ABSTRAK
Permasalahan transportasi yang terjadi akibat kenaikan harga bahan bakar
minyak (BBM) yang tinggi membuat para pengguna jasa transportasi berpikir
untuk dapat meminimalisasi biaya yang dikeluarkan. Salah satu cara untuk
meminimalisasi biaya adalah dengan menentukan jalur terpendek dalam
mengirimkan barang.
Metode yang dapat digunakan untuk menentukan jalur terpendek adalah
dengan menggunakan algoritma semut yang didasarkan pada cara kerja semut
untuk menentukan jalur terpendek dari sarang menuju sumber makanan. Semut
dapat menemukan jalur terpendek dengan memanfaatkan feromon sebagai
komunikasi tidak langsung antar semut. Jalur dengan konsentrasi feromon lebih
kuat yang dilewati semut merupakan jalur terpendek.
ABSTRACT
Problems
of
transportation
that happened effect of oil fuel increase of price
make service user of transportation think to be able to minimize it. One of the way
to minimize the cost by determining shortest trade in delivering goods.
The method that can be used to determining shortest trade by using ant
algorithm which based on ant’s activity in determining shortest way from den to
source of food. Ant can find shortest way by exploiting feromon as indirect
communications between ant. The way with stronger concentration of feromon
will be pass by ant representing the shortest way.
DAFTAR ISI
LEMBAR PENGESAHAN
SURAT PERNYATAAN
ABSTRAK i
ABSTRACT ii
KATA PENGANTAR
iii
DAFTAR ISI
v
DAFTAR TABEL
vii
DAFTAR GAMBAR
viii
DAFTAR PERSAMAAN
ix
BAB I PENDAHULUAN
I.1 Latar Belakang
1
I.2 Identifikasi Masalah
2
I.3 Tujuan
2
I.4 Pembatasan Masalah
2
I.5 Sistematika Penulisan
3
BAB II DASAR TEORI
II.1 Graf
4
II.1.1 Definisi Graf
4
II.1.2 Lintasan dan Sirkuit Hamilton
4
II.2 TSP (Travelling Salesman Problem)
6
II.3 Teori Tentang Semut
7
II.3.1 Kehidupan Nyata Semut
7
II.3.2 Optimasi Koloni Semut
10
BAB III PERANCANGAN PERANGKAT LUNAK
III.1.1 Koordinat Kota
18
III.1.2 Fungsi untuk Panjang Jalur
19
III.1.3 Jarak Antar Kota
19
III.1.4 Penyusunan Jalur Semut
20
III.1.5 Pemilihan Jalur Semut
21
III.1.6 Mencari Panjang Jalur dan Update Feromon
24
III.1.7 Jalur Terpendek
25
III.1.8 Mengulang Iterasi sampai Maksimum
26
BAB IV HASIL PENGAMATAN
IV.1 Percobaan untuk 6 Buah Koordinat Kota
28
IV.1.1 Percobaan Pertama dari 6 Koordinat Kota
30
IV.1.2 Percobaan Kedua dari 6 Koordinat Kota
32
IV.1.3 Percobaan Ketiga dari 6 Koordinat Kota
33
IV.1.4 Percobaan Keempat dari 6 Koordinat Kota
34
IV.2 Percobaan untuk 10 Buah Koordinat Kota
35
IV.2.1 Percobaan Pertama dari 10 Koordinat Kota
37
IV.2.2 Percobaan Kedua dari 10 Koordinat Kota
39
IV.2.3 Percobaan Ketiga dari 10 Koordinat Kota
40
IV.2.4 Percobaan Keempat dari 10 Koordinat Kota
41
BAB V KESIMPULAN DAN SARAN
V.1 Kesimpulan
42
V.2 Saran
42
DAFTAR PUSTAKA
43
LAMPIRAN A
A-1
DAFTAR TABEL
Tabel IV.1 Koordinat 6 buah kota
28
Tabel IV.2 Jarak antar kota pada 6 buah kota (d)
29
Tabel IV.3 Visibilitas antar kota pada 6 buah kota (
η
) 29
Tabel IV.4 Percobaan pertama (6 kota)
30
Tabel IV.5 Percobaan kedua (6 kota)
32
Tabel IV.6 Percobaan ketiga (6 kota)
33
Tabel IV.7 Percobaan keempat (6 kota)
34
Tabel IV.8 Koordinat 10 buah kota
35
Tabel IV.9: Jarak antar kota pada 10 buah kota (d
ij) 35
Tabel IV.9: Jarak antar kota pada 10 buah kota (d
ij)(lanjutan) 36
Tabel IV.10 Visibilitas antar kota pada 10 buah kota (
η
) 36
Tabel IV.11 Percobaan pertama (10 kota)
37
Tabel IV.12 Percobaan kedua (10 kota)
39
Tabel IV.13 Percobaan ketiga (10 kota)
40
DAFTAR GAMBAR
Gambar II.1 (a) Graf memiliki lintasan Hamilton ( misal : 3,2,1,4)
5
Gambar II.1(b) Graf memiliki sirkuit Hamilton ( 1,2,3,4,1)
5
Gambar II.1(c) Graf tidak memiliki lintasan maupun sirkuit Hamilton
5
Gambar II.2 Graf lengkap dengan 4 simpul
5
Gambar II.3 Contoh Karakteristik semut (1)
8
Gambar II.4 Contoh Karakteristik semut (2)
9
Gambar II.5 Jalur Solusi Semut (Ant System)
11
Gambar II.6 Diagram alir algoritma semut secara umum
15
Gambar III.1 Diagram alir program algoritma semut
17
Gambar III.2 Diagram alir dari koordinat kota
18
Gambar III.3 Diagram alir dari penyusunan jalur semut
20
Gambar III.4 Diagram alir dari pemilihan jalur semut
23
Gambar III.5 Diagram alir dari mencari panjang jalur dan update feromon
24
Gambar III.6 Diagram alir dari jalur terpendek
26
Gambar III.7 Diagram alir dari iterasi
27
Gambar IV.1 Tampilan jalur awal (6 kota)
31
Gambar IV.2 Tampilan iterasi ke –1 (6 kota)
31
Gambar IV.3 Tampilan jalur awal (10 kota)
38
DAFTAR PERSAMAAN
Persamaan II.1
12
Persamaan II.2
13
•
Kode program untuk 6 buah kota
funct ion Pj gJalur Ant = Pj gJalur Ant ( I ndeks) ;
global N D
Pj gJalur Ant = 0;
for i= 1: ( N- 1) ,
Pj gJalur Ant = Pj gJalurAnt + D( I ndeks( i) ,I ndeks( i+ 1) ) ;
end;
Pj gJalur Ant = Pj gJalur Ant + D( I ndeks( N) ,I ndeks( 1) ) ;
% Pr ogr am Penyelesaian j alur t er pendek pada TSP dengan
% Algor it m a Sem ut
clear;
clc;
global N D
% Koor dinat or kot a
X= [ ...
1 10
3 10
7 5
16 6
16 3
21 5
] ;
N = size( X,1) ;
I ndeks= 1: 1: N;
% Menghit ung j ar ak ant ar kot a
D = zer os( N,N) ;
for i= 1: ( N- 1) ,
for j = i+ 1: N,
D( i,j )
=
D( i,j ) + sqr t ( ( X( I ndeks( i) ,1) - X( I ndeks( j ) ,1) ) ^ 2
+
( X( I ndeks( i) ,2) - X( I ndek s( j ) ,2) ) ^ 2) ;
D( j ,i) = D( i,j ) ;
n( i,j ) = 1/ D( i,j ) ;
n( j ,i) = n( i,j ) ;
end;
end;
Pj gJalur = Pj gJalur Ant ( I ndeks) ;
% Menggam bar lokasi kot a
for i= 1: N,
XX = X( i,: ) ;
for j = 1: N,
plot ( [ XX( 1,1) ; X( j ,1) ] ,[ XX( 1,2) ; X( j ,2) ] ,'y- ') ;
hold on;
end;
plot ( X( : ,1) ,X( : ,2) ,'bs','linew idt h',4) ;
t ext ( X( : ,1) + 0.5, X( : ,2) + 0.5,num 2st r ( I ndeks') ) ;
axis equal; axis off;
plot ( [ X( I ndeks,1) ; X( I ndeks( 1) ,1) ] ,...
