Simulated annealing (dual_annealing) in SciPy

Introduction

Simulated annealing helps find the best answer when there are many possibilities. It tries different solutions and slowly focuses on the best one.

Finding the lowest cost route for delivery trucks.

Optimizing machine settings to get the best product quality.

Tuning parameters in a model when many options exist.

Scheduling tasks to finish work faster with limited resources.

Syntax

SciPy

from scipy.optimize import dual_annealing

result = dual_annealing(func, bounds)

# func: function to minimize
# bounds: list of (min, max) tuples for each variable

The func should take a list or array and return a number to minimize.

bounds define the search space for each variable.

Examples

Minimize a simple function with two variables between -5 and 5.

SciPy

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

bounds = [(-5, 5), (-5, 5)]
result = dual_annealing(f, bounds)
print(result.x, result.fun)

Minimize the sphere function in 3D space.

SciPy

def sphere(x):
    return sum(xi**2 for xi in x)

bounds = [(-10, 10)] * 3
result = dual_annealing(sphere, bounds)
print(result.x, result.fun)

Sample Program

This program finds the minimum of a simple 2D function using simulated annealing. It searches between -10 and 10 for both variables.

SciPy

from scipy.optimize import dual_annealing

def objective(x):
    # Simple function with minimum at (3, -1)
    return (x[0] - 3)**2 + (x[1] + 1)**2

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

result = dual_annealing(objective, bounds)

print(f"Best solution: {result.x}")
print(f"Minimum value: {result.fun}")

Important Notes

Simulated annealing can find good solutions even if the problem has many local minima.

Results may slightly vary each run because of randomness.

Set bounds carefully to limit the search space and speed up the process.

Summary

Simulated annealing tries many solutions and slowly focuses on the best one.

Use dual_annealing from scipy.optimize to minimize functions with bounds.

It works well for complex problems with many possible answers.