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SCJ 3553 Artificial Intelligence

Assignment (Genetic Algorithm) Name : Matric No. : Question 1 A population of 6 chromosomes as shown in Table 1 has been generated in order to perform the GA

operations. Binary encoding scheme was applied in this question as shown in Figure 1. Table 2 shows

the integer coded in binary form. Assume that Generational update was performed by replacing all the

parents from previous generation. Find the maximum value of the function x2 + y2, where parameter x

and y varies between 0 and 15.

Figure 1 Example of Chromosome

Table 1 Chromosome Generated

Parent Chromosome Fitness

A 0 0 1 0 0 1 0 1 29

B 0 1 1 1 0 0 0 1 50

C 1 0 1 1 0 0 1 1 130

D 1 0 0 1 1 1 0 0 225

E 1 0 1 0 1 0 0 0 164

F 0 1 0 0 0 1 1 0 52

Table 2 Integer coded in binary form.

x x x x y y y y

Integer Binary Integer Binary Integer Binary 1 0001 6 0110 11 1011 2 0010 7 0111 12 1100 3 0011 8 1000 13 1101 4 0100 9 1001 14 1110 5 0101 10 1010 15 1111

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(a) Find the solution produced by the 2 parents after Crossover operation, where single point

crossover was performed at bit number 4.

(i) A and D

(ii) B and E

(iii) C and F

(b) By using result from (a), find the solution produced after mutation operation, where flipping

mutation was performed

(i) At bit 1.

(ii) At bit 6.

(iii) At bit 4.

Q Child (a) Chromosome (b) Chromosome (i)

P (A and D)

Q (A and D)

(ii) R

(B and E)

S (B and E)

(iii) T

(C and F)

U (C and F)

(c) By using the result from (b), evaluate the fitness for each child.

Chromosome Chromosome String x Decoded Integer

Chromosome String y

Decoded Integer Fitness

Fitness Ratio (%)

Cumulative Fitness

Ratio (%) P Q R S T U

Total -

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(d) Based on the result in (c),

(i) Which children contain the best fitness and what is the value for parameter x and y?

(ii) If elitism was performed by selecting 2 parents from the previous generation,

(1) Which parent should be selected? Why?

(2) Which child should be replaced? Why?

(e) Based on your opinions, is it possible that all 6 children will contain the same chromosome

structure after 2000 iterations were performed? Why?

Question 2

(a) By using GA Toolbox, perform the experiment below.

Fitness function: @rastriginsfcn

Number of variables: 3

Lower Bounds: Default

Upper Bounds: Default

Population type: Double vector

Population size: 100

Creation function: Constraint dependent

Scaling function: Rank

Selection function: Roulette

Crossover fraction: 0.7

Mutation function: Uniform

Rate: Default

Crossover function: Single Point

Generation: 100

Stall Generation: 100

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Record your 10 times testing results in the table below.

No. Parameter 1 Parameter 2 Parameter 3 Fitness Value

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Average

(b) Which is the most optimum result for this testing?

(c) What is the most optimum values for Parameter 1, 2 and 3 based on the result shown in (a)?

Parameter 1: Parameter 2: Parameter 3:

(d) Perform another experiment by using setting below:

Fitness function: @rastriginsfcn

Number of variables: 3

Lower Bounds: Default

Upper Bounds: Default

Population type: Double vector

Population size: 100

Creation function: Constraint dependent

Scaling function: Rank

Selection function: Tournament

Tournament size: Default

Crossover fraction: Default

Mutation function: Uniform

Rate: Default

Crossover function: Two Points

Generation: 100

Stall Generation: 100

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Record your 10 times testing results in the table below.

No. Parameter 1 Parameter 2 Parameter 3 Fitness Value

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Average

(e) Which is the most optimum result for this testing?

(f) What is the most optimum value for Parameter 1, 2 and 3 based on the result shown in (d)?

Parameter 1: Parameter 2: Parameter 3:

(g) Which parameters setting performed better based on the result in (a) and (d)? Why?

(h) What will happen to the average of fitness when number of testing is increased?

Due date: Week 14 23/5/2013 (Thursday) 12.00 pm

Submit in hardcopy format to N28-Level 4-429-01.

No late submission.