[ X( I ndeks,2) ; X( I ndeks( 1) ,2) ] ,'b- ') ;
t it le( [ 'Jalur Aw al : ' int 2st r( I ndeks) ,' ',int 2st r ( I ndeks( 1) ) ...
'- > Panj ang Jalur = ' num 2st r ( Pj gJalur) ] ) ;
pause; hold off;
% inisialisasi
t = 0;
alfa= 1;
bet a= 2;
r ho= 0.5;
dTho= zer os( N,N) ;
b= fix( 1* r and( N,1) ) + 1;
NCMax= 100;
bb= b;
bTem p= zeros( N,1) ;
NC= 1;
Q = 1* ones( N,N) ;
m = sum ( b) ;
kTho= m / Pj gJalur ;
Tho= kTho* ones( N,N) ;
Pj gJalur Ter pendek= inf;
% m ulai it er asi
w hile ( NC< NCMax) ,
s= 1;
b= bb;
l= 0;
for i= 1: N,
for k= 1: b( i) ,
l= l+ 1;
Tabu( l,s) = i;
end;
end;
while s< N,
s= s+ 1;
bTem p= zer os( N,1) ;
for k= 1: m ,
Tot P= 0;
for j = 1: N,
t akada= isem pt y( find( Tabu( k,: ) = = j ) ) ;
if t ak ada,
p( j ) = ( Tho( Tabu( k ,s- 1) ,j ) ^ alfa* ...
n( Tabu( k ,s- 1) ,j ) ^ bet a) ;
Tot P= Tot P+ p( j ) ;
else p( j ) = 0;
q( l) = q( l- 1) + p( l) ;
end;
r = rand( 1) ;
disp( r )
t em u= 0 ; l= 1;
w hile ~ t em u,
if r < = q( 1) ,
t em u= 1;
Kot aDipilih= 1;
elseif ( r > q( l) ) &( r < = q( l+ 1) ) ;
t em u= 1;
Kot aDipilih= l+ 1;
end;
l= l+ 1;
end;
q= [ ] ;
bTem p( Kot aDipilih) = bTem p( Kot aDipilih) + 1;
Tabu( k,s) = Kot aDipilih;
end;
b= bTem p;
end;
for k= 1: m ,
Pj gJalur ( k) = Pj gJalur Ant ( Tabu( k,: ) ) ;
for s= 1: N- 1,
dTho( Tabu( k ,s) ,Tabu( k ,s+ 1) ) = dTho( Tabu( k,s) ,...
Tabu( k,s+ 1) ) + Q( Tabu( k,s) ,Tabu( k,s+ 1) ) / Pj gJalur ( k) ;
end;
dTho( Tabu( k,N) ,Tabu( k,1) ) = dTho( Tabu( k,N) ,...
Tabu( k,1) ) + Q( Tabu( k ,N) ,Tabu( k,1) ) / Pj gJalur ( k ) ;
end;
for i= 1: N,
for j = 1: N,
Tho( i,j ) = ( 1- rho) * Tho( i,j ) + dTho( i,j ) ;
end;
end;
t = t + N;
dTho= zer os( N,N) ;
for k= 1: m ,
if Pj gJalur ( k) < Pj gJalur Ter pendek,
Pj gJalur Ter pendek= Pj gJalur ( k) ;
I t erasi= NC;
L= Tabu( k ,: ) ;
end;
end;
if ( NC< NCMax) ,
TTabu= [ Tabu Pj gJalur ' ] ;
Tabu= [ ] ;
bTem p= zer os( N,1) ;
NC= NC+ 1;
end;
hold off;
plot ( [ X( L,1) ; X( L( 1) ,1) ] ,...
hold on;
plot ( X( : ,1) ,X( : ,2) ,'bs','linew idt h',4) ;
t it le( [ 'I t er asi ke- ' int 2st r ( NC- 1) ...
' - > Jalur : ' int 2st r ( L) ,' ',int 2st r( L( 1) ) ...
' - > Panj ang Jalur = ' num 2st r ( Pj gJalurTer pendek) ] ) ;
t ext ( X( : ,1) + 0.5,X( : ,2) + 0.5, int 2st r ( I ndeks') ) ;
axis equal; axis off; pause( 0.1) ;
end;
Jalur Ter pendek= L
Pj gJalur Ter pendek= Pj gJalur Ter pendek
Tho= Tho( i,j )
hold off;
plot ( [ X( L,1) ; X( L( 1) ,1) ] ,[ X( L,2) ; X( L( 1) ,2) ] ,...
'r - ','linew idt h',4) ; hold on;
plot ( X( : ,1) ,X( : ,2) ,'bs','linew idt h',4) ;
t ext ( X( : ,1) + 0.5,X( : ,2) + 0.5,int 2st r( I ndeks') ) ;
t it le( [ 'I t er asi ke- ' int 2st r ( NC) ' - > Jalur : ' ...
int 2st r( L) ,' ',int 2st r( L( 1) ) ' - > Panj ang Jalur = '
num 2st r ( Pj gJalur Ter pendek) ] ) ;
ax is equal; ax is off; hold off;
•
Kode program untuk 10 buah kota
funct ion Pj gJalur Ant = Pj gJalur Ant ( I ndeks) ;
global N D
Pj gJalur Ant = 0;
for i= 1: ( N- 1) ,
Pj gJalur Ant = Pj gJalurAnt + D( I ndeks( i) ,I ndeks( i+ 1) ) ;
end;
Pj gJalur Ant = Pj gJalur Ant + D( I ndeks( N) ,I ndeks( 1) ) ;
% Program Penyelesaian jalur terpendek pada TSP dengan
% Algoritma Semut
clear;
clc;
global N D
% Koordinator kota
X= [...
21 2
25 1
];
N = size(X,1);
Indeks=1:1:N;
% Menghitung jarak antar kota
D = zeros(N,N);
for i=1:(N-1),
for j=i+1:N,
D(i,j) = D(i,j)+sqrt((X(Indeks(i),1)-X(Indeks(j),1))^2 +
(X(Indeks(i),2)-X(Indeks(j),2))^2);
D(j,i) = D(i,j);
n(i,j) = 1/D(i,j);
n(j,i) = n(i,j);
end;
end;
PjgJalur=PjgJalurAnt(Indeks);
% Menggambar lokasi kota
for i=1:N,
XX = X(i,:);
for j =1:N,
plot([XX(1,1);X(j,1)],[XX(1,2);X(j,2)],'y-');
hold on;
end;
end;
plot(X(:,1),X(:,2),'bs','linewidth',4);
text(X(:,1)+0.5, X(:,2)+0.5,num2str(Indeks'));
axis equal; axis off;
plot([X(Indeks,1);X(Indeks(1),1)],...
[X(Indeks,2);X(Indeks(1),2)],'b-');
title(['Jalur Awal : ' int2str(Indeks),' ',int2str(Indeks(1))...
'-> Panjang Jalur = ' num2str(PjgJalur)]);
pause; hold off;
% inisialisasi
t=0;
alfa=1;
beta=2;
rho=0.5;
dTho=zeros(N,N);
b=fix(1*rand(N,1))+1;
NCMax=250;
bTemp=zeros(N,1);
NC=1;
Q = 1*ones(N,N);
m=sum(b);
kTho=m/PjgJalur;
Tho=kTho*ones(N,N);
PjgJalurTerpendek=inf;
%mulai iterasi
while (NC<NCMax),
s=1;
b=bb;
l=0;
for i=1:N,
for k=1:b(i),
l=l+1;
Tabu(l,s)=i;
end;
end;
while s<N,
s=s+1;
bTemp=zeros(N,1);
for k=1:m,
TotP=0;
for j=1:N,
takada=isempty(find(Tabu(k,:)==j));
if takada,
p(j)=(Tho(Tabu(k,s-1),j)^alfa*...
n(Tabu(k,s-1),j)^beta);
TotP=TotP+p(j);
else p(j)=0;
end;
end;
p=p/TotP;
q(1)=p(1);
for l=2:length(p),
q(l)=q(l-1)+p(l);
end;
r=rand(1);
%disp(r)
temu=0 ; l=1;
while ~temu,
if r<=q(1),
temu=1;
KotaDipilih=1;
KotaDipilih=l+1;
end;
l=l+1;
end;
q=[];
bTemp(KotaDipilih)=bTemp(KotaDipilih)+1;
Tabu(k,s)=KotaDipilih;
end;
b=bTemp;
end;
for k=1:m,
PjgJalur(k)=PjgJalurAnt(Tabu(k,:));
for s=1:N-1,
dTho(Tabu(k,s),Tabu(k,s+1))=dTho(Tabu(k,s),...
