Soal

Diketahui persamaan F(x123) = 2x13 –x2

2 +x3 dengan rentang, dengan rentang x1, x2, dan x3 yaitu x[0,1]. Tentukan berapa nilai x1, x2, dan x3 sehingga didapatkan F(x123) maksimum! Gunakan alur Alogaritma Genetika :

Representasi kromosom (float) Seleksi Orang tua (tournament) Crossover (multi parent) Mutasi (multi point) Replacement (steady state)

Penyelesaian

Cm = 0.6 ; Rentang x1, x2, dan x3 [0,1]

1. Populasi awal

X1 X2 X3

K1 0.6 0.2 0.3K2 0.2 0.6 1.0K3 0.4 0.4 0.6K4 1.0 0.3 0.6K5 0.5 0.7 0.4

2. Representasi kromosom

X1 X2 X3

K1 0.6 0.2 0.3K2 0.2 0.6 1.0K3 0.4 0.4 0.6K4 1.0 0.3 0.6K5 0.5 0.7 0.4

3. Loop start Loop I

a. Point

X1 X2 X3 Fitness{F(x)} PointK1 0.6 0.2 0.3 0.69 4K2 0.2 0.6 1.0 0.66 3K3 0.4 0.4 0.6 0.57 2K4 1.0 0.3 0.6 2.51 5K5 0.5 0.7 0.4 0.16 1

K1 | 4

K3 | 2

K3 | 2

K2 | 3

K1 | 4

K5 | 1

K4 | 5

K4 | 5

K2 | 3

(0.4)x0.6 + (0.6)x1A1 (0.4)x0.3 + (0.6)x0.6 (0.4)x1 + (0.6)x0.3

(0.4)x1 + (0.6)x0.6A2 (0.4)x0.3+ (0.6)x0.6 (0.4)x0.3 + (0.6)x1

(0.4)x0.4 + (0.6)x1A3 (0.4)x0.3 + (0.6)x0.2 (0.4)x0.3 + (0.6)x0.6

(0.4)x1 + (0.6)x0.3A4 (0.4)x0.2 + (0.6)x0.4 (0.4)x0.6 + (0.6)x0.6

0.84 0.48 0.58A1

0.76 0.48 0.58A2

0.76 0.24 0.48A3

0. 76 0.32 0.60A4

b. Seleksi Orang Tua (Tournament) = Random

c. Metode Perkawinan Poligami (Multi Parents)R=0.4

K1 0.6 0.2 0.3

K4 1.0 0.3 0.6

K2 0.2 0.6 1.0K4K1 K4K2 K2K1

A1

A2

K1K4 K4K2 K2K1

K4K1 K1K3 K3K4

K3K4 K4K1 K1K3K1 0.6 0.2 0.3

K3 0.4 0.4 0.6

K4 1.0 0.3 0.6

A3

A4

0.84

0.76

0.76

0.76

0.48 0.58

0.48 0.58

0.24 0.48

0.32 0.60

0.84

0.76

0.76

0.76

0.38 0.68

0.38 0.68

0.14 0.58

0.22 0.70A4

A3

A2

A1

d. MutasiConstanta mutasi: 0.1Titik mutasi pada bit ke 2(-) dan 3 (+)

e. Replacement

X1 X2 X3 Fitness{F(x)}

Steady State

K1 0.60 0.20 0.30 0.69 EliminateK2 0.20 0.60 1.0 0.65 EliminateK3 0.40 0.40 0.60 0.57 EliminateK4 1.00 0.30 0.60 2.51 K4K5 0.50 0.70 0.40 0.16 EliminateA1 0.84 0.38 0.68 1.72 K1A2 0.76 0.38 0.68 1.41 K2A3 0.76 0.14 0.58 1.43 K3A4 0.76 0.22 0.70 1.23 K5

Loop IIa. Point

X1 X2 X3 Fitness{F(x)} PointK1 0.84 0.38 0.68 1.72 4K2 0.76 0.38 0.68 1.41 2K3 0.76 0.14 0.58 1.43 3K4 1.00 0.30 0.60 2.51 5K5 0.76 0.22 0.70 1.23 1

