A Hybrid Global Optimization Algorithm: Particle Swarm Optimization in Association with a Genetic Algorithm - Complex System Modelling and Control Through Intelligent Soft Computations - page 54

in which f m is a positive constant. Limit represents the maximum number of iter-

ation restraining the changes in positions of the particles or chromosomes of the
entire swarm or population. Equations ( 10 ) and ( 11 ) are utilized to compute other
probabilities, as follows:

P tc ¼ n tc P g ð 10 Þ

P mc ¼ n mc P g ð 11 Þ

in which n mc are positive constants. P g denotes a fuzzy variable and its

membership functions and fuzzy rules are presented in Fig. 1 and Table 1 .
The inference result P g of the consequent variable can be computed via
employing the min-max-gravity method, or the simpli

n tc and

ed inference method, or the

product-sum-gravity method (Mizumoto 1996 ).
Single objective and multi-objective hybrid algorithms based on particle swarm
optimization and the genetic algorithm and the details including the pseudo code,
the parameter settings will be presented in the following section. These algorithms
will be evaluated with many challenging test functions.

Fig. 1 Membership functions
of fuzzy variable P g

Table 1 Fuzzy rules of fuzzy
variable P g

Antecedent variable Consequence variable

S 0.0

M 0.5

B 1.0