optimization algorithm from the "mco" library is not respecting the conditions from the "constraints"

[swaheera]

I am using the R programming language - I am trying to follow the answer from this stackoverflow post (https://stackoverflow.com/questions/68324822/correctly-specifying-logical-conditions-in-r) that shows how to perform "multi objective constrained optimization" using the "mco" library in R.

I created some data for this example:

#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)

I then defined a function ("funct_set") with "4 objectives" (f[1], f[2], f[3], f[4]) which are to be minimized for a set of "seven inputs" ([x1], [x2], [x3], x[4], x[5], x[6], x[7]):

#load libraries
    library(dplyr)
    library(mco)
    
#define function

funct_set <- function (x) {
    x1 <- x[1]; x2 <- x[2]; x3 <- x[3] ; x4 <- x[4]; x5 <- x[5]; x6 <- x[6]; x[7] <- x[7]
    f <- numeric(4)
    
    
    #bin data according to random criteria
    train_data <- train_data %>%
        mutate(cat = ifelse(a1 <= x1 & b1 <= x3, "a",
                            ifelse(a1 <= x2 & b1 <= x4, "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 = ifelse(c1 > x[5],1,0 )))
    
    table_b = data.frame(b_table%>% group_by(cat) %>%
                             mutate(quant = ifelse(c1 > x[6],1,0 )))
    
    table_c = data.frame(c_table%>% group_by(cat) %>%
                             mutate(quant = ifelse(c1 > x[7],1,0 )))
    
    f[1] = -mean(table_a$quant)
    f[2] = -mean(table_b$quant)
    f[3] = -mean(table_c$quant)
    
    
    #group all tables
    
    final_table = rbind(table_a, table_b, table_c)
    # calculate the total mean : this is what needs to be optimized
    
    f[4] = -mean(final_table$quant)
    
    
    return (f);
}

Next, I define a series of 4 "restrictions" (i.e. logical conditions/constrains) used in the optimization:

#define restrictions

restrictions <- function (x) {
    x1 <- x[1]; x2 <- x[2]; x3 <- x[3]; x4 <- x[4]; x5<- x[5] ; x6 <- x[6]; x7 <- x[7]
    restrictions <- logical(4)
    restrictions[1] <- (x3 - x1 >= 0)
    restrictions[2] <- (x4 - x2 >= 0)
    restrictions[3] <- (x7 - x6 >= 0)
 restrictions[4] <- (x6 - x5 >= 0)
    return (restrictions);
}

Finally, I run the optimization algorithm that attempts to simultaneously minimize all 4 objectives with respect to the restrictions:

#run optimization


optimization <- nsga2(funct_set, idim = 7, odim = 4 ,   constraints = restrictions, cdim = 4,
                      
                      generations=150,
                      popsize=100,
                      cprob=0.7,
                      cdist=20,
                      mprob=0.2,
                      mdist=20,
                      lower.bounds=rep(80,80,80,80, 100,200,300),
                      upper.bounds=rep(120,120,120,120,200,300,400)
)

The above code works fine.

Problem : I noticed that in the output of this code, the optimization algorithm is not respecting the restrictions. For example:

https://i.stack.imgur.com/04vBK.png

In the above picture, I have identified some rows where the logical conditions specified in the restrictions are violated.

Does anyone know why this is happening? Have I incorrectly specified the restrictions? Can someone please show me how to fix this?

Thanks