Multi Objective Optimization

[swaheera]

Hello!

Using the "ParBayesianOptimization" package, it possible to use this package for "multi objective optimization" (e.g. optimize several cost functions together)?

For example, below I have included an example of multi-objective optimization using an algorithm called "particle swarm optimization":

#Load library:
library(mopsocd)

#load libraries
library(dplyr)


# create some data for this example
a1 = rnorm(1000,100,10)
b1 = rnorm(1000,100,10)
c1 = sample.int(1000, 1000, replace = TRUE)
train_data = data.frame(a1,b1,c1)

#define function:

funct_set <- 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 = 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 )))
    
    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)
    
    #multiple functions are being optimized 
    return (c(f1, f2, f3, f4));
}

#constraints (I know this is not currently possible in ParBayesianOptimization)
  gn <- function(x) {
    g1 <- x[2] - x[1] > 0.0
    g2 <- x[4] - x[3] > 0.0
    g3 <- x[7] - x[6] >0
    g4<- x[6] - x[5] >0
    return(c(g1,g2,g3, g4))
}

## Set Arguments/Bounds 

varcount <- 7
fncount <- 4
lbound <- c(80,90,80,90,100, 200, 300)
ubound <- c(90,110,90,110,200, 300, 500)
optmin <- 0



#optimization of multiple cost functions
ex1 <- mopsocd(funct_set,gn, varcnt=varcount,fncnt=fncount,
               lowerbound=lbound,upperbound=ubound,opt=optmin)

Would it be possible to solve a similar style problem (i.e. optimization of multiple objective functions) using the ParBayesianOptimization library?

Thanks so much!

[AnotherSamWilson]

Feel free to send a pull request with the changes, but I don't think this is something I would implement myself.