MRR optimization subject to roughness constraint learning 2

Loading libraries, defining experimental design, and getting measurement results.

The same as done previously.

   fza  fzt vc       lc       Ra
1 0.50 0.10 40 emulsion 1.915556
2 1.25 0.10 40 emulsion 3.515556
3 0.50 0.20 40 emulsion 1.065556
4 1.25 0.20 40 emulsion 1.965556
5 0.50 0.15 20 emulsion 1.765556
6 1.25 0.15 20 emulsion 3.265556

SVR radial model

normalized_rec <- 
  recipe(Ra ~ ., data = plan_train) %>% 
  step_normalize(fza,fzt,vc) %>%
  step_dummy(all_nominal_predictors())

svm_r_spec <- 
  svm_rbf(cost = 3.17, rbf_sigma = 0.0774) %>% 
  set_engine("kernlab") %>% 
  set_mode("regression")

svm_wflow <- 
  workflow() %>%
    add_model(svm_r_spec) %>%
  add_recipe(normalized_rec)

svm_final_fit <- fit(svm_wflow, data = plan_train)

augment(svm_final_fit, new_data = plan_test) %>%
  rsq(truth = Ra, estimate = .pred)

# A tibble: 1 × 3
  .metric .estimator .estimate
  <chr>   <chr>          <dbl>
1 rsq     standard       0.894

augment(svm_final_fit, new_data = plan_test) %>%
  rmse(truth = Ra, estimate = .pred)

# A tibble: 1 × 3
  .metric .estimator .estimate
  <chr>   <chr>          <dbl>
1 rmse    standard       0.300

svm_fit <- svm_final_fit %>% 
  extract_fit_parsnip()

svm_fit 

parsnip model object

Support Vector Machine object of class "ksvm" 

SV type: eps-svr  (regression) 
 parameter : epsilon = 0.1  cost C = 3.17 

Gaussian Radial Basis kernel function. 
 Hyperparameter : sigma =  0.0774 

Number of Support Vectors : 23 

Objective Function Value : -19.2442 
Training error : 0.169076 

Optimization of material removal rate with Ra contraint learning

First MRR function is defined.

MRR <- function(x){

  z <- 2
  Db <- 25
  Dt <- 14
  Dh <- Db-Dt
  
  f1 <- 250*z*(Db^3/(Dh*Dt))*x[3]*((x[1]*10^-3)/x[2])*sqrt((x[1]*10^-3)^2 + (x[2]*Dh/Db)^2)
  
  return(f1)
} 

Writing Cubist constraint. Change lc ("emulsion" or "mql") as desired.

g1 <- function(x) {
  g1 <- predict(svm_final_fit, new_data = data.frame(fza = x[1], 
                                                     fzt = x[2],
                                                     vc = x[3],
                                                     lc = "emulsion")) - (2 - 0.4441)
  
    return(g1)
}

Testing objective function and constraint.

x_test <- c(0.875, 0.15, 40)
MRR(x_test)

[1] 781.3187

g1(x_test)

      .pred
1 0.4580388

Fitness function considering Objective function and penalty term regarding constraint.

fitness <- function(x) 
{ 
  f <- MRR(x)                        
  pen <- sqrt(.Machine$double.xmax)  # penalty term
  penalty1 <- max(g1(x),0)*pen       # penalisation for 1st inequality constraint
  f - penalty1                       # fitness function value
}

Defining algorithims to the optimization.

ALGOS <- c("ALO", "DA", "GWO", "MFO", "WOA")
  
#  c("ABC", "ALO", "BA", "BHO", "CLONALG", "CS", "CSO", "DA", "DE", "FFA", "GA", "GBS", "GOA", "GWO", "HS", "KH", "MFO", "PSO", "SCA", "SFL", "WOA")

# Convergiram:
# "ABC", "ALO", "DA", "DE", "GWO", "MFO", "PSO", "WOA"

# Tempo satisfatorio entre os que convergiram:
# "ALO", "DA", "GWO", "MFO", "WOA"

Optimization.

result_meta

$result
         var1 var2 var3
ALO 0.9102454  0.2   60
DA  0.9102454  0.2   60
GWO 0.9100841  0.2   60
MFO 0.9102454  0.2   60
WOA 0.9102452  0.2   60

$optimumValue
    optimum_value
ALO      1219.144
DA       1219.144
GWO      1218.928
MFO      1219.144
WOA      1219.144

$timeElapsed
     user system elapsed
ALO 59.65   1.53   61.80
DA  55.92   1.42   57.70
GWO 58.91   1.77   61.05
MFO 57.36   1.81   59.63
WOA 59.11   1.47   61.14