Tabu(k,s+1))+Q(Tabu(k,s),Tabu(k,s+1))/PjgJalur(k);
end;
dTho(Tabu(k,N),Tabu(k,1))=dTho(Tabu(k,N),...
Tabu(k,1))+Q(Tabu(k,N),Tabu(k,1))/PjgJalur(k);
end;
for i=1:N,
for j=1:N,
Tho(i,j)=(1-rho)*Tho(i,j)+dTho(i,j);
end;
end;
t=t+N;
dTho=zeros(N,N);
for k=1:m,
if PjgJalur(k)<PjgJalurTerpendek,
PjgJalurTerpendek=PjgJalur(k);
Iterasi=NC
Bilanganrandom=r
L=Tabu(k,:);
end;
end;
if (NC<NCMax),
TTabu=[ Tabu PjgJalur' ];
Tabu=[];
bTemp=zeros(N,1);
NC=NC+1;
end;
hold off;
plot([X(L,1);X(L(1),1)],...
[X(L,2);X(L(1),2)],'m-','linewidth',2);
hold on;
' -> Jalur : ' int2str(L),' ',int2str(L(1))...
' -> Panjang Jalur = ' num2str(PjgJalurTerpendek)]);
text(X(:,1)+0.5,X(:,2)+0.5, int2str(Indeks'));
axis equal;axis off; pause(0.01);
end;
JalurTerpendek=L
PjgJalurTerpendek=PjgJalurTerpendek
hold off;
plot([X(L,1);X(L(1),1)],[X(L,2);X(L(1),2)],...
'r-','linewidth',4); hold on;
plot(X(:,1),X(:,2),'bs','linewidth',4);
text(X(:,1)+0.5,X(:,2)+0.5,int2str(Indeks'));
title(['Iterasi ke- ' int2str(NC) ' -> Jalur :' ...
int2str(L),' ',int2str(L(1)) ' -> Panjang Jalur = '
num2str(PjgJalurTerpendek)]);
D =
√
(xj-xi)
2
+(yj-yi)
2
0 2
7.8102
15.524
16.553
20.616
2 0
6.4031
13.601
14.765
18.682
7.8102
6.4031 0 9.0554
9.2195
14
15.524 13.601 9.0554
0
3
5.099
16.553 14.765 9.2195
3
0
5.3852
20.616 18.682
14
5.099 5.3852
0
η
ij = 1 / Dij
0 0.5
0.128
0.0644
0.0604
0.0485
0.5
0
0.1562 0.0735 0.0677 0.0535
0.128 0.1562
0
0.1104 0.1085 0.0714
0.0644 0.0735 0.1104
0
0.3333 0.1961
0.0604 0.0677 0.1085 0.3333
0
0.1857
0.0485 0.0535 0.0714 0.1961 0.1857
0
Dimana
τ
ij
= m
/
panjang jalur = 6 / 46.4592 = 0.129
(
)
[
[ ]
(
(
)
]
)
[
[
(
(
)
]
)
]
Tabu
k
⎪
⎪
⎩
⎪
⎪
⎨
⎧
⋅
⋅
=
Ρ
∑
,
j
, lainnya
0
ε
η
τ
η
τ
ε
Tabu
k¾
Perhitungan secara teori tanpa menggunakan bilangan random
* Semut pertama
[0.129 ]1 . [0.5]2
P
k(1,2) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129]1.[0.0604]2+[0.129]1.[0.0485]2
0.03225
= ________ = 0.904. ( Terpilih) 0.035668
[0.129 ]1 . [0.128]2
P
k(1,3)=_________________________________________________________
[0.129]
1.[0.5]2+[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2
0.00211
= ________ = 0.059. 0.035668
[0.129 ]1 . [0.0644]2
P
k(1,4)=_________________________________________________________
[0.129]
1.[0.5]2+[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2
0.000535
= _________ = 0.0149. 0.035668
[0.129 ]1 . [0.0604]2
P
k(1,5)=_________________________________________________________
[0.129]
1.[0.5]2+[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2
0.00047
= ________ = 0.0131. 0.035668
[0.129 ]1 . [0.0485]2
P
k(1,6)=_________________________________________________________
[0.129]
1.[0.5]2+[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]20.000303
= ________ = 0.0085. 0.035668
Jalur pertama dari semut pertama adalah 1 – 2.
[0.129 ]1 . [0.1562]2P
k(2,3) = ____________________________________________________________________________[0.129]1.[0.1562]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.00315
[0.129 ]1 . [0.0735]2
P
k(2,4) = ____________________________________________________________________________[0.129]1.[0.1562]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.000696
= ________ = 0.145. 0.004805
[0.129 ]1 . [0.0677]2
P
k(2,5) = ____________________________________________________________________________[0.129]1.[0.1562]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.00059
= ________ = 0.123.
0.004805
[0.129 ]1 . [0.0535]2
P
k(2,6) = ____________________________________________________________________________[0.129]1.[0.1562]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.000369
= ________ = 0.076.
0.004805
Jalur kedua dari semut pertama adalah 1 – 2 – 3.
[0.129 ]1 . [0.1104]2
P
k(3,4) = ____________________________________________________________________________[0.129]1.[0.1104]2+[0.129]1.[0.1085 ]2+[0.129]1.[0.0714]2
0.00157
= ________ = 0.419. ( Terpilih)
0.003747
[0.129 ]1 . [0.1085]2
P
k(3,5) = ____________________________________________________________________________[0.129]1.[0.1104]2+[0.129]1.[0.1085 ]2+[0.129]1.[0.0714]2
0.00152
= ________ = 0.405.
0.003747
[0.129 ]1 . [0.0714]2
P
k(3,6) = ____________________________________________________________________________[0.129]1.[0.1104]2+[0.129]1.[0.1085 ]2+[0.129]1.[0.0714]2
0.000657
= ________ = 0.175.
0.003747
[0.129 ]1 . [0.3333]2
P
k(4,5) = ____________________________________________________________________________[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.0143
= ________ = 0.742. ( Terpilih) 0.01926
[0.129 ]1 . [0.1961]2
P
k(4,6) = ____________________________________________________________________________[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.00496
= ________ = 0.257. 0.01926
Jalur keempat dari semut pertama adalah 1 – 2 – 3 – 4 – 5.
[0.129 ]1 . [0.1857]2
P
k(5,6) = ____________________________________________________________________________[0.129]1.[0.1857 ]2
0.00445
= ________ = 1. ( Terpilih) 0.00445
Jalur kelima dari semut pertama adalah 1 – 2 – 3 – 4 – 5 – 6.
Jadi, jalur semut pertama adalah 1 – 2 – 3 – 4 – 5 – 6 – 1 dengan panjang jalur
adalah 46.4592.
* Semut kedua
[0.129 ]1 . [0.5]2
P
k(2,1) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.1562]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.03225
= ________ = 0.871. ( Terpilih) 0.037
[0.129 ]1 . [0.1562]2
P
k(2,3) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.1562]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.00315
[0.129 ]1 . [0.0735]2
P
k(2,4) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.1562]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.000696
= ________ = 0.0188. 0.037
[0.129 ]1 . [0.0677]2
P
k(2,5) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.1562]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.00059
= ________ = 0.0159. 0.037
[0.129 ]1 . [0.0535]2
P
k(2,6) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.1562]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.000369
= ________ = 0.00997. 0.037
Jalur kesatu dari semut kedua adalah 2 – 1.
[0.129 ]1 . [0.128]2
P
k(1,3)=_________________________________________________________
[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2 0.00211
= ________ = 0.617. ( Terpilih) 0.003418
[0.129 ]1 . [0.0644]2
P
k(1,4)=_________________________________________________________
[0.129]
1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2
0.000535
= _________ = 0.156. 0.003418
[0.129 ]1 . [0.0604]2
P
k(1,5)=_________________________________________________________
[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2
0.00047
[0.129 ]1 . [0.0485]2
P
k(1,6)=_________________________________________________________
[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2
0.000303
= ________ = 0.0886. 0.003418
Jalur kedua dari semut kedua adalah 2 – 1 – 3.
