Global optimization (differential_evolution) in SciPy - Mini Project: Build & Apply

Global Optimization with Differential Evolution

📖 Scenario: You are working as a data scientist helping a company find the best settings for a machine to minimize its error. The error depends on two settings, and you want to find the lowest error possible.

🎯 Goal: Build a program that uses the differential_evolution method from scipy.optimize to find the minimum value of a given error function within specified bounds.

📋 What You'll Learn

Create a function error_function that takes a list of two variables and returns a calculated error.

Define the bounds for each variable as a list of tuples.

Use differential_evolution from scipy.optimize to find the minimum error.

Print the result showing the best variables and the minimum error.

💡 Why This Matters

🌍 Real World

Global optimization helps find the best settings or parameters in engineering, finance, and machine learning when the problem has many possible solutions.

💼 Career

Data scientists and engineers use global optimization methods like differential evolution to improve models, tune parameters, and solve complex problems that simple methods cannot handle.

1

Define the error function

Create a function called error_function that takes a single argument x (a list of two numbers). Inside the function, calculate the error as (x[0] - 3) ** 2 + (x[1] + 1) ** 2 and return this value.

SciPy

# Define the error_function that calculates (x[0] - 3)**2 + (x[1] + 1)**2
# Your code here

Need a hint?

Remember, the function must take one argument x and return the calculated error.

2

Set the bounds for variables

Create a variable called bounds and set it to a list of two tuples: (-10, 10) for the first variable and (-5, 5) for the second variable.

SciPy

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

# Define bounds for x[0] and x[1]
# Your code here

Need a hint?

Bounds must be a list of tuples specifying the minimum and maximum for each variable.

3

Use differential_evolution to find minimum

Import differential_evolution from scipy.optimize. Then create a variable called result and assign it the output of calling differential_evolution with error_function and bounds as arguments.

SciPy

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

bounds = [(-10, 10), (-5, 5)]

# Import differential_evolution and find the minimum
# Your code here

Need a hint?

Use from scipy.optimize import differential_evolution and call it with the function and bounds.

4

Print the optimization result

Write a print statement that outputs the best variables found and the minimum error value from result. Use result.x for the variables and result.fun for the minimum error.

SciPy

from scipy.optimize import differential_evolution

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

bounds = [(-10, 10), (-5, 5)]

result = differential_evolution(error_function, bounds)

# Print the best variables and minimum error
# Your code here

Need a hint?

Use print(f"Best variables: {result.x}") and print(f"Minimum error: {result.fun}").