Final Answer from mlrMBO outside of the specified variable ranges (multi objective function) about mlrmbo HOT 2 OPEN

library(mlrMBO)
library(dplyr)
library(ParamHelpers)

a1 = rnorm(1000,100,10)
b1 = rnorm(1000,100,9)
c1 = sample.int(1000, 1000, replace = TRUE)
train_data = data.frame(a1,b1,c1)


obj.fun = makeMultiObjectiveFunction(
    name = "Some function",
    fn = function(x1,x2,x3,x4) {
        #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 > 150,1,0 )))
        
        table_b = data.frame(b_table%>% group_by(cat) %>%
                                 mutate(quant = ifelse(c1 > 300,1,0 )))
        
        table_c = data.frame(c_table%>% group_by(cat) %>%
                                 mutate(quant = ifelse(c1 > 400,1,0 )))
        
        f1 = mean(table_a$quant)
        f2 = mean(table_b$quant)
        f3 = 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
        
        f4 = mean(final_table$quant)
        
        
        return (f1, f2, f3, f4);
    },
    par.set = makeParamSet(
        makeNumericParam("x1", lower = 80, upper = 90),
        makeNumericParam("x2", lower = 95, upper = 110),
        makeNumericParam("x3", lower = 80, upper = 90),
        makeNumericParam("x4", lower = 95, upper = 110),
        forbidden = expression(x2 >x1 & x4 >x3)
    ),
    minimize = TRUE
)

ctrl = makeMBOControl()
ctrl = setMBOControlTermination(ctrl, iters = 20L)

# we can basically do an exhaustive search in 3 values
ctrl = setMBOControlInfill(ctrl, crit = makeMBOInfillCritEI())
# opt.restarts = 1L, opt.focussearch.points = 3L, opt.focussearch.maxit = 1L)

#design = generateDesign(20L, getParamSet(obj.fun), fun = lhs::maximinLHS)

lrn = makeMBOLearner(ctrl, obj.fun)

res = mbo(obj.fun, design = NULL, learner = lrn, control = ctrl, show.info = TRUE)