[0.129 ]1 . [0.1104]2
P
k(3,4) = ____________________________________________________________________________[0.129]1.[0.1104]2+[0.129]1.[0.1085 ]2+[0.129]1.[0.0714]2
0.00157
= ________ = 0.419. ( Terpilih)
0.003747
[0.129 ]1 . [0.1085]2
P
k(3,5) = ____________________________________________________________________________[0.129]1.[0.1104]2+[0.129]1.[0.1085 ]2+[0.129]1.[0.0714]2
0.00152
= ________ = 0.405.
0.003747
[0.129 ]1 . [0.0714]2
P
k(3,6) = ____________________________________________________________________________[0.129]1.[0.1104]2+[0.129]1.[0.1085 ]2+[0.129]1.[0.0714]2
0.000657
= ________ = 0.175.
0.003747
Jalur ketiga dari semut kedua adalah 2 – 1 – 3 – 4.
[0.129 ]1 . [0.3333]2P
k(4,5) = ____________________________________________________________________________[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.0143
= ________ = 0.742. ( Terpilih) 0.01926
[0.129 ]1 . [0.1961]2
P
k(4,6) = ____________________________________________________________________________[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.00496
= ________ = 0.257. 0.01926
[0.129 ]1 . [0.1857]2
P
k(5,6) = ____________________________________________________________________________[0.129]1.[0.1857 ]2
0.00445
= ________ = 1. ( Terpilih) 0.00445
Jalur kelima dari semut kedua adalah 2 – 1 – 3 – 4 – 5 – 6.
Jadi, jalur semut kedua adalah 2 – 1 – 3 – 4 – 5 – 6 – 2 dengan panjang jalur
adalah 45.9323.
*Semut ketiga
[0.129 ]1 . [0.128]2
P
k(3,1)=_________________________________________________________
[0.129]
1.[0.128 ]2+[0.129]1.[0.1562]2+[0.129]1.[0.1104 ]2+[0.129]1.[0.1085]2+[0.129]1.[0.0714]2
0.00211
= ________ = 0.234. 0.009
[0.129 ]1 . [0.1562]2
P
k(3,2) = ____________________________________________________________________________[0.129]1.[0.128 ]2+[0.129]1.[0.1562]2+[0.129]1.[0.1104 ]2+[0.129]1.[0.1085]2+[0.129]1.[0.0714]2
0.00315
= ________ = 0.35. ( Terpilih) 0.009
[0.129 ]1 . [0.1104]2
P
k(3,4) = ____________________________________________________________________________[0.129]1.[0.128 ]2+[0.129]1.[0.1562]2+[0.129]1.[0.1104 ]2+[0.129]1.[0.1085]2+[0.129]1.[0.0714]2
0.00157
= ________ = 0.174. 0.009
[0.129 ]1 . [0.1085]2
P
k(3,5) = ____________________________________________________________________________[0.129]1.[0.128 ]2+[0.129]1.[0.1562]2+[0.129]1.[0.1104 ]2+[0.129]1.[0.1085]2+[0.129]1.[0.0714]2
0.00152
[0.129 ]1 . [0.0714]2
P
k(3,6) = ____________________________________________________________________________[0.129]1.[0.128 ]2+[0.129]1.[0.1562]2+[0.129]1.[0.1104 ]2+[0.129]1.[0.1085]2+[0.129]1.[0.0714]2
0.000657
= ________ = 0.073. 0.009
Jalur kesatu dari semut ketiga adalah 3 – 2.
[0.129 ]1 . [0.5]2
P
k(2,1) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.03225
= ________ = 0.948. ( Terpilih) 0.034
[0.129 ]1 . [0.0735]2
P
k(2,4) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.000696 = ________ = 0.02.
0.034
[0.129 ]1 . [0.0677]2
P
k(2,5) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2
0.00059
= ________ = 0.017. 0.034
[0.129 ]1 . [0.0535]2
P
k(2,6) = ____________________________________________________________________________[0.129]1.[0.5]2+[0.129]1.[0.0735 ]2+[0.129]1.[0.0677]2+[0.129]1.[0.0535]2 0.000369
= ________ = 0.01. 0.034
Jalur kedua dari semut ketiga adalah 3 – 2 – 1.
[0.129 ]1 . [0.0644]2
P
k(1,4)=_________________________________________________________
[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2
0.000535
= _________ = 0.409. ( Terpilih)
[0.129 ]1 . [0.0604]2
P
k(1,5)=_________________________________________________________
[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2
0.00047
= ________ = 0.359. 0.001308
[0.129 ]1 . [0.0485]2
P
k(1,6)=_________________________________________________________
[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2 0.000303
= ________ = 0.231. 0.001308
Jalur ketiga dari semut ketiga adalah 3 – 2 – 1 – 4.
[0.129 ]1 . [0.3333]2
P
k(4,5) = ____________________________________________________________________________[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.0143
= ________ = 0.742. ( Terpilih) 0.01926
[0.129 ]1 . [0.1961]2
P
k(4,6) = ____________________________________________________________________________[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.00496
= ________ = 0.257. 0.01926
Jalur keempat dari semut ketiga adalah 3 – 2 – 1 – 4 – 5.
[0.129 ]1 . [0.1857]2
P
k(5,6) = ____________________________________________________________________________[0.129]1.[0.1857 ]2
0.00445
= ________ = 1. ( Terpilih) 0.00445
Jalur kelima dari semut ketiga adalah 3 – 2 – 1 – 4 – 5 – 6.
*Semut keempat
[0.129 ]1 . [0.0644]2
P
k(4,1)=___________________________________________________________
[0.129]
1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2+[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.000535
= _________ = 0.0243.
0.022
[0.129 ]1 . [0.0735]2
P
k(4,2) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2+[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.000696
= ________ = 0.0316. 0.022
[0.129 ]1 . [0.1104]2
P
k(4,3) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2+[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.00157
= ________ = 0.0713. 0.022
[0.129 ]1 . [0.3333]2
P
k(4,5) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2+[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.0143
= ________ = 0.65. ( Terpilih) 0.022
[0.129 ]1 . [0.1961]2
P
k(4,6) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2+[0.129]1.[0.3333]2+[0.129]1.[0.1961 ]2
0.00496
= ________ = 0.225. 0.022
Jalur kesatu dari semut keempat adalah 4 – 5.
[0.129 ]1 . [0.0604]2P
k(5,1)=_________________________________________________________
[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2+[0.129]1.[0.1857]2
0.00047
[0.129 ]1 . [0.0677]2
P
k(5,2) = ____________________________________________________________________________[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2+[0.129]1.[0.1857]2
0.00059
= ________ = 0.084. 0.007
[0.129 ]1 . [0.1085]2
P
k(5,3) = ____________________________________________________________________________[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2+[0.129]1.[0.1857]2
0.00152
= ________ = 0.217. 0.007
[0.129 ]1 . [0.1857]2
P
k(5,6) = ____________________________________________________________________________[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2+[0.129]1.[0.1857]2
0.00445
= ________ = 0.635. ( Terpilih) 0.007
Jalur kedua dari semut keempat adalah 4 – 5 – 6.
[0.129 ]1 . [0.0485]2
P
k(6,1)=_________________________________________________________
[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2 0.000303
= ________ = 0.228. 0.001329
[0.129 ]1 . [0.0535]2
P
k(6,2) = ____________________________________________________________________________[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2
0.000369
= ________ = 0.277. 0.001329
[0.129 ]1 . [0.0714]2
P
k(6,3) = ____________________________________________________________________________[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2
0.000657
= ________ = 0.494. ( Terpilih) 0.001329
[0.129 ]1 . [0.128]2
P
k(3,1)=_________________________________________________________
[0.129]
1.[0.128 ]2+[0.129]1.[0.1562]2
0.00211
= ________ = 0.401. 0.00526
[0.129 ]1 . [0.1562]2
P
k(3,2) = ____________________________________________________________________________[0.129]1.[0.128 ]2+[0.129]1.[0.1562]2
0.00315
= ________ = 0.598. ( Terpilih) 0.00526
Jalur keempat dari semut keempat adalah 4 – 5 – 6 – 3 – 2.
