Page 15 - Algorithm Collections for Digital Signal Processing Applications using MATLAB

1. Artificial Intelligence 3

Figure 1-3. Vector Representation of PSO Algorithm

‘a’ based on the above knowledge, finally decides to move towards the
.
position ‘g’ as the linear combination of ‘oa’ , ‘ac’ and ‘ad’ [As ‘d’ is the
common position decided].The linear combination of ‘oa’ and scaled ‘ac’
(ie) ‘af’ is the vector ‘of’. The vector ‘of’ combined with vector ‘fg’ (ie)
scaled version of ‘ad’ to get ‘og’ and hence final position decided by ‘a’ is
‘g’.
Similarly, ‘b’ decides the position ‘h’ as the final position. It is the linear
combination of ‘ob’ and ‘bh’(ie) scaled version of ‘bd’. Note as ‘d’ is the
common position decided by ‘a’ and ‘b’, the final position is decided by
linear combinations of two vectors alone.
Thus finally the swarms ‘a’ and ‘b’ moves towards the position ‘g’ and
‘h’ respectively for reaching the final destination position ‘e’. The swarm ‘a’
and ‘b’ randomly select scaling value for linear combination. Note that ‘oa’
and ‘ob’ are scaled with 1 (ie) actual values are used without scaling. Thus
the decision of the swarm ‘a’ to reach ‘e’ is decided by its own intuition
along with its neighbor’s intuition.
Now let us consider three swarms (A,B,C) are trying to reach the
particular destination point ‘D’. A decides A’, B decides B’ and C decides
C’ as the next position. Let the distance between the B’ and D is less
compared with A’D and C’ and hence, B’ is treated as the global decision
point to reach the destination faster.
Thus the final decision taken by A is to move to the point, which is the
linear combination of OA, AA’ and AB’. Similarly the final decision taken