Page 58 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

46 Chapter 1

Table 1-3. Initialization of 5 values to the 5 Ants (say)

ANT ORDERS COST
ANT 1 7 1 3 6 2 5 4 8 C1
ANT 2 2 4 8 6 3 7 5 1 C2
ANT 3 7 2 3 5 1 6 4 8 C3
ANT 4 1 5 4 8 7 3 2 6 C4
ANT 5 4 8 5 3 6 2 7 1 C5

th
Step 2: Pheromone is the value assigned for selecting the i number for the
th
j position of the sequence selected by all the ants.(i.e) it is the
matrix in which the value at the index (i ,j) is the value assigned for
selecting the ith number for the jth position of the order selected by
all the ants. Initially the values of the matrix are completely filled up
with ones. The values of the Pheromone matrix are updated in every
iteration as

Pheromone matrix (n+1) = Pheromone matrix (n) + Updating Pheromone matrix

The value of the updating pheromone matrix must be high if the minimum
cost is assigned. Hence the matrix is filled up with the inverse values of the
corresponding cost as displayed below.

Table 1-4. Updating Pheromone Matrix

1 2 3 4 5 6 7 8
1 1/C4 1/C1 0 0 1/C3 0 0 1/C2+1/C5

2 1/C2 1/C3 0 0 1/C1 1/C5 1/C4 0
3 0 0 1/C1+1/C3 1/C5 1/C2 1/C4 0 0
4 1/C5 1/C2 1/C4 0 0 0 1/C1+1/C3 0

5 0 1/C4 1/C5 1/C3 0 1/C1 1/C2 0
6 0 0 0 1/C1+1/C2 1/C5 1/C3 0 1/C4
7 1/C1+1/C3 0 0 0 1/C4 1/C2 1/C5 0
8 0 1/C5 1/C2 1/C4 0 0 0 1/C1+1/C3