Upload
rizky-tri
View
58
Download
9
Tags:
Embed Size (px)
Citation preview
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