Testing Results of dfoptim::nmkb (version 2018.2-1)

nmkb_debug.R

library(dfoptim)
fopt <- "dfoptim"

# Choose objective function  ----
rosbkext <- function(x) {
  # Extended Rosenbrock function
  n <- length(x)
  sum (100*(x[1:(n-1)]^2 - x[2:n])^2 + (x[1:(n-1)] - 1)^2)
}
# moved rastrigin by 1 so that the global optimum is at rep(1, 6)
rastrigin <- function(x) 10*length(x) + sum((x-1)^2 - 10*cos(1*pi*(x-1))) 
# EDIT HERE:
f <- rastrigin
fs <- "rastrigin"

# Activate output ----
con <- file(paste0("./test/", fs, "_", fopt, ".txt"))
sink(con, append=TRUE)
sink(con, append=TRUE, type="message")

# Run! ----
df <- data.frame()
np <- 6
loops <- 5E3

print(paste(fs, fopt, sep = "-"))
print(date())

for (box in c(0, 2, 4, 12, 24, 32, 64, 128)) {
  #set.seed(123)
  for(trial in 1:loops) {
    p0 <- rnorm(np)
    p0[p0 > +2] <- +2 - 1E-8
    p0[p0 < 0] <- 0 + 1E-8
    
    ctrl <- list(maxfeval = 5E4)
    if(box == 0) {
      o  <- nmk(fn = f, par = p0, control = ctrl)
    } else {
      tryCatch( {
        o <- nmkb(fn = f, par = p0, lower = 0, upper = +box, control = ctrl)
      }, error = function(e) {
        o <<- list(convergence = 666, value = NA, par = rep(0, np), message = e$message)
        #print(paste("Crash:", e$message))
      },
      warning = function(e) print(paste("Warn:", e$message))
      )
    }
    df <- rbind(df, list(box, 
                         ifelse(o$convergence == 0,  o$value < 1e-6, NA), 
                         o$convergence,
                         ifelse(box == 0, FALSE, (any(o$par < 0) | any(o$par > box)))
    ))
  }
}

# Wrap up ----
names(df) <- c("Box", "GlobalOpt", "ExitCode", "OOB")
df$Box <- as.factor(df$Box)

result <- table(df[1:2], useNA = "ifany")
colnames(result) <- c("Local", "Global", "NotConverged")

oob <- table(df[c("Box", "OOB")], dnn = c("OOB"))
if(ncol(oob) == 1) colnames(oob) <- "InBounds" else colnames(oob) <- c("InBounds", "OoB")
result <- cbind( result, oob )

crash <- table(df[c("Box", "ExitCode")], dnn = c("Error"))
x <- matrix(c("0", "Success", "1", "FEval", "2", "Stagnation", "666", "Error"), byrow = TRUE, ncol=2)
colnames(crash) <- x[match(colnames(crash), x[,1]),2]
result <- cbind( result, crash )

if (any(df$OOB >= .Machine$double.eps)) print("Out of bounds detected")

save(df, result, file=paste0("./test/", fs, "_", fopt, ".RData"))

warnings()

# Close output ----
sink()
sink(type="message")

rastrigin_results_dfoptim_nmkb.txt

Result of 5000 runs of the Nelder-Mead implementation in dfoptim using a slightly modified rastrigin function.

Box  Local Global NotConverged InBounds Success Stagnation Error
0    3020   1980            0     5000    5000          0     0
2    3440     54         1506     5000    3494       1049   457
4    3643     18         1339     5000    3661        983   356
12   4036     45          919     5000    4081        913     6
24   4180     44          776     5000    4224        772     4
32   4263     37          700     5000    4300        594   106
64   4515     51          434     5000    4566        429     5
128  4650     50          300     5000    4700        293     7

All cells show counts. The "Box" column shows the size of the box constraint `x in (0, box)`.
* Local = result of optimisation was a local minimum
* Global = result was the global minimum
* NotConverged = algorithm did not converge at all
* InBounds = Results were inside the specified box constraint
* Success = algorithm terminated with success (exit code 0)
* Stagnation = reason for termination is "stagnation" (exit code 2)
* Error = function crashed with an error message "system is exactly singular"

rosenbrock_results_dfoptim_nmkb.txt

Result of 5000 runs of the Nelder-Mead implementation in dfoptim using a rosenbrock function.

Box Local Global NotConverged InBounds Success Stagnation Error
0     332   4668            0     5000    5000          0     0
2    4569     40          391     5000    4609        362    29
4    4781     50          169     5000    4831        169     0
12   4913     32           55     5000    4945         54     1
24   4959     23           18     5000    4982         18     0
32   4965     26            9     5000    4991          9     0
64   4977     21            2     5000    4998          2     0
128  4982     18            0     5000    5000          0     0

All cells show counts. The "Box" column shows the size of the box constraint `x in (0, box)`.
* Local = result of optimisation was a local minimum
* Global = result was the global minimum
* NotConverged = algorithm did not converge at all
* InBounds = Results were inside the specified box constraint
* Success = algorithm terminated with success (exit code 0)
* Stagnation = reason for termination is "stagnation" (exit code 2)
* Error = function crashed with an error message "system is exactly singular"