Simulated annealing (dual_annealing) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the dual_annealing function from scipy.optimize.

SciPy

from scipy.optimize import [1]

Drag options to blanks, or click blank then click option'

Adual_annealing

Banneal

Cminimize

Dbasinhopping

Attempts:

3 left

💡 Hint

Common Mistakes

Importing 'anneal' which is deprecated.

Importing 'minimize' which is for other optimization methods.

Importing 'basinhopping' which is a different algorithm.

The dual_annealing function is imported from scipy.optimize to perform simulated annealing optimization.

2fill in blank

medium

Complete the code to define the objective function that returns the sum of squares of x.

SciPy

def objective(x):
    return [1]

Drag options to blanks, or click blank then click option'

Asum(x)

Bsum(x**2)

Cmax(x)

Dmin(x)

Attempts:

3 left

💡 Hint

Common Mistakes

Using sum(x) which sums elements but not squared.

Using max(x) or min(x) which do not represent sum of squares.

The objective function returns the sum of squares of the input array x, which is a common test function for optimization.

3fill in blank

hard

Fix the error in the bounds definition to correctly specify bounds for two variables between -5 and 5.

SciPy

bounds = [[1], [1]]

Drag options to blanks, or click blank then click option'

A[-5, 5]

B(5, -5)

C(-5, 5)

D[5, -5]

Attempts:

3 left

💡 Hint

Common Mistakes

Using lists instead of tuples for bounds.

Reversing the order of bounds as (5, -5).

Bounds must be tuples specifying (min, max) for each variable. Using (-5, 5) is correct.

4fill in blank

hard

Fill both blanks to run dual_annealing with the objective function and bounds, storing the result in 'result'.

SciPy

result = [1](objective, [2])

Drag options to blanks, or click blank then click option'

Adual_annealing

Bobjective

Cbounds

Dminimize

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the objective function as the second argument.

Using 'minimize' instead of 'dual_annealing'.

The dual_annealing function is called with the objective function and bounds to perform optimization.

5fill in blank

hard

Fill all three blanks to print the minimum value found and the corresponding variables from the result.

SciPy

print('Minimum value:', result.[1])
print('At variables:', result.[2])
print('Number of function evaluations:', result.[3])

Drag options to blanks, or click blank then click option'

Ax

Bfun

Cnfev

Dsuccess

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing 'x' and 'fun' attributes.

Using 'success' which is a boolean, not a value.

The result.fun gives the minimum value, result.x the variables, and result.nfev the number of function evaluations.

Practice

1. What is the main purpose of using dual_annealing in scipy.optimize?

easy

A. To find the minimum value of a function within given bounds

B. To sort a list of numbers in ascending order

C. To calculate the mean of a dataset

D. To generate random numbers following a normal distribution

Solution

1. Step 1: Understand the purpose of dual_annealing

   dual_annealing is an optimization method used to find the minimum of a function, especially when the function is complex and has many local minima.

2. Step 2: Identify the correct use case

   Among the options, only finding the minimum value of a function within bounds matches the purpose of dual_annealing.

3. Final Answer:

   To find the minimum value of a function within given bounds -> Option A

4. Quick Check:

   Optimization = Find minimum [OK]

Hint: dual_annealing is for minimizing functions with bounds [OK]

Common Mistakes:

• Confusing optimization with sorting or statistics
• Thinking dual_annealing generates random numbers
• Assuming it calculates averages

2. Which of the following is the correct way to import dual_annealing from scipy.optimize?

easy

A. from scipy.optimize import dual_annealing

B. import dual_annealing from scipy.optimize

C. from scipy import dual_annealing.optimize

D. import scipy.optimize.dual_annealing

Solution

1. Step 1: Recall Python import syntax

   The correct syntax to import a function from a module is from module import function.

2. Step 2: Match syntax to options

   from scipy.optimize import dual_annealing matches the correct syntax: from scipy.optimize import dual_annealing. Other options have incorrect syntax.

