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".

akrun · Accepted Answer · 2020-12-05 22:45:53Z

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(.))

edited Dec 5, 2020 at 22:45

answered Dec 5, 2020 at 22:40

akrun

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2 Comments

Ketty Over a year ago

Thanks, akrun! But how can we make it general (i.e. for brad_1, brand_2, ..., brand_n)?

akrun Over a year ago

@Ketty Sure, we can get all the elements loaded as

mget(ls(pattern = '^brand_\\d+$')) %>% bind_cols %>%  complete(!!! rlang::syms(names(.))) %>%      mutate(all_obj = rowSums(.))

Ronak Shah · Accepted Answer · 2020-12-06 02:56:17Z

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

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