)))) %>%
  do.call(crossing, .) %>%
  mutate(all_obj = rowSums(.))

#      a1    b1    a2    b2 all_obj
#   <dbl> <dbl> <dbl> <dbl>   <dbl>
# 1     1     2     4     1       8
# 2     1     2     4     2       9
# 3     1     2     5     1       9
# 4     1     2     5     2      10
# 5     1     5     4     1      11
# 6     1     5     4     2      12
# 7     1     5     5     1      12
# 8     1     5     5     2      13
# 9     3     2     4     1      10
#10     3     2     4     2      11
#11     3     2     5     1      11
#12     3     2     5     2      12
#13     3     5     4     1      13
#14     3     5     4     2      14
#15     3     5     5     1      14
#16     3     5     5     2      15

Answer 2

We can use expand.grid

out <- expand.grid(c(brand_1, brand_2))
names(out) <- make.unique(names(out))
out$all_obj <- rowSums(out)

-output

out
#   a b a.1 b.1 all_obj
#1  1 5   5   2      13
#2  3 5   5   2      15
#3  1 2   5   2      10
#4  3 2   5   2      12
#5  1 5   4   2      12
#6  3 5   4   2      14
#7  1 2   4   2       9
#8  3 2   4   2      11
#9  1 5   5   1      12
#10 3 5   5   1      14
#11 1 2   5   1       9
#12 3 2   5   1      11
#13 1 5   4   1      11
#14 3 5   4   1      13
#15 1 2   4   1       8
#16 3 2   4   1      10     

---

Or with complete

library(dplyr)
library(tidyr)
bind_cols(brand_1, brand_2)  %>%
    complete(!!! rlang::syms(names(.))) %>% 
    mutate(all_obj = rowSums(.))