function - R: x 'probs' outside [0,1]

Question

I am using the R programming language.

I am trying to follow the instructions from the "optimization" package in R (https://cran.r-project.org/web/packages/optimization/optimization.pdf) and use functions from this package on a specific function.

For this example, I first generate some random data:

#load libraries
library(dplyr)


# 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)

From here, I define the function that I want to optimize ("fitness"). This function takes 7 inputs and calculates a "total" mean (a single scalar value). The inputs required for this function are:

• "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 )

The function to optimize is defined as follows:

library(optimization)

fitness <- function(x) {
  #bin data according to random criteria
  train_data <- train_data %>% 
                 mutate(cat = ifelse(a1 <= x[1] & b1 <= x[3], "a", 
                               ifelse(a1 <= x[2] & b1 <= x[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)
    
   
    
    #calculate  quantile ("quant") for each bin
    
    table_a = data.frame(a_table%>% group_by(cat) %>%
                             mutate(quant = quantile(c1, prob = x[5])))
    
    table_b = data.frame(b_table%>% group_by(cat) %>%
                             mutate(quant = quantile(c1, prob = x[6])))
    
    table_c = data.frame(c_table%>% group_by(cat) %>%
                             mutate(quant = quantile(c1, prob = x[7])))
    
    
    
    
    #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)
    
    
}

From here, I am trying to run the following optimization function:

Output <- optim_nm(fitness, k = 7, trace = TRUE)

plot(output)
 plot(Output, 'contour')

But these return the following errors:

 Error: Problem with `mutate()` column `quant`.
i `quant = quantile(c1, prob = x[6])`.
x 'probs' outside [0,1]
Run `rlang::last_error()` to see where the error occurred. 

Error in plot(Output) : object 'Output' not found

I think error is that the "split_1", "split_2" and "split_3" variables are being assigned values outside of 0 and 1 : since the function is using these variables are used to calculate percentiles (e.g. quant = quantile(c1, prob = x[5] ) , this will naturally result in an error?

I tried to use another optimization algorithm from this package where the ranges for these 7 inputs are explicitly defined, but this is also producing the same error :

ro_sa <- optim_sa(fun = fitness,
start = c(runif(7, min = -1, max = 1)),
lower = c(80,80,80,80,0,0,0),
upper = c(120,120,120,120,1,1,1),
trace = TRUE,
control = list(t0 = 100,
nlimit = 550,
t_min = 0.1,
dyn_rf = FALSE,
rf = 1,
r = 0.7
)
)

 Error: Problem with `mutate()` column `quant`.
i `quant = quantile(c1, prob = x[6])`.
x 'probs' outside [0,1]

This also doesn't work if you provide an initial starting point:

optim_nm(fitness, start = c(80,80,80,80,0.5,0.6,0.7))

 Error: Problem with `mutate()` column `quant`.
i `quant = quantile(c1, prob = x[5])`.
x 'probs' outside [0,1]
i The error occurred in group 1: cat = a.

Question: Can someone please show me how to fix this, so that I can run the optimization functions?

#desired functions to run:

Output <- optim_nm(fitness, k = 7, trace = TRUE)

plot(output)
 plot(Output, 'contour')

ro_sa <- optim_sa(fun = fitness,
start = c(runif(7, min = -1, max = 1)),
lower = c(80,80,80,80,0,0,0),
upper = c(120,120,120,120,1,1,1),
trace = TRUE,
control = list(t0 = 100,
nlimit = 550,
t_min = 0.1,
dyn_rf = FALSE,
rf = 1,
r = 0.7
)
)

optim_nm(fitness, start = c(80,80,80,80,0.5,0.6,0.7))

Thanks

Answer 1

The x values generated are random and they can be positive or negative. probs argument of quantile needs to have values between 0 and 1. One way would be to take the absolute value of x[5:7] and turn them to ratio using prop.table.

x[5:7] <- prop.table(abs(x[5:7]))

Complete function -

library(optimization)

fitness <- function(x) {
  #bin data according to random criteria
  train_data <- train_data %>% 
    mutate(cat = ifelse(a1 <= x[1] & b1 <= x[3], "a", 
                        ifelse(a1 <= x[2] & b1 <= x[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)
  
  
  x[5:7] <- prop.table(abs(x[5:7]))
  
  #calculate  quantile ("quant") for each bin
  
  table_a = data.frame(a_table%>% group_by(cat) %>%
                         mutate(quant = quantile(c1, prob = x[5])))
  
  table_b = data.frame(b_table%>% group_by(cat) %>%
                         mutate(quant = quantile(c1, prob = x[6])))
  
  table_c = data.frame(c_table%>% group_by(cat) %>%
                         mutate(quant = quantile(c1, prob = x[7])))
  
  
  #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) 
}

You can apply and plot this function -

Output <- optim_nm(fitness, k = 7, trace = TRUE)
plot(Output)