DEEPSO basics

The DEEPSO algorithm is equal to EPSO in its development sequence; however, the movement rule should now be expressed by

 

where

1. A, B and C are the weights that may be mutated, as in the general EPSO scheme
2. is given by
   

The elements X_r should be any pair of distinct particles already visited. These particles should be ordered such that, for minimization,

This assures that a proper atractor is created and that the "macro-gradient" points to a descending direction. In the movement equation, this is translated into the matrix Sign , which is a diagonal matrix whose ,ain diagonal elements are either 1 or --1, depending on the comparison of f(X_r1)with f(X_r2).

In the best variant of DEEPSO, the element X_r2 is made equal to the present particle X. The element X_r1 is sampled from the set P_b of the particles (the swarm) best ancestors - remember that  P_b = {b₁, b₂, ..., b_n} for a swarm of n particles. This sampling may be made randomly in each dimension of vector X, meaning that a uniform recombinantion of the best ancestors of all particles is used, generating a new recombined indicidual X_r (= X_r1).

Also, there is no need to calculate f(X_r) to set straight the signal of the difference between X_r and X if, in each dimension i, one uses the value of f(b_i), where b_i is the particle i best ancestor (in the traditional sense of EPSO and PSO), already calculated for the particle i sampled to be a donor, in dimension i, to the recombined individual X_r.