[Solved] 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]... Which code correctly uses dual_annealing to find the minimum within these bounds? | SciPy

SciPy - Advanced Optimization

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?

Abounds = [(0, 1), (2, 4)] result = dual_annealing(f)

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

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

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

Step-by-Step Solution

Solution:

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.
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.
Final Answer:
bounds = [(0, 1), (2, 4)] result = dual_annealing(f, bounds) -> Option D
Quick Check:
Correct bounds and function call = bounds = [(0, 1), (2, 4)] result = dual_annealing(f, bounds) [OK]

Quick Trick: 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

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Which code correctly uses dual_annealing to find the minimum within these bounds?

Step 1: Understand the function and bounds

Step 2: Check code options for correct bounds and usage

Final Answer:

Quick Check:

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