Critique of the Compositional Paradigm

Adaptation in selecto-recombinative genetic systems is widely believed to occur by the recombination of pre-adapted genetic material. This belief is at the core of the paradigm under which most GA and all EDA research currently occurs. It underlies the construction of several new varieties of genetic algorithms that purportedly work by combining pre-adapted genetic material in some sophisticated way (e.g. cohort GAs, messy GAs, LLGA, ECGA, BOA, hBOA, etc.).

In this paradigm, each post-selection population is thought to harbor “good” genetic material. Recombination operators, and estimation of distribution procedures, are thought drive adaptation by composing this material to produce good or better individuals in the next generation.When adaptation stalls it is thought to be because “good” genetic material is unavailable, or because recombination of this material was not performed effectively.

Let us call this general set of beliefs the Compositional Paradigm. This paradigm draws its support from Holland’s Building Block Hypothesis. Its widespread acceptance in the GA community signals the implicit acceptance of the BBH as an accurate description of how the simple GA performs adaptation. It also signals the acceptance of a generalization of the BBH, namely that all varieties of recombinative GAs perform adaptation by recombining pe-adapted genetic material.

The Building Block Hypothesis however has never been conclusively validated. It has in fact been sharply criticized by a few (e.g. see section 5 of Wright et. al. Implicit Parallelism, GECCO 2003), and many have suggested that it be treated with more skepticism. Nevertheless, it and its generalization – what I call the Compositional Hypothesis – remain widely accepted. I believe that this is so because of two reasons:

1. The Compositional Hypothesis seems right. Recombination of genetic material occurs at the individual level, so the recombination of “good” genetic material must be the mechanism by which adaptation occurs at the system level. Right?
2. Real paradigmatic scrutiny only occurs when an alternate hypothesis is submitted for consideration. Despite the publication of a large number of studies of the foundations of genetic algorithms no alternate hypothesis that explains adaptation has been proposed so far.

In my own studies I’ve been fortunate to obtain theoretical and empirical results that suggest an alternate non-compositional hypothesis for adaptation in selecto-recombinative genetic systems. Right now I’m in the process of finding the best way to present it.

Critique of the Compositional Paradigm

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