Optimization

Taufiq Luthfi Nurrohim

2023-12-08

library(mosaicCalc)

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Di artikel ini kita akan membahas apa itu Optimization. Optimization adalah proses mencari nilai minimum atau maksimum dari suatu fungsi. Nilai minimum atau maksimum ini disebut sebagai nilai optimal. Optimization sering digunakan dalam berbagai bidang, seperti ekonomi, teknik, ilmu alam, dan lainnya, untuk menyelesaikan masalah yang melibatkan biaya, keuntungan, efisiensi, keseimbangan, dan sebagainya.

Salah satu fungsi yang dapat Kita gunakan untuk Optimization adalah optimize (). Fungsi ini memungkinkan Kita untuk mencari nilai minimum atau maksimum dari suatu fungsi dalam suatu interval. Kita perlu memberikan tiga argumen ke fungsi optimize (): fungsi yang ingin dioptimalkan, interval pencarian, dan apakah Kita ingin mencari nilai minimum atau maksimum.

# Langkah 1: Mendefinisikan fungsi yang ingin dioptimalkan
f <- function(x) { x^3 - 6*x^2 + 9*x - 4 }

# Langkah 2: Mencari nilai minimum dan maksimum fungsi f di interval [-1, 4]
x <- seq(-1, 4, length.out = 1000)
y <- f(x)
min_f_x <- x[which.min(y)]
min_f_y <- min(y)
max_f_x <- x[which.max(y)]
max_f_y <- max(y)

# Langkah 3: Menampilkan hasil Optimization
cat("Minimum:", min_f_x, "f(min) =", min_f_y, "\n")

## Minimum: -1 f(min) = -20

cat("Maksimum:", max_f_x, "f(max) =", max_f_y, "\n")

## Maksimum: 4 f(max) = 0

# Langkah 4: Membuat plot fungsi f
plot(x, y, type = "l", xlim = c(min_f_x - 1, 4), ylim = c(min_f_y - 2, max_f_y + 2))
points(min_f_x, min_f_y, col = "black", pch = 19)
points(max_f_x, max_f_y, col = "deeppink", pch = 19)
text(min_f_x, min_f_y - 1, "Min", col = "black")
text(max_f_x, max_f_y + 1, "Max", col = "deeppink")