K3 | 3

K4 | 5

K3 | 3

K2 | 2

K1 | 4

K5 | 1

K4 | 5

K2 | 2

K1 | 4

K2K4 K1K2 K,K4A1

K1K4 K2,K4 K2K1A2

K4K3 K4K2 K3K2A3

K4K2 K2K3 K2K4A4

b. Seleksi Orang Tua

c. Metode Perkawinan Poligami (Multi Parents)R=0.4

K1 0.84 0.38 0.68

K2 0.76 0.38 0.68

K4 1.00 0.30 0.60

A1 (0.4)x0.76 + (0.6)x1.00 (0.4)x0.38 + (0.6)x0.38 (0.4)x0.68 + (0.6)x0.60A2 (0.4)x0.84+ (0.6)x1.00 (0.4)x0.38 + (0.6)x0.30 (0.4)x0.68 + (0.6)x0.68A3 (0.4)x1.00 + (0.6)x0.76 (0.4)x0.38 + (0.6)x0.30 (0.4)x0.58 + (0.6)x0.68A4 (0.4)x1.00 + (0.6)x0.76 (0.4)x0.38 + (0.6)x0.14 (0.4)x0.68 + (0.6)x0.60

A1 0.90 0.38 0.63A2 0.93 0.33 0.68A3 0.86 0.35 0.64A4 0.86 0.24 0.63

d. MutasiConstanta mutasi: 0.1Titik mutasi pada bit ke 1(-) dan 3 (+)

A1 0.90 0.38 0.63 → 0.80 0.38 0.73A2 0.93 0.33 0.68 → 0.83 0.33 0.78A3 0.86 0.35 0.64 → 0.76 0.35 0.74A4 0.86 0.24 0.63 → 0.76 0.24 0.73

K2 0.76 0.38 0.68

K3 0.76 0.14 0.58

K4 1.00 0.30 0.60

K3 | 3

K4 | 5

K3 | 3

K2 | 2

K1 | 4

K5 | 1

K4 | 5

K2 | 2

K1 | 4

e. Replacement

X1 X2 X3 Fitness{F(x)} Steady StateK1 0.8

40.38 0.68 1.72 K1

K2 0.76

0.38 0.68 1.41 Eliminate

K3 0.76

0.14 0.58 1.43 Eliminate

K4 1.00

0.30 0.60 2.51 K4

K5 0.76

0.22 0.70 1.23 Eliminate

A1 0.80

0.38 0.73 1.61 K3

A2 0.83

0.33 0.78 1.81 K5

A3 0.76

0.35 0.74 1.49 Eliminate

A4 0.76

0.24 0.73 1.55 K2

Loop IIIa. Point

X1 X2 X3 Fitness{F(x)} PointK1 0.84 0.38 0.68 1.72 3K2 0.76 0.24 0.73 1.55 1K3 0.80 0.38 0.73 1.61 2K4 1.00 0.30 0.60 2.51 5K5 0.83 0.33 0.78 1.81 4

b. Seleksi Orang Tua

c. Metode Perkawinan Poligami (Multi Parents)R=0.4

K1 0.84 0.38 0.68A1 K1 K3 K1 K3 K1 K5K3 0.80 0.38 0.73

K5 0.83 0.33 0.78A2 K5 K3 K1 K5 K3 K1

A3 K1 K4 K4 K2 K2 K4K1 0.84 0.38 0.68K2 0.76 0.24 0.73

A4 K2 K4 K1 K4 K1 K2K4 1.00 0.30 0.60

A1 (0.4)x0.84 + (0.6)x0.80 (0.4)x0.38 + (0.6)x0.38 (0.4)x0.68 + (0.6)x0.78A2 (0.4)x0.83 + (0.6)x0.80 (0.4)x0.38 + (0.6)x0.33 (0.4)x0.73 + (0.6)x0.68A3 (0.4)x0.84 + (0.6)x1.00 (0.4)x0.30 + (0.6)x0.24 (0.4)x0.73 + (0.6)x0.60A4 (0.4)x0.76 + (0.6)x1.00 (0.4)x0.38 + (0.6)x0.30 (0.4)x0.68 + (0.6)x0.73

A1 0.82 0.38 0.74A2 0.81 0.35 0.70A3 0.94 0.26 0.65A4 0.45 0.33 0.71

d. MutasiCM=0.1Titik mutasi pada bit ke 1(-) dan 2 (+)