[0.129 ]1 . [0.5]2
P
k(2,1) = ____________________________________________________________________________[0.129]1 . [0.5]2
0.03225
= ________ = 1. ( Terpilih) 0.03225
Jalur kelima dari semut keempat adalah 4 – 5 – 6 – 3 – 2 – 1 .
Jadi, jalur semut keempat adalah 4 – 5 – 6 – 3 – 2 – 1 – 4 dengan panjang jalur
adalah 46.3125.
*Semut kelima
[0.129 ]1 . [0.0604]2
P
k(5,1)=___________________________________________________________
[0.129]
1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2+[0.129]1.[0.3333]2+[0.129]1.[0.1857]2
0.00047
= ________ = 0.022. 0.02133
[0.129 ]1 . [0.0677]2
P
k(5,2) = ______________________________________________________________________________[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2+[0.129]1.[0.3333]2+[0.129]1.[0.1857]2
0.00059
[0.129 ]1 . [0.1085]2
P
k(5,3) = ______________________________________________________________________________[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2+[0.129]1.[0.3333]2+[0.129]1.[0.1857]2
0.00152
= ________ = 0.071. 0.02133
[0.129 ]1 . [0.3333]2
P
k(5,4) = ______________________________________________________________________________[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2+[0.129]1.[0.3333]2+[0.129]1.[0.1857]2
0.0143
= ________ = 0.67. ( Terpilih) 0.02133
[0.129 ]1 . [0.1857]2
P
k(5,6) = ______________________________________________________________________________[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2+[0.129]1.[0.3333]2+[0.129]1.[0.1857]2
0.00445
= ________ = 0.208. 0.02133
Jalur kesatu dari semut kelima adalah 5 – 4.
[0.129 ]1 . [0.0644]2
P
k(4,1)=___________________________________________________________
[0.129]
1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2+[0.129]1.[0.1961 ]2
0.000535
= _________ = 0.0689.
0.07761
[0.129 ]1 . [0.0735]2
P
k(4,2) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2+[0.129]1.[0.1961 ]2
0.000696
= ________ = 0.0896. 0.07761
[0.129 ]1 . [0.1104]2
P
k(4,3) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2+[0.129]1.[0.1961 ]2
0.00157
[0.129 ]1 . [0.1961]2
P
k(4,6) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2+[0.129]1.[0.1961 ]2
0.00496
= ________ = 0.639. ( Terpilih) 0.07761
Jalur kedua dari semut kelima adalah 5 – 4 – 6.
[0.129 ]1 . [0.0485]2
P
k(6,1)=_________________________________________________________
[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2
0.000303
= ________ = 0.228. 0.001329
[0.129 ]1 . [0.0535]2
P
k(6,2) = ____________________________________________________________________________[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2
0.000369
= ________ = 0.277. 0.001329
[0.129 ]1 . [0.0714]2
P
k(6,3) = ____________________________________________________________________________[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2
0.000657
= ________ = 0.494. ( Terpilih) 0.001329
Jalur ketiga dari semut kelima adalah 5 – 4 – 6 – 3.
[0.129 ]1 . [0.128]2P
k(3,1)=_________________________________________________________
[0.129]
1.[0.128 ]2+[0.129]1.[0.1562]2
0.00211
= ________ = 0.401. 0.00526
[0.129 ]1 . [0.1562]2
P
k(3,2) = ____________________________________________________________________________[0.129]1.[0.128 ]2+[0.129]1.[0.1562]2
0.00315
= ________ = 0.598. ( Terpilih) 0.00526
[0.129 ]1 . [0.5]2
P
k(2,1) = ____________________________________________________________________________[0.129]1 . [0.5]2
0.03225
= ________ = 1. ( Terpilih) 0.03225
Jalur kelima dari semut kelima adalah 5 – 4 – 6 – 3 – 2 – 1.
Jadi, jalur semut kelima adalah dengan 5 – 4 – 6 – 3 – 2 – 1 – 5 dengan panjang
jalur adalah 47.0551.
*Semut keenam
[0.129 ]1 . [0.0485]2
P
k(6,1)=__________________________________________________________
[0.129]
1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2+[0.129]1.[0.1961 ]2+[0.129]1.[0.1857]2
0.000303
= ________ = 0.028. 0.001074
[0.129 ]1 . [0.0535]2
P
k(6,2) = ______________________________________________________________________________[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2+[0.129]1.[0.1961 ]2+[0.129]1.[0.1857]2
0.000369
= ________ = 0.034. 0.001074
[0.129 ]1 . [0.0714]2
P
k(6,3) = ______________________________________________________________________________[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2+[0.129]1.[0.1961 ]2+[0.129]1.[0.1857]2
0.000657
= ________ = 0.061. 0.001074
[0.129 ]1 . [0.1961]2
P
k(6,4) = ______________________________________________________________________________[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2+[0.129]1.[0.1961 ]2+[0.129]1.[0.1857]2
0.00496
[0.129 ]1 . [0.1857]2
P
k(6,5) = ______________________________________________________________________________[0.129]1.[0.0485]2+[0.129]1.[0.0535]2+[0.129]1.[0.0714]2+[0.129]1.[0.1961 ]2+[0.129]1.[0.1857]2
0.00445
= ________ = 0.414. 0.001074
Jalur kesatu dari semut keenam adalah 6 – 4.
[0.129 ]1 . [0.0644]2
P
k(4,1)=___________________________________________________________
[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2++[0.129]1.[0.3333]2
0.000535
= _________ = 0.0312. 0.0171
[0.129 ]1 . [0.0735]2
P
k(4,2) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2++[0.129]1.[0.3333]2
0.000696
= ________ = 0.0407. 0.0171
[0.129 ]1 . [0.1104]2
P
k(4,3) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2++[0.129]1.[0.3333]2
0.00157
= ________ = 0.0918. 0.0171
[0.129 ]1 . [0.3333]2
P
k(4,5) = ______________________________________________________________________________[0.129]1.[0.0644]2+[0.129 ]1.[0.0735]2+[0.129]1.[0.1104]2++[0.129]1.[0.3333]2
0.0143
= ________ = 0.836. ( Terpilih) 0.0171
Jalur kedua dari semut keenam adalah 6 – 4 – 5.
[0.129 ]1 . [0.0604]2P
k(5,1)=___________________________________________________________
[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2 0.00047
[0.129 ]1 . [0.0677]2
P
k(5,2) = ______________________________________________________________________________[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2
0.00059
= ________ = 0.228 0.00258
[0.129 ]1 . [0.1085]2
P
k(5,3) = ______________________________________________________________________________[0.129]1.[0.0604]2+[0.129 ]1.[0.0677]2+[0.129]1.[0.1085]2
0.00152
= ________ = 0.589. ( Terpilih) 0.00258
Jalur ketiga dari semut keenam adalah 6 – 4 – 5 – 3.
[0.129 ]1 . [0.128]2
P
k(3,1)=_________________________________________________________
[0.129]
1.[0.128 ]2+[0.129]1.[0.1562]2
0.00211
= ________ = 0.401. 0.00526
[0.129 ]1 . [0.1562]2
P
k(3,2) = ____________________________________________________________________________[0.129]1.[0.128 ]2+[0.129]1.[0.1562]2
0.00315
= ________ = 0.598. ( Terpilih) 0.00526
Jalur keempat dari semut keenam adalah 6 – 4 – 5 – 3 – 2.
[0.129 ]1 . [0.5]2
P
k(2,1) = ____________________________________________________________________________[0.129]1 . [0.5]2
0.03225
= ________ = 1. ( Terpilih) 0.03225
Jalur kelima dari semut keenam adalah 6 – 4 – 5 – 3 – 2 – 1.
¾
Tabu(tempat menyimpan jalur semut) =
Semut pertama
1 – 2 – 3 – 4 – 5 – 6 – 1 dengan panjang jalur 46.4592.
Semut kedua
2 – 1 – 3 – 4 – 5 – 6 – 2 dengan panjang jalur 45.9323.
