I am working with R.

I have some data ("train_data") below:

```
# create some data for this example
a1 = rnorm(1000,100,10)
b1 = rnorm(1000,100,5)
c1 = sample.int(1000, 1000, replace = TRUE)
train_data = data.frame(a1,b1,c1)
#view data
head(train_data)
a1 b1 c1
1 110.36832 90.66670 662
2 96.28321 102.68244 810
3 101.95640 98.17639 956
4 121.58001 93.04896 697
5 95.08541 104.64527 712
```

In this example, I am interested in performing an arbitrary task:

- Choose 7 random numbers (
`"random_1"`

(between 80 and 120),`"random_2"`

(between "random_1" and 120) ,`"random_3"`

(between 85 and 120),`"random_4"`

(between random_2 and 120),`"split_1"`

(between 0 and 1),`"split_2"`

(between 0 and 1),`"split_3"`

(between 0 and 1 )) - Using these random numbers, perform a series of data manipulation procedures on "train_data" (these data manipulation procedures will be defined in the function below). For a specific set of 7 numbers, these data manipulation procedures will calculate a "total" mean.
- Repeat steps 1) and 2) and see if you can find the set of these 7 numbers that produce the biggest value of the "total" mean.

Thus, I am trying to perform an optimization task.

Earlier, I was able to solve this task using a "random search":

```
# code for random search
results_table <- data.frame()
for (i in 1:10 ) {
#generate random numbers
random_1 = runif(1, 80, 120)
random_2 = runif(1, random_1, 120)
random_3 = runif(1, 85, 120)
random_4 = runif(1, random_3, 120)
#bin data according to random criteria
train_data <- train_data %>% mutate(cat = ifelse(a1 <= random_1 & b1 <= random_3, "a", ifelse(a1 <= random_2 & b1 <= random_4, "b", "c")))
train_data$cat = as.factor(train_data$cat)
#new splits
a_table = train_data %>%
filter(cat == "a") %>%
select(a1, b1, c1, cat)
b_table = train_data %>%
filter(cat == "b") %>%
select(a1, b1, c1, cat)
c_table = train_data %>%
filter(cat == "c") %>%
select(a1, b1, c1, cat)
split_1 = runif(1,0, 1)
split_2 = runif(1, 0, 1)
split_3 = runif(1, 0, 1)
#calculate random quantile ("quant") for each bin
table_a = data.frame(a_table%>% group_by(cat) %>%
mutate(quant = quantile(c1, prob = split_1)))
table_b = data.frame(b_table%>% group_by(cat) %>%
mutate(quant = quantile(c1, prob = split_2)))
table_c = data.frame(c_table%>% group_by(cat) %>%
mutate(quant = quantile(c1, prob = split_3)))
#create a new variable ("diff") that measures if the quantile is bigger tha the value of "c1"
table_a$diff = ifelse(table_a$quant > table_a$c1,1,0)
table_b$diff = ifelse(table_b$quant > table_b$c1,1,0)
table_c$diff = ifelse(table_c$quant > table_c$c1,1,0)
#group all tables
final_table = rbind(table_a, table_b, table_c)
#create a table: for each bin, calculate the average of "diff"
final_table_2 = data.frame(final_table %>%
group_by(cat) %>%
summarize(
mean = mean(diff)
))
#add "total mean" to this table
final_table_2 = data.frame(final_table_2 %>% add_row(cat = "total", mean = mean(final_table$diff)))
#format this table: add the random criteria to this table for reference
final_table_2$random_1 = random_1
final_table_2$random_2 = random_2
final_table_2$random_3 = random_3
final_table_2$random_4 = random_4
final_table_2$split_1 = split_1
final_table_2$split_2 = split_2
final_table_2$split_3 = split_3
final_table_2$iteration_number = i
results_table <- rbind(results_table, final_table_2)
final_results = dcast(setDT(results_table), iteration_number + random_1 + random_2 + random_3 + random_4 + split_1 + split_2 + split_3 ~ cat, value.var = 'mean')
#keep 5 largest resuts
final_results <- head(final_results[order(-total)], 5)
}
```

Now, we can view the results of the random search:

```
#view results
final_results
iteration_number random_1 random_2 random_3 random_4 split_1 split_2 split_3 a b c total
1: 8 104.52182 104.8939 96.63609 99.14640 0.45389635 0.7970865 0.8264969 0.4560440 0.7954545 0.8265306 0.755
2: 10 119.04797 119.9907 93.13250 93.62925 0.27018809 0.5025505 0.6707737 0.2758621 0.5000000 0.6681465 0.632
3: 1 114.69535 117.7922 109.89274 116.39624 0.61857197 0.9609914 0.2661892 0.6180022 0.9615385 0.2702703 0.623
4: 6 85.64905 100.8127 94.02205 106.41212 0.00197946 0.7476889 0.1235777 0.2500000 0.7470588 0.1234568 0.442
5: 3 106.14908 119.7681 95.61753 100.73192 0.20678470 0.1787206 0.7166830 0.2111801 0.1802030 0.7146067 0.423
```

According to the above table (for a very small random search of 10 iterations), the combination of " `random_1, random_2, random_3, random_4, split_1, split_2, split_3`

" = ( 104.52182 104.8939 96.63609 99.14640 0.45389635 0.7970865 0.8264969) produces the highest "total" of 0.755 .