A1 0.82 0.38 0.74 → 0.72 0.48 0.74A2 0.81 0.35 0.70 → 0.71 0.45 0.70A3 0.94 0.26 0.65 → 0.84 0.36 0.65A4 0.45 0.33 0.71 → 0.35 0.43 0.71

K3 | 3

K5 | 1

K3 | 3

K2 | 4

K1 | 5

K5 | 1

K4 | 2

K2 | 4

K1 | 5

e. Replacement

X1 X2 X3 Fitness{F(x)} Steady StateK1 0.8

40.38 0.68 1.72 K3

K2 0.76

0.24 0.73 1.55 Eliminate

K3 0.80

0.38 0.73 1.61 K5

K4 1.00

0.30 0.60 2.51 K1

K5 0.83

0.33 0.78 1.81 K2

A1 0.72

0.48 0.74 1.26 Eliminate

A2 0.71

0.45 0.70 1.21 Eliminate

A3 0.84

0.36 0.65 1.70 K4

A4 0.35

0.43 0.71 0.61 Eliminate

Loop IVa. Point

X1 X2 X3 Fitness{F(x)} PointK1 1.00 0.30 0.60 2.51 5K2 0.83 0.33 0.78 1.81 4K3 0.84 0.38 0.68 1.72 3K4 0.84 0.36 0.65 1.70 2K5 0.80 0.38 0.73 1.61 1

b. Seleksi Orang Tua

c. Metode Perkawinan Poligami (Multi Parents)

K1 1.00 0.30 0.60A1 K1 K5 K1 K4 K4 K5K4 0.84 0.36 0.65

K5 0.80 0.38 0.73A2 K5 K4 K1 K5 K4 K1

A3 K1 K2 K3 K2 K2 K1K1 1.00 0.30 0.60K3 0.84 0.38 0.68

A4 K2 K1 K1 K3 K3 K2K2 0.83 0.33 0.78

A1 (0.4)x1.00 + (0.6)x0.80 (0.4)x0.30 + (0.6)x0.36 (0.4)x0.65 + (0.6)x0.73A2 (0.4)x0.80 + (0.6)x0.84 (0.4)x0.30 + (0.6)x0.38 (0.4)x0.65 + (0.6)x0.60A3 (0.4)x1.00 + (0.6)x0.83 (0.4)x0.38 + (0.6)x0.33 (0.4)x0.78 + (0.6)x0.60A4 (0.4)x0.83 + (0.6)x1.00 (0.4)x0.30 + (0.6)x0.38 (0.4)x0.68 + (0.6)x0.78

A1 0.88 0.34 0.70A2 0.82 0.35 0.70A3 0.90 0.35 0.67A4 0.93 0.35 0.63

d. MutasiCM: 0.1Titik mutasi pada bit ke 1(-) dan 2 (+)

A1 0.88 0.34 0.70 → 0.78 0.44 0.70A2 0.82 0.35 0.70 → 0.72 0.45 0.70A3 0.90 0.35 0.67 → 0.80 0.45 0.67A4 0.93 0.35 0.63 → 0.83 0.45 0.63

e. Replacement

X1 X2 X3 Fitness{F(x)} Steady StateK1 1.0

00.30 0.60 2.51

K2 0.83

0.33 0.78 1.81

K3 0.84

0.38 0.68 1.72

K4 0.84

0.36 0.65 1.70

K5 0.80

0.38 0.73 1.61

A1 0.78

0.44 0.70 1.45

A2 0.72

0.45 0.70 1.24

A3 0.80

0.45 0.67 1.50

A4 0.83

0.45 0.63 1.57

GRAFIK NILAI FITNESS MAKSIMUM

Loop Individu Maksimum Nilai fitnessI K4 2.51II K4 2.51III K4 2.51IV K1 2.51

Loop Total Fitness ParentI 4.59II 8.3III 9.2IV 9.35

Loop Fitness Parent TerendahI 0.16II 1.23III 1.55IV 1.61

Loop I Loop II Loop III Loop IV0

1

2

3

4

5

6

7

8

9

10

2.51 2.51 2.51 2.51

4.59

8.39.2 9.35

0.16

1.23 1.55 1.61

Nilai Fitness

Individu Terbaik Total Fitness Parent Individu fitness Terendah

Nila

i Fitn

ess