3. Final Answer:

   from scipy.optimize import dual_annealing -> Option A

4. Quick Check:

   Correct import syntax = from scipy.optimize import dual_annealing [OK]

Hint: Use 'from module import function' to import dual_annealing [OK]

Common Mistakes:

• Using 'import function from module' which is invalid
• Trying to import submodules incorrectly
• Using dot notation in import statements wrongly

3. What will be the output of the following code snippet?

from scipy.optimize import dual_annealing

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

bounds = [(-5, 5), (-5, 5)]
result = dual_annealing(f, bounds)
print(round(result.fun, 2))

medium

A. 10.00

B. 0.00

C. 4.00

D. Error

Solution

1. Step 1: Understand the function and bounds

   The function f(x) calculates the sum of squares of (x[0]-3) and (x[1]+1). The minimum is at x[0]=3 and x[1]=-1, where the function value is 0.

2. Step 2: dual_annealing finds the minimum within bounds

   The bounds allow x[0]=3 and x[1]=-1. So the optimizer should find the minimum function value close to 0. The print statement rounds the result to 2 decimals.

3. Final Answer:

   0.00 -> Option B

4. Quick Check:

   Minimum value = 0.00 [OK]

Hint: Minimum of squared distance function is zero at target point [OK]

Common Mistakes:

• Assuming the minimum is outside bounds
• Confusing function value with input values
• Expecting an error due to function shape

4. Identify the error in the following code using dual_annealing:

from scipy.optimize import dual_annealing

def f(x):
    return x**2

bounds = [(-2, 2)]
result = dual_annealing(f, bounds)
print(result.x)

medium

A. dual_annealing requires no bounds argument

B. Bounds should be a tuple, not a list

C. Function f expects a scalar but dual_annealing passes an array

D. Missing import for numpy

Solution

1. Step 1: Check function input type

   dual_annealing passes an array (even if one variable), but f(x) expects a scalar x. This mismatch causes an error.

2. Step 2: Verify bounds and imports

   Bounds as a list of tuples is correct. dual_annealing requires bounds. No numpy import needed here.

3. Final Answer:

   Function f expects a scalar but dual_annealing passes an array -> Option C

4. Quick Check:

   Function input type mismatch = Function f expects a scalar but dual_annealing passes an array [OK]

Hint: dual_annealing passes array input; function must accept array [OK]

Common Mistakes:

• Assuming bounds format is wrong
• Thinking numpy import is mandatory here
• Ignoring input type mismatch

5. You want to minimize the function f(x) = (x[0]-2)^2 + (x[1]-3)^2 but only allow x[0] between 0 and 1, and x[1] between 2 and 4. Which code correctly uses dual_annealing to find the minimum within these bounds?

hard

A. bounds = [(0, 1), (2, 4)]
result = dual_annealing(f)

B. bounds = [(2, 3), (3, 4)]
result = dual_annealing(f, bounds)

C. bounds = [(0, 2), (2, 3)]
result = dual_annealing(f, bounds)

D. bounds = [(0, 1), (2, 4)]
result = dual_annealing(f, bounds)

Solution

1. Step 1: Understand the function and bounds

   The function minimum is at x[0]=2, x[1]=3. But bounds restrict x[0] to [0,1] and x[1] to [2,4]. So the optimizer must search within these bounds.

2. Step 2: Check code options for correct bounds and usage

   The code bounds = [(0, 1), (2, 4)] result = dual_annealing(f, bounds) correctly sets bounds as [(0,1), (2,4)] and passes them to dual_annealing. The code bounds = [(2, 3), (3, 4)] result = dual_annealing(f, bounds) has wrong bounds. The code bounds = [(0, 2), (2, 3)] result = dual_annealing(f, bounds) has wrong bounds. The code bounds = [(0, 1), (2, 4)] result = dual_annealing(f) misses bounds argument.

3. Final Answer:

   bounds = [(0, 1), (2, 4)] result = dual_annealing(f, bounds) -> Option D

4. Quick Check:

   Correct bounds and function call = bounds = [(0, 1), (2, 4)] result = dual_annealing(f, bounds) [OK]

Hint: Bounds must match variable limits and be passed to dual_annealing [OK]

Common Mistakes:

• Using wrong bounds that exclude minimum
• Not passing bounds argument to dual_annealing
• Confusing variable order in bounds