## Evolutionary Algorithms Which Generate Models Directly

The genetic algorithm for rule-set production (GARP) classifier, used in species distribution modeling, is perhaps the best-known evolutionary modeling system. Classifier systems directly generate models consisting of logic rules. GARP evolves rules predicting the suitability of sites for a target species, based on characteristics of sites where the species is known to occur. Unlike the previous examples, GARP makes only very weak assumptions about the data - that it may be effectively modeled by logic rules. The evolutionary algorithm is assigned the task of finding the detailed form, and even the number, of rules required.

Even these weak assumptions may be dispensed with: the form of dependence between variables may be left entirely to the evolutionary algorithm, giving rise to a variant of GAs known as genetic programming (GP).

Evolutionary algorithms directly generating models generally have to deal with two interrelated problems. Since the complexity of the model is seldom known a priori, the evolutionary system must allow some latitude to evolve models of appropriate complexity. But freeing up model complexity brings the risk of over-fitting.

On the other hand, variable-complexity evolutionary systems notoriously suffer from the bloat phenomenon, wherein individuals accumulate large amounts of ineffective code (simple examples: '+0' or '*1' in arithmetic domains, 'and TRUE' in Boolean domains; but most real examples are far more complex). Bloat is not all bad. In practice, evolutionary algorithms impose a complexity limit on individuals - either their depth or their overall size. Bloat, by taking up available code space, puts selective pressure on the size of the effective code, and can ameliorate the tendency to overfit. However, this effect is unpredictable, and may exert excessive parsimony pressure in one context, too little (more commonly) in another.

At the time of writing (2006) these are still hot research issues; the previously described application of multi-objective methods is currently the most effective method.

When an evolutionary algorithm is used to generate a model, the expressed aim is usually to generate a good predictive model. In practice, researchers often hope to generate an explanatory model - one which reflects the actual ecological processes - as well. Thus, the white-box nature of evolutionary representations is sometimes contrasted with the black-box opacity of neural networks. In practice, bloat and over-fitting often render it difficult to disentangle the effective model from the ineffective code in which it is embedded.

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