Evolutionary Optimization Algorithms

Abstract

As pointed out in the previous chapters, both fuzzy logic and neural networks imply optimization processes. For fuzzy logic in particular, optimization algorithms are needed that will allow determinations of the number of rules, the number of fuzzy sets and their position in the universe of discourse to be based on optimum criteria instead of on empirical techniques. This process generally involves a large number of variables and thus requires particularly efficient optimization algorithms. Similarly, in the field of neural networks, what can be of considerable use are optimization algorithms capable of finding the global minimum of a function with many variables, in order to overcome the intrinsic limitations inherent in learning algorithms based on the gradient technique. Therefore, this chapter will describe evolutionary algorithms that seem to respond to the characteristics required by soft computing, both with regard to versatility and to the efficiency and goodness of the results obtained. Genetic algorithms have proved to be a valid procedure for global optimization, applicable in very many sectors of engineering [10–15]. Ease of implementation and the potentiality inherent in an evolutionist approach make genetic algorithms a powerful optimization tool for non-convex functions. The genetic algorithms (GA) represent a new optimization procedure based on Darwin’s natural evolution principle. Adopting this analogy, inside a population in continuous evolution, the individual who best adapts to environmental constraints corresponds to the optimal solution of the problem to be solved.