Evolutionary Computation - Computational Intelligence in Time Series Forecasting - page 194

against being trapped in local minima. On the other hand, GAs differ from pure
random search algorithms in that they, from the very beginning, search for the
relatively “prospective” regions in the search space.

Typically, GAs are characterized by the following features:

x genetic representation, i.e. encoding of the feasible solutions of given
optimization problems
x a population of encoded solutions
x a fitness function that evaluates the optimality or quality of each solution
x genetic operators that generate a new population from the existing
population
x control parameters.

A typical execution of a GA involves the following steps:

x Random generation of an initial population X ( t ): = ( x 1 , x 2 , . . . , x N ) with N
individuals at t = 0.
x Computation of fitness F ( x j ) of each individual x j in the current population
X ( t ).
x Checking whether the termination condition is met.

1. If YES, then pick up the best individual, i.e. the one with the highest

fitness value and stop the search process.

2. If NO, then create new population X ( t +1) with N new individuals,

applying the reproduction, mutation and crossover genetic operators,
from the current population X ( t ) and start the new iteration step with a
fitness computation.

In the recent past, GAs have been used, along with other evolutionary
algorithms, to train neural networks (Harrald and Kamastra, 1997) and neuro-fuzzy
networks (Palit and Popovic, 2000), as well as for the design of fuzzy-rule-based
systems through fuzzy clustering (Klawonn, 1998), for identification, modeling
and classification (Roubos and Setnes, 2001), etc . In the following, the application
of binary-coded GA in training neuro-fuzzy networks is presented. The simple
two-step approach that combines fuzzy clustering for initial modeling and a real-
coded GA for fine-tuning and optimization of the fuzzy rule base can be found in
detail in Panchariya et al ., (2004).
The structure of the GA implemented for the neuro-fuzzy network training is
shown in Figure 5.1, in which P ( C ), P ( M ), and P ( R ) stand for operators of the
adaptive genetic algorithm (AGA) as described in Chapter 9.

5.2.1 Genetic Operators

In what follows, a short description of individual GA operators is given.