**My Problem:** The "random search" is not a very effective way at solving this problem. I am trying to use a different optimization algorithm to try and identify a set of `random_1, random_2, random_3, random_4, split_1, split_2, split_3`

that produces the biggest value of `total`

.

From the following link (A quick tour of GA), I decided to follow the example for optimizing this problem using an optimization algorithm called the "genetic algorithm":

```
#example of the genetic algorithm
#load library
library(GA)
#define function
Rastrigin <- function(x1, x2)
{
20 + x1^2 + x2^2 - 10*(cos(2*pi*x1) + cos(2*pi*x2))
}
x1 <- x2 <- seq(-5.12, 5.12, by = 0.1)
f <- outer(x1, x2, Rastrigin)
#run optimization algorithm
GA <- ga(type = "real-valued",
fitness = function(x) -Rastrigin(x[1], x[2]),
lower = c(-5.12, -5.12), upper = c(5.12, 5.12),
popSize = 50, maxiter = 1000, run = 100)
#view results of the genetic algorithm (the answer that optimizes the function in this example is (x1 = 5.4 e-05, x2 = 6.400 e-05)
summary(GA)
x1 x2
[1,] 5.41751e-05 6.400989e-05
```

I now want to apply the "genetic algorithm" to my problem. This requires the user to define a "fitness function" that formalizes the requirements and directions for the "genetic algorithm". For my problem, I defined the "fitness function" as follows:

```
#define fitness function
fitness <- function(random_1, random_2, random_3, random_4, split_1, split_2, split_3) {
#bin data according to random criteria
train_data <- train_data %>% mutate(cat = ifelse(a1 <= random_1 & b1 <= random_3, "a", ifelse(a1 <= random_2 & b1 <= random_4, "b", "c")))
train_data$cat = as.factor(train_data$cat)
#new splits
a_table = train_data %>%
filter(cat == "a") %>%
select(a1, b1, c1, cat)
b_table = train_data %>%
filter(cat == "b") %>%
select(a1, b1, c1, cat)
c_table = train_data %>%
filter(cat == "c") %>%
select(a1, b1, c1, cat)
split_1 = runif(1,0, 1)
split_2 = runif(1, 0, 1)
split_3 = runif(1, 0, 1)
#calculate quantile ("quant") for each bin
table_a = data.frame(a_table%>% group_by(cat) %>%
mutate(quant = quantile(c1, prob = split_1)))
table_b = data.frame(b_table%>% group_by(cat) %>%
mutate(quant = quantile(c1, prob = split_2)))
table_c = data.frame(c_table%>% group_by(cat) %>%
mutate(quant = quantile(c1, prob = split_3)))
#create a new variable ("diff") that measures if the quantile is bigger tha the value of "c1"
table_a$diff = ifelse(table_a$quant > table_a$c1,1,0)
table_b$diff = ifelse(table_b$quant > table_b$c1,1,0)
table_c$diff = ifelse(table_c$quant > table_c$c1,1,0)
#group all tables
final_table = rbind(table_a, table_b, table_c)
# calculate the total mean : this is what needs to be optimized
mean = mean(final_table$diff)
}
```

Just to test that this function works:

```
#call function for a specific set of the 7 numbers
a = fitness(85, 100, 90, 110, 0.5, 0.7, 0.3)
# view the corresponding "total mean"
a
[1] 0.845
```

Now, I am trying to put everything together and instruct the "genetic algorithm" to optimize the "fitness function" I defined by considering different ranges of values for `"random_1, random_2, random_3, random_4, split_1, split_2, split_3"`

#genetic algorithm for my example:

```
GA <- ga(type = "real-valued",
fitness = fitness,
lower = c(80, 80, 80, 80, 0,0,0), upper = c(120, 120, 120, 120, 1,1,1),
popSize = 50, maxiter = 1000, run = 100)
```

But this produces the following error:

```
Error: Problem with `mutate()` column `cat`.
i `cat = ifelse(...)`.
x argument "random_3" is missing, with no default
Run `rlang::last_error()` to see where the error occurred.
In addition: Warning message:
Error: Problem with `mutate()` column `cat`.
i `cat = ifelse(...)`.
x argument "random_3" is missing, with no default
Run `rlang::last_error()` to see where the error occurred.
```

Does anyone know why this error is being produced? Can someone please show me what I am doing wrong?

Thanks