Semut ketiga
3 – 2 – 1 – 4 – 5 – 6 – 3 dengan panjang jalur 46.3125.
Semut keempat
4 – 5 – 6 – 3 – 2 – 1 – 4 dengan panjang jalur 46.3125.
Semut kelima
5 – 4 – 6 – 3 – 2 – 1 – 5 dengan panjang jalur 47.0551.
Semut keenam
6 – 4 – 5 – 3 – 2 – 1 – 6 dengan panjang jalur 46.3371.
¾
Hitung feromon setiap semut dengan menggunakan rumus
Δτ
kij
=1/L
k, dimana L
kadalah panjang jalur.
-
Semut pertama
= 1 / 46.4592 = 0.02152
-
Semut kedua
= 1 / 45.9323 = 0.02177
-
Semut ketiga
= 1 / 46.3125 = 0.0216
-
Semut keempat
= 1 / 46.3125 = 0.0216
-
Semut kelima
= 1 / 47.0551 = 0.02125
-
Semut keenam
= 1 / 46.3371 = 0.02158
Δτ
kij =
0 0.02152
0.02177
0.0432
0.02125
0.02158
0.1078
0
0.02152
0 0 0
0 0.08603 0 0.04329
0
0
0 0 0 0
0.10807
0.02125
0
0 0.02158
0.02125
0 0.08649
0.02152 0.02177 0.03445 0.02158
0
0
¾
Lakukan update jumlah feromon menggunakan persamaan II.2
m
τ
i,j(t+1)= (1-
ρ
).
τ
i,j(t) +
∑
[
Δτ
kij(t)]
k=1
=
(1–0.5).(0.129)+
0 0.02152 0.02177 0.0432 0.02125 0.02158
0.1078 0 0.02152 0 0 0
0 0.08603 0 0.04329 0 0
0 0 0 0 0.10807 0.02125
0 0 0.02158 0.02125 0
0.08649
0.02152 0.02177 0.06445 0.02158 0 0
¾
Setelah dilakukan update feromon, tentukan kembali jalur yang akan dipilih
sampai didapat jalur terpendek
•
Semut pertama
[0.08612 ]1 . [0.5]2
P
k(1,2)=________________________________________________________________________________[0.08612]1.[0.5]2+[0.08637]1.[0.128 ]2+[0.1078]1.[0.0644]2+[0.08585]1.[0.0604]2+[0.08618]1.[0.0485]2
0.02153
= ________ = 0.9. ( Terpilih) 0.023908
[0.08637 ]1 . [0.128]2
P
k(1,3)=_____________________________________________________________
[0.08612]1.[0.5]2+[0.08637]1.[0.128 ]2+[0.1078]1.[0.0644]2+[0.08585]1.[0.0604]2+[0.08618]1.[0.0485]2
0.001415
= ________ = 0.0592. 0.023908
[0.1078]1. [0.0644]2
P
k(1,4)=_____________________________________________________________
[0.08612]1.[0.5]2+[0.08637]1.[0.128 ]2+[0.1078]1.[0.0644]2+[0.08585]1.[0.0604]2+[0.08618]1.[0.0485]2
0.000447
= _________ = 0.0187. 0.023908
[0.08585]1. [0.0604]2
P
k(1,5)=_____________________________________________________________
[0.08612]1.[0.5]2+[0.08637]1.[0.128 ]2+[0.1078]1.[0.0644]2+[0.08585]1.[0.0604]2+[0.08618]1.[0.0485]2
0.000313
= ________ = 0.0131. 0.023908
[0.08618 ]1 . [0.0485]2
P
k(1,6)=_____________________________________________________________
[0.08612]1.[0.5]2+[0.08637]1.[0.128 ]2+[0.1078]1.[0.0644]2+[0.08585]1.[0.0604]2+[0.08618]1.[0.0485]2
0.000203
= ________ = 0.0085. 0.023908
Jalur pertama dari semut pertama adalah 1 – 2.
[0.08612 ]1 . [0.1562]2P
k(2,3) = ____________________________________________________________________________[0.08612]1.[0.1562]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.0021
[0.0646 ]1 . [0.0735]2
P
k(2,4) = ____________________________________________________________________________[0.08612]1.[0.1562]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.000349
= ________ = 0.119. 0.00293
[0.0646 ]1 . [0.0677]2
P
k(2,5) = ____________________________________________________________________________[0.08612]1.[0.1562]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.000296
= ________ = 0.101. 0.00293
[0.0646 ]1 . [0.0535]2
P
k(2,6) = ____________________________________________________________________________[0.08612]1.[0.1562]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.000185
= ________ = 0.063. 0.00293
Jalur kedua dari semut pertama adalah 1 – 2 – 3.
[0.10789 ]1 . [0.1104]2
P
k(3,4) = ____________________________________________________________________________[0.10789]1.[0.1104]2+[0.0646]1.[0.1085 ]2+[0.0646]1.[0.0714]2
0.00131
= ________ = 0.546. 0.0024
[0.0646 ]1 . [0.1085]2
P
k(3,5) = ____________________________________________________________________________[0.10789]1.[0.1104]2+[0.0646]1.[0.1085 ]2+[0.0646]1.[0.0714]2
0.00076
= ________ = 0.316. ( Terpilih) 0.0024
[0.0646 ]1 . [0.0714]2
P
k(3,6) = ____________________________________________________________________________[0.10789]1.[0.1104]2+[0.0646]1.[0.1085 ]2+[0.0646]1.[0.0714]2
0.00033
= ________ = 0.1375. 0.0024
[0.08585]1 . [0.3333]2
P
k(5,4) = ____________________________________________________________________________[0.08585]1.[0.3333]2+[0.15109]1.[0.1857 ]2
0.00953
= ________ = 0.646. 0.01474
[0.15109]1.[0.1857 ]2
P
k(5,6) = ____________________________________________________________________________[0.08585]1.[0.3333]2+[0.15109]1.[0.1857 ]2
0.00521
= ________ = 0.353. ( Terpilih) 0.01474
Jalur keempat dari semut pertama adalah 1 – 2 – 3 – 5 – 6.
[0.08618 ]1 . [0.1961]2P
k(6,4) = ____________________________________________________________________________[0.08618 ]1 . [0.1961]2
0.00331
= ________ = 1. ( Terpilih) 0.00331
Jalur kelima dari semut pertama adalah 1 – 2 – 3 – 5 – 6 – 4 – 1.
Jadi, jalur semut pertama adalah 1 – 2 – 3 – 5 – 6 – 4 – 1 dengan panjang jalur
adalah 43.6310.
* Semut kedua
[0.1724 ]1 . [0.5]2
P
k(2,1)=_________________________________________________________________________________[0.1724]1.[0.5]2+[0.08612]1.[0.1562]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.0431
= ________ = 0.936. ( Terpilih) 0.04603
[0.08612 ]1 . [0.1562]2
P
k(2,3)=_________________________________________________________________________________[0.1724]1.[0.5]2+[0.08612]1.[0.1562]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.0021
[0.0646 ]1 . [0.0735]2
P
k(2,4)=_________________________________________________________________________________[0.1724]1.[0.5]2+[0.08612]1.[0.1562]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.000349
= ________ = 0.0076. 0.04603
[0.0646 ]1 . [0.0677]2
P
k(2,5) =________________________________________________________________________________[0.1724]1.[0.5]2+[0.08612]1.[0.1562]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.000296
= ________ = 0.0064. 0.04603
[0.0646 ]1 . [0.0535]2
P
k(2,6) = ________________________________________________________________________________[0.1724]1.[0.5]2+[0.08612]1.[0.1562]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.000185
= ________ = 0.004. 0.04603
Jalur kesatu dari semut kedua adalah 2 – 1.
