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Q1.
Which
of the following statement is FALSE?
Multidimensional direct search
methods are similar to one-dimensional direct search methods.
Enumerating all possible solutions in
a search space and selecting the optimal solutions is an effective
method for problems with very high dimensional
solution spaces.
Multidimensional
direct search methods do not require a twice differentiable function as
an optimization function
Genetic
Algorithms belong to the family of multidimensional direct search
methods.
Q2. Which of the following
statements is FALSE?
Multidimensional
direct search methods require an upper and lower bound for their search
region.
Coordinate
cycling method relies on single dimensional search methods to determine
an optimal solution along each coordinate direction iteratively.
If the
optimization function is twice differentiable, multidimensional direct
search methods cannot be used to find an optimal solution.
Multidimensional
direct search methods are not guaranteed to find the global optimum.
Q3. The
first cycle of Example 1 in Chapter 09.03 results in an optimal solution
of
 for
the gutter design problem. The next iteration starts with a search along
dimension l (length) looking for the optimal solution of the
function
 as
shown in Table 3 and reproduced below where
 and .
What is the optimal solution for the length of the gutter side at the
end of iteration 10?
|
Iteration |
 |
 |
 |
 |
 |
 |
 |
|
1 |
0.0000 |
3.0000 |
1.8541 |
1.1459 |
4.9354 |
3.8871 |
3.0000 |
|
2 |
1.1459 |
3.0000 |
2.2918 |
1.8541 |
5.0660 |
4.9354 |
1.8541 |
|
3 |
1.8541 |
3.0000 |
2.5623 |
2.2918 |
4.9491 |
5.0660 |
1.1459 |
|
4 |
1.8541 |
2.5623 |
2.2918 |
2.1246 |
5.0660 |
5.0627 |
0.7082 |
|
5 |
2.1246 |
2.5623 |
2.3951 |
2.2918 |
5.0391 |
5.0660 |
0.4377 |
|
6 |
2.1246 |
2.3951 |
2.2918 |
2.2279 |
5.0660 |
5.0715 |
0.2705 |
|
7 |
2.1246 |
2.2918 |
2.2279 |
2.1885 |
5.0715 |
5.0708 |
0.1672 |
|
8 |
2.1885 |
2.2918 |
2.2523 |
2.2279 |
5.0704 |
5.0715 |
0.1033 |
|
9 |
2.1885 |
2.2523 |
2.2279 |
2.2129 |
5.0715 |
5.0716 |
0.0639 |
|
10 |
2.1885 |
2.2279 |
2.2129 |
2.2035 |
5.0716 |
5.0714 |
0.0395 |
2.1885
2.2279
5.0715
2.2082
Q4. What is the maximum size for
the area of gutter at the optimal point determined in multiple-choice
question 3? (Hint: You do not need to do any calculations to answer this
question)
5.0716
5.0714
5.0715
2.2082
Q5. To
find the minimum of the function hold
 and
use 2 and -2 as your upper and lower bounds for your one-dimensional
search along the
 coordinate
using golden search method. What would be the optimal solution for
after
the first iteration?
3.1146
0.4721
0
0.0015
Q6. Considering the scenario in
Question 5, what would be the optimal solution for after the first
iteration? (Can you explain the difference?)
0
0.7639
0.4721
7.5728
Complete Solution
Multiple choice questions on other topics
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