Dynamic Neighborhood-Based Particle Swarm Optimization for Multimodal Problems

Algorithm 1

Dynamic ε-neighborhood selection of particle X_i.

 Input: Population size, N_PSO, MinPts, the i-th particle in the population, X_i;

 Output: Ndr: Directly neighborhood-reachable group of Xi; Nr: neighborhood-reachable group of X_i;

(1) For j = 1: N_PSO;

(2) While X_i∼ = X_j do;

(3)  Calculate the Euclidean distance between X_i and X_j;

(4) End;

(5) End;

(6) Take the nearest MinPts particles with X_i, 1, …, MinPts, and store them in Ndr;

(7) The maximum distance between X_i and the particles in Ndr is denoted as dismax, and set ε_i = dismax;

(8) For k = 1: MinPts;

(9)  For j = 1: N_PSO;

(10)   While 1-MinPts∼ = X_j & X_i∼ = X_j do;

(11)    Calculate the Euclidean distance between k and X_j. If the distance is less than ε_i, then put it into Nr.

(12)   End;

(13)  End;

(14)  End.