Page 56 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

44 Chapter 1

6. ANT COLONY OPTIMIZATION

Ant colony optimization techniques exploit the natural behavior of ants in
finding the shortest path to reach destination from the source.
The figure 1-24 is the top view of the ants moving from source to
destination in search of food. There is the obstacle in the middle. There are
two paths available so that the ants can choose to move from source to
destination. As expected after some time duration ants prefer to choose
path1, which is the shortest distance between source and destination. This is
due to the fact that ants excrete the pheromones when they are moving. As
more ants have crossed the shortest path within the stipulated time when
compared to the other path, more pheromones are excreted in the shortest
path. This helps the following ants to choose the shortest path to cross the
obstacles.
The mathematical equivalent of this behavior is used in optimization
technique as the Ant colony optimization.

6.1 Algorithm

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

Figure 1-24. Illustration of Ant Colony