Basin-hopping for global minima in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of basin-hopping on a simple function

What is the output of the following code that uses basin-hopping to find the minimum of a quadratic function?

SciPy

import numpy as np
from scipy.optimize import basinhopping

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

initial_guess = [0, 0]
result = basinhopping(func, initial_guess, niter=10)
print(result.x.round(2))

A [nan, nan]

B [0.0, 0.0]

C [3.0, -1.0]

D [-3.0, 1.0]

💡 Hint

Think about where the quadratic function reaches its lowest value.

The function has a minimum at x=3 and y=-1. Basin-hopping finds this global minimum starting from [0,0].

❓ data_output

intermediate

Number of iterations performed

After running basin-hopping with niter=15 on the function below, how many iterations does the result report?

SciPy

import numpy as np
from scipy.optimize import basinhopping

def func(x):
    return np.sin(x[0]) + (x[1] - 2)**2

result = basinhopping(func, [0, 0], niter=15)
print(result.nit)

A 15

B 14

C 16

D 0

💡 Hint

The nit attribute shows the number of iterations performed.

The niter parameter sets the number of basin-hopping iterations. The result.nit matches this value.

🧠 Conceptual

advanced

Understanding the role of the 'stepsize' parameter

What effect does increasing the 'stepsize' parameter have in the basin-hopping algorithm?

A It decreases the number of iterations performed.

B It increases the size of random jumps, helping escape local minima more easily.

C It changes the function to be minimized.

D It sets the tolerance for convergence.

💡 Hint

Think about how the algorithm explores the search space.

The 'stepsize' controls how far the algorithm jumps randomly to explore new areas, helping to avoid getting stuck.

🔧 Debug

advanced

Identify the error in basin-hopping usage

What error will this code raise when executed?

SciPy

from scipy.optimize import basinhopping

def f(x):
    return x**2

result = basinhopping(f, 5, niter='10')

A No error, runs successfully

B ValueError: initial guess must be an array

C SyntaxError: invalid syntax

D TypeError: 'str' object cannot be interpreted as an integer

💡 Hint

Check the type of the niter parameter.

The niter parameter must be an integer, but a string was passed, causing a TypeError.

🚀 Application

expert

Choosing the best initial guess for basin-hopping

You want to find the global minimum of a function with many local minima. Which initial guess strategy is best to improve basin-hopping results?

A Use multiple random initial guesses and run basin-hopping separately for each.

B Use a fixed initial guess at zero always.

C Use the derivative of the function as the initial guess.

D Use the maximum value of the function as the initial guess.

💡 Hint

Think about how to avoid getting stuck in local minima.

Starting from multiple points increases the chance of finding the global minimum in complex landscapes.