Algebraic Theory of Automata by Abraham Ginzburg

By Abraham Ginzburg

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The idea of information having its own existence is not as science-fiction-like as it may seem. The interested reader may consult the books by Barrow & Tipler (1988) and Stonier (1990), which discuss these issues in more detail. CONCEPTS OF EVOLUTIONARY MODELING AND ALGORITHMS 25 At this point, we leave philosophical and biological issues and move on to the topic of computation. Formal Representation of Evolutionary Algorithms We shall progress now to the presentation of formal notation of basic concepts in evolutionary algorithms.

The process of mating and cross-over continues for as long as the desired number of new individuals is created (Step 4). These individuals constitute a new population. Fitness is calculated for them (Step 5), and the process of selection-mating-cross-over is repeated until designated criteria for termination are met (Step 6). During evolution, that is the operation of the algorithm, other operators may intervene. For example, mutation causes random changes in chromosomes and learning changes the fitness of individuals.

In some implementations of evolutionary algorithms, mutation has been found to be a highly disruptive operator that did not contribute to the progress of an evolutionary algorithm at all (Krzanowski, 1997). In other implementations [such as in evolutionary programming (EP) or evolutionary strategies (ES)] it is the only operator causing changes in the chromosomes and consequently driving the progress of evolution. In canonical genetic algorithms (CGA), GP, and their derivatives, mutation is a part of an evolutionary process [along with the cross-over and (or) other operators] but its activation frequency is relatively low.

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