Basin-hopping for global minima in SciPy - Mini Project: Build & Apply

Basin-hopping for Global Minima

📖 Scenario: You are working as a data scientist helping a company find the lowest point of a complex landscape. This is like finding the deepest valley in a mountain range. The company wants to use a smart method called basin-hopping to find the lowest point (global minimum) of a tricky function that has many hills and valleys.

🎯 Goal: Build a Python program that uses scipy.optimize.basinhopping to find the global minimum of a given function. You will first define the function, then set up the basin-hopping configuration, run the algorithm, and finally print the best solution found.

📋 What You'll Learn

Define a function func that takes a list or array x and returns a value.

Create a starting point variable x0 as a list with two numbers.

Set up a basin-hopping configuration variable niter to control the number of iterations.

Use scipy.optimize.basinhopping with func, x0, and niter to find the global minimum.

Print the best solution's coordinates and function value.

💡 Why This Matters

🌍 Real World

Basin-hopping is used in chemistry, physics, and engineering to find the lowest energy states or best solutions in complex problems with many local minima.

💼 Career

Understanding global optimization techniques like basin-hopping is valuable for data scientists working on optimization problems, machine learning model tuning, and scientific computing.

1

Define the function to minimize

Define a function called func that takes a single argument x. Inside, return the value of (x[0] - 1)**2 + (x[1] - 2)**2 + 1. This function represents a simple landscape with a minimum.

SciPy

# Define the function func(x) here
# Your code here

Need a hint?

Remember, x is a list or array with two elements. Use x[0] and x[1] to access them.

2

Set the starting point and iteration count

Create a variable called x0 and set it to the list [0, 0]. Then create a variable called niter and set it to 100. These will be used as the starting point and number of iterations for basin-hopping.

SciPy

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

# Create x0 and niter variables here
# Your code here

Need a hint?

Use a list for x0 with two numbers, and an integer for niter.

3

Run basin-hopping to find the global minimum

Import basinhopping from scipy.optimize. Then run basinhopping with func, x0, and niter as the number of iterations. Store the result in a variable called result.

SciPy

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

x0 = [0, 0]
niter = 100

# Import basinhopping and run it to get result
# Your code here

Need a hint?

Use from scipy.optimize import basinhopping and call basinhopping(func, x0, niter=niter).

4

Print the best solution found

Print the best solution's coordinates using result.x and the function value at that point using result.fun. Use two separate print statements with the exact text: print("Best coordinates:", result.x) and print("Function value:", result.fun).

SciPy

from scipy.optimize import basinhopping

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

x0 = [0, 0]
niter = 100

result = basinhopping(func, x0, niter=niter)

# Print the best coordinates and function value
# Your code here

Need a hint?

Use print("Best coordinates:", result.x) and print("Function value:", result.fun).