Global optimization (differential_evolution) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of differential_evolution on a simple function

What is the output of the following code snippet using scipy.optimize.differential_evolution to minimize a simple quadratic function?

SciPy

from scipy.optimize import differential_evolution

func = lambda x: (x[0] - 3)**2 + (x[1] + 1)**2
bounds = [(-5, 5), (-5, 5)]
result = differential_evolution(func, bounds, seed=42)
print((round(result.x[0], 2), round(result.x[1], 2)))

A (3.0, -1.0)

B (-3.0, 1.0)

C (0.0, 0.0)

D (5.0, -5.0)

💡 Hint

Recall that differential_evolution tries to find the minimum of the function within the given bounds.

The function is minimized at x=3 and y=-1, so the output is (3.0, -1.0).

❓ data_output

intermediate

Number of iterations in differential_evolution result

After running differential_evolution on the Rosenbrock function with bounds [(-2, 2), (-1, 3)], what is the value of result.nit (number of iterations)?

SciPy

from scipy.optimize import differential_evolution

def rosenbrock(x):
    return (1 - x[0])**2 + 100*(x[1] - x[0]**2)**2

bounds = [(-2, 2), (-1, 3)]
result = differential_evolution(rosenbrock, bounds, seed=0)
print(result.nit)

A 25

B 15

C 20

D 11

💡 Hint

Check the nit attribute of the result object.

The differential_evolution algorithm converges in 11 iterations for this setup and seed.

🔧 Debug

advanced

Identify the error in differential_evolution usage

What error will the following code raise when trying to run differential_evolution?

SciPy

from scipy.optimize import differential_evolution
import math

def f(x):
    return math.pow(x, 2)

bounds = [(-1, 1)]
result = differential_evolution(f, bounds)
print(result.fun)

A No error, prints 0.0

B TypeError: only size-1 arrays can be converted to Python scalars

C AttributeError: 'OptimizeResult' object has no attribute 'fun'

D ValueError: x must be a 1-D array

💡 Hint

Check how the function f expects its input and what differential_evolution passes.

The function f expects a scalar but differential_evolution passes an array, causing a TypeError.

🧠 Conceptual

advanced

Understanding differential_evolution parameters

Which parameter of scipy.optimize.differential_evolution controls the mutation constant that influences the differential weight in the algorithm?

A recombination

B popsize

C mutation

D tol

💡 Hint

Mutation controls the differential weight in the mutation step.

The 'mutation' parameter sets the mutation constant, which controls the differential weight in the algorithm.

🚀 Application

expert

Global minimum found by differential_evolution on a noisy function

Given the noisy function f(x) = (x[0]-2)^2 + (x[1]+3)^2 + noise where noise is a small random value, which of the following is the closest output of result.x after running differential_evolution with bounds [(-5,5), (-5,5)] and seed=1?

SciPy

import numpy as np
from scipy.optimize import differential_evolution

np.random.seed(1)
noise = lambda: np.random.normal(0, 0.1)

def f(x):
    return (x[0]-2)**2 + (x[1]+3)**2 + noise()

bounds = [(-5, 5), (-5, 5)]
result = differential_evolution(f, bounds, seed=1)
print((round(result.x[0], 1), round(result.x[1], 1)))

A (2.0, -3.0)

B (1.0, -3.0)

C (2.0, -2.0)

D (0.0, 0.0)

💡 Hint

The noise is small, so the optimizer should find a point close to the true minimum (2, -3).

Despite noise, differential_evolution finds a point close to (2, -3), the true minimum of the noiseless function.