Model Parameter Encoding

The choice of representation of the problem in terms of how many model parameters, their encoding, range of values and required resolution is perhaps the most important decision we face when using genetic algorithms. In particular, we must decide whether to use ``direct'' representation of the problem (in terms of floating point numbers,for example) or to ``encode'' the solution in terms of a suitable ``alphabet'', usually binary. In his pioneering work in genetic algorithms Holland employed the binary representation to prove his schemata theorem which provides the theoretical foundation for the workings of the genetic algorithm Goldberg (1989a); Holland (1975). This theorem proves that short, low order schemata are more likely to be preserved by the evolution process in contrast to long high order schemata which are more likely to be disrupted by crossover and mutation . Short, low order schemata, therefore, are likely to end up associated with highly fit individuals, that is, with the best solutions to the problem. Therefore, if we can encode our model parameters in such a way that the promising short low-order schemata are produced, we may achieve a faster convergence and obtain a better solution. If we use binary encoding, in order to have short, low-order schemata, the model parameters must be suitably encoded with related model parameters being put close together in the binary string representing an individual Goldberg (1989a). The problem is that in general we may not know before hand which parameters are related to others or to what extent they are related. Therefore, in general it is difficult to establish the order of the predominant schemata in a given encoding of the model parameters.