A Hybrid Global Optimization Algorithm: Particle Swarm Optimization in Association with a Genetic Algorithm - Complex System Modelling and Control Through Intelligent Soft Computations - page 66

22

20

18

16

14

GA with traditional crossover
GA with multiple crossover
Standard PSO
Hybrid algorithm

12

10

8

6

4

2

0 2000 4000 6000 8000 10000

Iteration

Fig. 10 The evolutionary trajectory of the single-objective optimization algorithm on the Ackley
test function

chromosomes which are not chosen for genetic operations are enhanced via particle
swarm optimization. Then, the archive is pruned and updated. This cycle is repeated
until the user-de ned stopping criterion is met. Figure 11 illustrates the fl ow chart

of this algorithm.
The set of non-dominated solutions is saved in a different location named
archive. If all of the non-dominated solutions are saved in the archive, the size of
archive enhances rapidly. On the other hand, since the archive must be updated at
each iteration, the size of archive will expand signi

cantly. In this respect, a sup-
plementary criterion is needed that resulted in saving a bounded number of non-
dominated solutions. To this end, the dynamic elimination approach is utilized here
to prune the archive (Mahmoodabadi et al. 2013 ). In this method, if the Euclidean
distance between two particles is less than R elimination which is the elimination radius
of each particle, then one of them will be eliminated. As an example, it is illustrated
in Fig. 12 . To gain the value of R elimination , the following equation is utilized:

(

¼

t
a maximum iteration

t
b

t
b

if fix

R elimination ¼ ð 12 Þ

0 else