Cfrgtkky

[edited] I compiled this code for an Operations Research class. I ended up submitting another format that relied on R packages; however, I feel that I am close to a functioning algorithm.

I derived this code from another R program I complied for the 'Golden Search' algorithm. That program conducted 'bracket' searches until it found the optimal min/max. Each time I run this algorithm, it fails to conduct a 'bracket' search. After multiple hours, I have failed to find the issue. Any help finding the error in my code would be appreciated.

My submitted (and confirmed) algorithm returned a minimum (x) value of 0.8095 with a f(x) value of -24.3445 utilizing a Fibonacci search method.

# Step One: Initialization



## Input user-defined function

f = function(x)

{

  (x^4)-(14*(x^3))+(60*(x^2))-(70*(x))

}



## Input user-defined parameters

Lb <- 0 ### Lower Bound

Ub <- 2 ### Upper Bound

Tl <- .3 ### Tolerance



n <- (Ub-Lb)/Tl

n<- as.integer(n)



fibonacci.search = function(f, lower.bound, upper.bound, tolerance)

{

  iteration = 0



  Fn = fibonacci(n, sequence = FALSE)



    ### Use the fibonacci ratios to set the initial test points



  x1 = lower.bound + ((fib(n-2)/fib(n)) * (upper.bound - lower.bound))

  x2 = lower.bound + ((fib(n-1)/fib(n)) * (upper.bound))



  ### Evaluate the function at the test points

  f1 = f(x1)

  f2 = f(x2)



  while ((lower.bound - upper.bound) > tolerance)

  {

    iteration = iteration + 1

    n = n - 1

    cat('', 'n')

    cat('Iteration #', iteration, 'n')

    cat('f1 =', f1, 'n')

    cat('f2 =', f2, 'n')



    if (f1 < f2)

    {

      cat('f(x1) < f(x2)', 'n')

      # If f(x1) < f(x2), then the new interval is [x1,b]:

      # a becomes the previous x1, b does not change



      lower.bound = x1

      upper.bound = upper.bound



      # x1 becomes the previous x2, n = n-1



      x1 = x2

      f1 = f2



      cat('New Upper Bound =', upper.bound, 'n')

      cat('New Lower Bound =', lower.bound, 'n')

      cat('New Upper Test Point = ', x1, 'n')



      ### Find the new x2 using the formula in Step2.

      x2 = lower.bound + (fib(n-1)/fib(n)) * (upper.bound)

      cat('New Lower Test Point = ', x1, 'n')

      f2 = f(x2)

    } 

    else 

    {

      cat('f(x1) > f(x2)', 'n')

      # If f(x1) > f(x2), then the new interval is [a,x2]:

      # a does not change, b becomes the previous x2



      upper.bound = x2

      lower.bound = lower.bound



      # x2 becomes the previous x1, n = n-1



      x2 = x1

      f2 = f1 



      cat('New Upper Bound =', upper.bound, 'n')

      cat('New Lower Bound =', lower.bound, 'n')

      cat('New Lower Test Point = ', x1, 'n')



      # Find the new x1 using the formula in Step2.

      x1 = lower.bound + (fib(n-2)/fib(n)) * (upper.bound - lower.bound)

      cat('New Upper Test Point = ', x2, 'n')

      f1 = f(x1)

    }

  }



  ### Use the mid-point of the final interval as the estimate of the optimzer

  cat('', 'n')

  cat('Final Lower Bound =', lower.bound, 'n')

  cat('Final Upper Bound =', upper.bound, 'n')

  estimated.minimizer = (lower.bound + upper.bound)/2

  cat('Estimated Minimum Value (x) =', estimated.minimizer, 'n')

  cat('Estimated F(x)', f(estimated.minimizer),'n')



  # Step Three: Results



  ## Plot the curve of the user-defined function

  curve(f, from = Lb, to = Ub, main = expression("(x^4)-(14*(x^3))+(60*(x^2))-(70*(x))"))



  ## Plot the solution as a point

  points(estimated.minimizer, f(estimated.minimizer), col="red", pch=19) 



  ## Draw a square around the optima to highlight it

  rect(estimated.minimizer-0.1, f(estimated.minimizer)-01, estimated.minimizer+0.1, f(estimated.minimizer)+01, lwd=2)

}



# Step Two: Loop Function

fibonacci.search(f, Lb, Ub, Tl)