[0.08637 ]1 . [0.128]2
P
k(1,3)=_____________________________________________________
[0.08637]
1.[0.128 ]2+[0.1078]1.[0.0644]2+[0.08585 ]1.[0.0604]2+[0.08618]1.[0.0485]2
0.001415
= ________ = 0.595. ( Terpilih) 0.002378
[0.1078 ]1 . [0.0644]2
P
k(1,4)=_____________________________________________________
[0.08637]
1.[0.128 ]2+[0.1078]1.[0.0644]2+[0.08585 ]1.[0.0604]2+[0.08618]1.[0.0485]2
0.000447
= _________ = 0.188. 0.002378
[0.08585 ]1 . [0.0604]2
P
k(1,5)=_____________________________________________________
[0.08637]
1.[0.128 ]2+[0.1078]1.[0.0644]2+[0.08585 ]1.[0.0604]2+[0.08618]1.[0.0485]2
0.000313
[0.8618 ]1 . [0.0485]2
P
k(1,6)=_________________________________________________________
[0.08637]
1.[0.128 ]2+[0.1078]1.[0.0644]2+[0.08585 ]1.[0.0604]2+[0.08618]1.[0.0485]2
0.000203
= ________ = 0.085. 0.002378
Jalur kedua dari semut kedua adalah 2 – 1 – 3.
[0.10789 ]1 . [0.1104]2
P
k(3,4) = ____________________________________________________________________________[0.10789]1.[0.1104]2+[0.0646]1.[0.1085 ]2+[0.0646]1.[0.0714]2
0.00131
= ________ = 0.546. 0.0024
[0.0646 ]1 . [0.1085]2
P
k(3,5) = ____________________________________________________________________________[0.10789]1.[0.1104]2+[0.0646]1.[0.1085 ]2+[0.0646]1.[0.0714]2
0.00076
= ________ = 0.316. ( Terpilih) 0.0024
[0.0646 ]1 . [0.0714]2
P
k(3,6) = ____________________________________________________________________________[0.10789]1.[0.1104]2+[0.0646]1.[0.1085 ]2+[0.0646]1.[0.0714]2
0.00033
= ________ = 0.1375. 0.0024
Jalur ketiga dari semut kedua adalah 2 – 1 – 3 – 5.
[0.08585]1 . [0.3333]2
P
k(5,4) = ____________________________________________________________________________[0.08585]1.[0.3333]2+[0.15109]1.[0.1857 ]2
0.00953
= ________ = 0.646. 0.01474
[0.15109]1.[0.1857 ]2
P
k(5,6) = ____________________________________________________________________________[0.08585]1.[0.3333]2+[0.15109]1.[0.1857 ]2
0.00521
= ________ = 0.353. ( Terpilih) 0.01474
[0.08618 ]1 . [0.1961]2
P
k(6,4) = ____________________________________________________________________________[0.08618 ]1 . [0.1961]2
0.00331
= ________ = 1. ( Terpilih) 0.00331
Jalur kelima dari semut kedua adalah 2 – 1 – 3 – 5 – 6 – 4.
Jadi, jalur semut kedua adalah 2 – 1 – 3 – 5 – 6 – 4 – 2 dengan panjang jalur
adalah 43.1154.
*Semut ketiga
[0.0646 ]1 . [0.128]2
P
k(3,1)=________________________________________________________________
[0.0646]1.[0.128 ]2+[0.15063]1.[0.1562]2+[0.10789]1.[0.1104 ]2+[0.0646]1.[0.1085]2+[0.0646]1.[0.0714]2
0.00106
= ________ = 0.148. 0.00713
[0.15063 ]1 . [0.1562]2
P
k(3,2)=_________________________________________________________________________________[0.0646]1.[0.128 ]2+[0.15063]1.[0.1562]2+[0.10789]1.[0.1104 ]2+[0.0646]1.[0.1085]2+[0.0646]1.[0.0714]2
0.00367
= ________ = 0.514. ( Terpilih) 0.00713
[0.10789 ]1 . [0.1104]2
P
k(3,4)=_________________________________________________________________________________[0.0646]1.[0.128 ]2+[0.15063]1.[0.1562]2+[0.10789]1.[0.1104 ]2+[0.0646]1.[0.1085]2+[0.0646]1.[0.0714]2
0.00131
= ________ = 0.183. 0.00713
[0.0646 ]1 . [0.1085]2
P
k(3,5) =________________________________________________________________________________[0.0646]1.[0.128 ]2+[0.15063]1.[0.1562]2+[0.10789]1.[0.1104 ]2+[0.0646]1.[0.1085]2+[0.0646]1.[0.0714]2
0.00076
[0.0646]1 . [0.0714]2
P
k(3,6) = ________________________________________________________________________________[0.0646]1.[0.128 ]2+[0.15063]1.[0.1562]2+[0.10789]1.[0.1104 ]2+[0.0646]1.[0.1085]2+[0.0646]1.[0.0714]2
0.00033
= ________ = 0.046. 0.00713
Jalur kesatu dari semut ketiga adalah 3 – 2.
[0.1724 ]1 . [0.5]2
P
k(2,1) = _________________________________________________________________[0.1724]1.[0.5]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.0431
= ________ = 0.981. ( Terpilih) 0.04393
[0.0646 ]1 . [0.0735]2
P
k(2,4) = ____________________________________________________________________________[0.1724]1.[0.5]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.000349
= ________ = 0.008. 0.04393
[0.0646 ]1 . [0.0677]2
P
k(2,5) = ____________________________________________________________________________[0.1724]1.[0.5]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.000296
= ________ = 0.0067. 0.04393
[0.0646 ]1 . [0.0535]2
P
k(2,6) = ____________________________________________________________________________[0.1724]1.[0.5]2+[0.0646]1.[0.0735 ]2+[0.0646]1.[0.0677]2+[0.0646]1.[0.0535]2
0.000185
= ________ = 0.0042. 0.04393
Jalur kedua dari semut ketiga adalah 3 – 2 – 1.
[0.1078 ]1 . [0.0644]2
P
k(1,4)=_________________________________________________________
[0.1078]1.[0.0644]2+[0.08585 ]1.[0.0604]2+[0.08618]1.[0.0485]2 0.000447
= _________ = 0.464. ( Terpilih)
[0.08585 ]1 . [0.0604]2
P
k(1,5)=_________________________________________________________
[0.1078]1.[0.0644]2+[0.08585 ]1.[0.0604]2+[0.08618]1.[0.0485]2
0.000313
= ________ = 0.325. 0.000963
[0.08618 ]1 . [0.0485]2
P
k(1,6)=_________________________________________________________
[0.129]1.[0.128 ]2+[0.129]1.[0.0644]2+[0.129 ]1.[0.0604]2+[0.129]1.[0.0485]2 0.000203
= ________ = 0.210. 0.000963
Jalur ketiga dari semut ketiga adalah 3 – 2 – 1 – 4.
[0.17267 ]1 . [0.3333]2P
k(4,5) = ____________________________________________________________________________[0.17267]1.[0.3333]2+[0.08585]1.[0.1961 ]2
0.0192
= ________ = 0.368. 0.0522
[0.08585]1 . [0.1961]2
P
k(4,6) = ____________________________________________________________________________[0.17267]1.[0.3333]2+[0.08585]1.[0.1961 ]2
0.033
= ________ = 0.632. ( Terpilih) 0.0522
Jalur keempat dari semut ketiga adalah 3 – 2 – 1 – 4 – 6.
[0.0646 ]1 . [0.1857]2P
k(6,5) = ____________________________________________________________________________[0.0646]1.[0.1857 ]2
0.00223
= ________ = 1. ( Terpilih) 0.00223
Jalur kelima dari semut ketiga adalah 3 – 2 – 1 – 4 – 6 – 5.
*Semut keempat
[0.0646 ]1 . [0.0644]2
P
k(4,1)=___________________________________________________________
[0.0646]1.[0.0644]2+[0.0646]1.[0.0735]2+[0.0646]1.[0.1104]2+[0.17267]1.[0.3333]2+[0.08585]1.[0.1961 ]2
0.000268
= _________ = 0.005.
