Page 60 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

48 Chapter 1

Select the number corresponding to the position of the lowest value of the
Normalized vector8. Suppose if q3 is the lowest among the values in the
vector, the number 3 is assigned to the variable u8.
This process is repeated to obtain the orders selected by the Ant 2, Ant3,
An4 and Ant 5.This is called one iteration.

Step 4:

• The updating pheromone matrix for the second iteration is computed as
described in the step 2 using the set of orders selected by the five ants in
the first iteration. This is called as Updating pheromone matrix (2).

nd
• Pheromone matrix used in the 2 iteration is computed as

Pheromone matrix (2) = Pheromone matrix (1) +Updating Pheromone matrix (2)

Step 5: Next set of orders selected by the five ants are computed as
described in the step 3.

Step 6: The step 3 to step 5 is repeated for the particular number of
iterations. Thus best set of orders selected by the five ants are
obtained using Ant colony optimization.

Note that best among the best set of orders selected by the five ants
in the last iteration is selected as the global best order.

6.2 Example

Consider the problem of finding the optimum order in which the numbers from
1 to 8 are arranged so that the cost of the order is maximized. Cost of the
particular order is computed as described in the section 6.1. The matrices A and
B are given below.

A= 9 0 0 0 0 0 0 0 0
0 9 0 0 0 0 0 0 0
0 0 9 0 0 0 0 0 0
0 0 0 9 0 0 0 0 0
0 0 0 0 9 0 0 0 0
0 0 0 0 0 9 0 0 0
0 0 0 0 0 0 9 0 0
0 0 0 0 0 0 0 9 0
0 0 0 0 0 0 0 0 9