BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI - Universitatea ...

208 Teodor Milos et al
(10)
k
i
ij
k −1
j
V = m + V = m + V
Based on the algorithm described, computer program named BEL_KAL was
designed in Borland PASCAL language.
Were made following nomenclatures: N is the order of the graph, V ( I,
J ) is
the column vector built at each iteration k, X ( I ) is the sequence of minimum
road; VAL - the minimum road graph, M ( I, J ) - matrix associated with graph,
whose elements are:
(11)
⎧
⎪
⎨
⎪
⎪
⎩
ij
i
λ(
u j ) − if arc ( xi,x
j )
( u ) − if arc ( x ,x )
n
i
mij = ∑ λ j
i j
i,j=
1
0 −
for i
= j
k
j
exist
.
not exist
Are introduced as data entry, graph order and its associated matrix, on lines,
i
whose elements are considered equal to λ ( u j ) , if there arc ( i j ) x x , , or equal to
0, otherwise (MATR_EX1.dat file).
As the data output sequence result road peaks of minimum values and value
of the road.
3. Case Study
Apply dynamic programming method to solve the problem of site selection
and capture of a main route to supply water through a sequential optimization
where deterministic, discrete.
It is considered a line of supply for locality L, departing from two locations
of S1 and S2 capture (fig. 1). Possible routes through the required A, B, C, D, E,
forming three sectors.
Putting the problem of determining the route for which the total cost is
minimum is determined for each track investments and prepare partial sequence
graph in Figure 2, where each arc is associated a cost, in conventional units.
They noted with x1 , 2 and the decision variables for each sector. These
variables will not take numeric values, but will be vertices of graph that you are
on the same alignment.
x 3 x
.