0.0536
[0.0646 ]1 . [0.0735]2
P
k(4,2) = _______________________________________________________________________________[0.0646]1.[0.0644]2+[0.0646]1.[0.0735]2+[0.0646]1.[0.1104]2+[0.17267]1.[0.3333]2+[0.08585]1.[0.1961 ]2
0.000349
= ________ = 0.0065. 0.0536
[0.0646 ]1 . [0.1104]2
P
k(4,3) = _______________________________________________________________________________[0.0646]1.[0.0644]2+[0.0646]1.[0.0735]2+[0.0646]1.[0.1104]2+[0.17267]1.[0.3333]2+[0.08585]1.[0.1961 ]2
0.000787
= ________ = 0.0146. 0.0536
[0.17267 ]1 . [0.3333]2
P
k(4,5) = _______________________________________________________________________________[0.0646]1.[0.0644]2+[0.0646]1.[0.0735]2+[0.0646]1.[0.1104]2+[0.17267]1.[0.3333]2+[0.08585]1.[0.1961 ]2
0.0192
= ________ = 0.358. 0.0536
[0.08585 ]1 . [0.1961]2
P
k(4,6) = _______________________________________________________________________________[0.0646]1.[0.0644]2+[0.0646]1.[0.0735]2+[0.0646]1.[0.1104]2+[0.17267]1.[0.3333]2+[0.08585]1.[0.1961 ]2
0.033
= ________ = 0.615. ( Terpilih) 0.0536
Jalur kesatu dari semut keempat adalah 4 – 6.
[0.08612 ]1 . [0.0485]2P
k(6,1)=_____________________________________________________
[0.08612]
1.[0.0485]2+[0.08637 ]1.[0.0535]2+[0.12905]1.[0.0714]2+[0.0646]1.[0.1857]2
0.000202
[0.08637 ]1.[0.0535]2
P
k(6,2) = ____________________________________________________________________________[0.08612]1.[0.0485]2+[0.08637 ]1.[0.0535]2+[0.12905]1.[0.0714]2+[0.0646]1.[0.1857]2
0.000247
= ________ = 0.074. 0.003336
[0.12905 ]1 . [0.0714]2
P
k(6,3) = ____________________________________________________________________________[0.08612]1.[0.0485]2+[0.08637 ]1.[0.0535]2+[0.12905]1.[0.0714]2+[0.0646]1.[0.1857]2
0.00657
= ________ = 0.196. 0.003336
[0.0646]1.[0.1857]2
P
k(6,5) = ____________________________________________________________________________[0.08612]1.[0.0485]2+[0.08637 ]1.[0.0535]2+[0.12905]1.[0.0714]2+[0.0646]1.[0.1857]2
0.00223
= ________ = 0.668. ( Terpilih) 0.003336
Jalur kedua dari semut keempat adalah 4 – 6 – 5.
[0.0646 ]1 . [0.0604]2
P
k(5,1)=_________________________________________________________
[0.0646 ]1 . [0.0604]2
+[0.0646]
1.[0.0677]2+[0.08618]1.[0.1085]20.000235
= ________ = 0.152. 0.001541
[0.0646 ]1 .[0.0677]2
P
k(5,2) = ____________________________________________________________________________[0.0646 ]1 . [0.0604]2
+[0.0646]
1.[0.0677]2+[0.08618]1.[0.1085]2 0.000296= ________ = 0.192. 0.001541
[0.08618]1.[0.1085]2
P
k(5,3) = ____________________________________________________________________________[0.0646 ]1 . [0.0604]2
+[0.0646]
1.[0.0677]2+[0.08618]1.[0.1085]2 0.00101= ________ = 0.6554. ( Terpilih) 0.001541
[0.0646 ]1 . [0.128]2
P
k(3,1)=_________________________________________________________
[0.0646]
1.[0.128 ]2+[0.15603]1.[0.1562]2
0.00106
= ________ = 0.224. 0.00473
[0.15063 ]1 . [0.1562]2
P
k(3,2) = ____________________________________________________________________________[0.0646]1.[0.128 ]2+[0.15603]1.[0.1562]2
0.00367
= ________ = 0.775. ( Terpilih) 0.00473
Jalur keempat dari semut keempat adalah 4 – 6 – 5 – 3 – 2.
[0.1724 ]1 . [0.5]2P
k(2,1) = ____________________________________________________________________________[0.1724]1 . [0.5]2
0.0431
= ________ = 1. ( Terpilih) 0.0431
Jalur kelima dari semut keempat adalah 4 – 6 – 5 – 3 – 2 – 1 .
Jadi, jalur semut keempat adalah 4 – 6 – 5 – 3 – 2 – 1 – 4 dengan panjang jalur
adalah 43.6310
*Semut kelima
[0.0646 ]1 . [0.0604]2
P
k(5,1)=___________________________________________________________
[0.0646]1.[0.0604]2+[0.0646 ]1.[0.0677]2+[0.08618]1.[0.1085]2+[0.08585]1.[0.3333]2+[0.15109]1.[0.1857]2
0.000235
= ________ = 0.0144. 0.016281
[0.0646 ]1 . [0.0677]2
P
k(5,2) = _______________________________________________________________________________[0.0646]1.[0.0604]2+[0.0646 ]1.[0.0677]2+[0.08618]1.[0.1085]2+[0.08585]1.[0.3333]2+[0.15109]1.[0.1857]2
0.000296
[0.08618 ]1 . [0.1085]2
P
k(5,3) = _______________________________________________________________________________[0.0646]1.[0.0604]2+[0.0646 ]1.[0.0677]2+[0.08618]1.[0.1085]2+[0.08585]1.[0.3333]2+[0.15109]1.[0.1857]2
0.00101
= ________ = 0.062. 0.016281
[0.08585 ]1 . [0.3333]2
P
k(5,4) = _______________________________________________________________________________[0.0646]1.[0.0604]2+[0.0646 ]1.[0.0677]2+[0.08618]1.[0.1085]2+[0.08585]1.[0.3333]2+[0.15109]1.[0.1857]2
0.00953
= ________ = 0.585. ( Terpilih) 0.016281
[0.15109 ]1 . [0.1857]2
P
k(5,6) = _______________________________________________________________________________[0.0646]1.[0.0604]2+[0.0646 ]1.[0.0677]2+[0.08618]1.[0.1085]2+[0.08585]1.[0.3333]2+[0.15109]1.[0.1857]2
0.00521
= ________ = 0.32. 0.016281
Jalur kesatu dari semut kelima adalah 5 – 4.
[0.0646 ]1 . [0.0644]2
P
k(4,1)=___________________________________________________________
[0.0646]
1.[0.0644]2+[0.0646 ]1.[0.0735]2+[0.0646]1.[0.1104]2+[0.08585]1.[0.1961 ]2
0.000268
= _________ = 0.00779.
0.034404
[0.0646 ]1 . [0.0735]2
P
k(4,2) = ______________________________________________________________________________[0.0646]1.[0.0644]2+[0.0646 ]1.[0.0735]2+[0.0646]1.[0.1104]2+[0.08585]1.[0.1961 ]2
0.000349
= ________ = 0.0101. 0.034404
[0.0646 ]1 . [0.1104]2
P
k(4,3) = ______________________________________________________________________________[0.0646]1.[0.0644]2+[0.0646 ]1.[0.0735]2+[0.0646]1.[0.1104]2+[0.08585]1.[0.1961 ]2
0.000787
[0.08585 ]1 . [0.1961]2
P
k(4,6) = ______________________________________________________________________________[0.0646]1.[0.0644]2+[0.0646 ]1.[0.0735]2+[0.0646]1.[0.1104]2+[0.08585]1.[0.1961 ]2
0.033
= ________ = 0.96. ( Terpilih) 0.034404
Jalur kedua dari semut kelima adalah 5 – 4 – 6.
[0.08612 ]1 . [0.0485]2
P
k(6,1)=_________________________________________________________
[0.08612]1.[0.0485]2+[0.08637]1.[0.0535]2+[0.12905]1.[0.0714]2
0.000202
= ________ = 0.182. 0.001106
[0.08637]1 . [0.0535]2
P
k(6,2) = ____________________________________________________________________________[0.08612]1.[0.0485]2+[0.08637]1.[0.0535]2+[0.12905]1.[0.0714]2
0.000247
= ________ = 0.223. 0.001106
[0.12905 ]1 . [0.0714]2
P
k(6,3) = ____________________________________________________________________________[0.08612]1.[0.0485]2+[0.08637]1.[0.0535]2+[0.12905]1.[0.0714]2
0.000657
= ________ = 0.594. ( Terpilih) 0.001106
Jalur ketiga dari semut kelima adalah 5 – 4 – 6 – 3.
[0.0646 ]1 . [0.128]2
P
k(3,1)=_________________________________________________________
[0.0646]
1.[0.128 ]2+[0.15063]1.[0.1562]2
0.00106
