BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI - Universitatea ...

210 Teodor Milos et al
elements mi,j defined by relations (1), where λ(
u )
edge u U .
i j ∈
(12)
1
2
3
M =
4
5
6
7
1
0
∞
∞
∞
∞
∞
∞
2
42
0
∞
∞
∞
∞
∞
3
53
∞
0
∞
∞
∞
∞
4
∞
∞
92
0
∞
∞
∞
5
∞
73
61
∞
0
∞
∞
6
∞
73
82
∞
∞
0
∞
7
∞
∞
∞
61
92
82
0
i j
is the value attributed to
V
61
92
82
0
0
i
∞
∞
∞
V
1
i
∞
153
153
61
92
82
0
V
2
i
197
153
153
61
92
82
0
V
3
i
197
153
153
.
61
Route with minimum total cost is given by way of minimum value in this
graph, which is determined using Bellman-Kalaba algorithm.
For each V ( k = 0,
1,...
is added to previous matrix a column in which
values are inserted properly. It follows successively:
k
i )
0
a) Calculate the values i mi7
V = (i = 1, ..., 7), which pass into the column
92
82
0
0
V i .
b) Calculate values 1
V i for i =1,...,7 (j =1,...,7), which is passing in that
column:
(13)
⎧V
⎪
⎪
⎪V
⎪
⎪V
⎪
⎪
⎨V
⎪
⎪V
⎪
⎪
⎪V
⎪
⎪V
⎩
1
1
1
2
1
3
1
4
1
5
1
6
1
7
= min
= min
= min
= min
= min
= min
= 0
j≠1
j≠
2
j≠3
j≠
4
j≠5
j≠
6
0
0 0
0
( V j + m1
j ) = min(
V2
+ m12,
V3
+ m13,...,
V7
+ m17
)
0
0
0
0
( V j + m2
j ) = min(
V1
+ m21,
V3
+ m23,...,
V7
+ m27
)
0
0 0
0
( V j + m3
j ) = min(
V1
+ m31,
V2
+ m32,...,
V7
+ m37
)
0
0
0
0
( V j + m4
j ) = min(
V1
+ m41,
V2
+ m41,...,
V7
+ m47
)
0
0 0
0
( V j + m5
j ) = min(
V1
+ m51,
V2
+ m51,...,
V7
+ m57
)
0
0 0
0
( V + m ) = min(
V + m , V + m ,..., V + m )
j
6 j
1
61
2
61
7
67
= ∞
= 153
= 153
= 61 .
= 92
= 82