C 3 . 1 Introduction

This section provides a general introduction to search operators which have been proposed and investigated for various evolutionary computation techniques. Any evolutionary system processes a population of individuals, P(t) = {a1, . . . ,an} (t is the iteration number), where each individual represents a potential solution to the problem at hand. As discussed in Chapter C1, many possible representations can be used for coding individuals; these representations may C1 vary from binary strings to complex data structures I . Each solution ati is evaluated to give some measure of its fitness. Then a new population (iteration C4 t + 1) is formed by selecting the more-fit individuals (the selection step of the evolutionary algorithm). C2 Some members of the new population undergo transformations by means of ‘genetic’ operators to form new solutions. There are unary transformations mi (mutation type), which create new individuals by a (usually small) change in a single individual (mi : I → I ), and higher-order transformations cj (crossover, or recombination type), which create new individuals by combining parts from several (two or more, up to the population size μ) individuals (cj : I s → I , 2 ≤ s ≤ μ). It seems that, for any evolutionary computation technique, the representation of an individual in the population and the set of operators used to alter its genetic code constitute probably the two most important components of the system, and often determine the system’s success or failure. Thus, a representation of object variables must be chosen along with the consideration of the evolutionary computation operators which are to be used in the simulation. Clearly, the reverse is also true: the operators of any evolutionary system must be chosen carefully in accordance with the selected representation of individuals. Because of this strong relationship between representations and operators, the latter are discussed with respect to some (standard) representations. In general, Chapter C3 of the handbook provides a discussion on many operators which have been developed since the mid-1960s. Section C3.2 deals with mutation operators. Accordingly, several C3.2 representations are considered (binary strings, real-valued vectors, permutations, finite-state machines, parse trees, and others) and for each representation one or more possible mutation operators are discussed. Clearly, it is impossible to provide a complete overview of all mutation operators, since the number of possible representations is unlimited. However, Section C3.2 provides a complete description of standard mutation operators which have been developed for standard data structures. Additionally, throughout the handbook the reader will find various mutations defined on other data structures (see, for example, Section G9.9 for a description of two problem-specific mutation operators which transform matrices). G9.9 Section C3.3 deals with recombination operators. Again, as for mutation operators, several C3.3 representations are considered (binary strings, real-valued vectors, permutations, finite-state machines, parse trees, and others) and for each representation several possible recombination operators are discussed. Recombination operators exchange information between individuals and are considered to be the main ‘driving force’ behind genetic algorithms, while playing no role in evolutionary programming. There are many important and interesting issues connected with recombination operators; these include properties that recombination operators should have to be useful (these are outlined by Radcliffe (1993)), the number of parents involved in recombination process (Eiben et al (1994) described experiments with multiparent recombination operators—so-called orgies), or the frequencies of recombination operators (these are discussed in Chapter E1 of the handbook together with heuristics for other parameter settings, E1 c © 1997 IOP Publishing Ltd and Oxford University Press Handbook of Evolutionary Computation release 97/1 C3.1:1