Optimasi tanpa kendala

Pengantar Optimasi di Python

Jasmin Ludolf

Content Developer

Apa itu optimasi tanpa kendala?

Mencari maksimum atau minimum fungsi tanpa kendala pada variabel input

SciPy

Grafik tren positif dengan panah ke atas

Optimasi univariat tanpa kendala

from scipy.optimize import minimize_scalar


def objective_function(x): 
  return x**2 - 12*x + 4


result = minimize_scalar(objective_function) 
print(result)

     fun: -32.0
 message: 'Optimization terminated successfully; The
 returned value satisfies the termination criteria 
 (using xtol = 1.48e-08 )'
    nfev: 10
     nit: 4
 success: True
       x: 6.000000000000001

Grafik 2 * x**2 - 3 * x + 1

Hasil optimasi univariat tanpa kendala

     fun: -32.0
 message: 'Optimization terminated successfully; The
 returned value satisfies the termination criteria 
 (using xtol = 1.48e-08 )'
    nfev: 10
     nit: 4
 success: True
       x: 6.000000000000001

result.x

6.000000000000001

fun: nilai fungsi pada minimum
message: status
nfev: jumlah evaluasi fungsi oleh algoritma
nit: jumlah iterasi hingga solusi tercapai
success: boolean apakah optimum ditemukan
x: nilai optimal

Menemukan nilai maksimum

Masalah maksimisasi digambarkan.

def objective_function(x): 
  return 40 * q - 0.5 * q**2

-1*(40 * q - 0.5 * q**2)
-40 * q + 0.5 * q**2

def negated_function(x): 
  return -40 * q + 0.5 * q**2
result = minimize_scalar(negated_function) 
print(f"The maximum is {result.x:.2f} in two 
      decimals")

The maximum is 40.00 in two decimals

Optimasi multivariat tanpa kendala

from scipy.optimize import minimize


def objective_function(a): 
  return (a[0] - 2)**2 + (a[1] - 3)**2 + 1.5


x0 = [1, 2]

result = minimize(objective_function, x0)

a[0] mewakili x dan a[1] mewakili y

Hasil optimasi multivariat tanpa kendala

print(result)
print(f"minimum is (x, y) = ({result.x[0]:.2f}, {result.x[1]:.2f}) in two decimals.")

      fun: 1.5000000000000002

 hess_inv: array([[ 0.75, -0.25],
       [-0.25,  0.75]])

      jac: array([0., 0.])

  message: 'Optimization terminated successfully.'
     nfev: 9
      nit: 2
     njev: 3

   status: 0

  success: True
        x: array([1.99999999, 2.99999999])
minimum is (x, y) = (2.00, 3.00) in two decimals.

Ayo berlatih!

Pengantar Optimasi di Python