Critical control of a genetic algorithm

Based on speculations coming from statistical mechanics and the conjectured existence of critical states, I propose a simple heuristic in order to control the mutation probability and the population size of a genetic algorithm. Genetic algorithms are widely used nowadays, as well as their cousins evolutionary algorithms. The most cited initial references on genetic algorithms are the beautiful books of Holland [10], who tried to initiate a theoretical analysis of these processes, and of Goldberg [9], who made a very attractive exposition of these algorithms. The literature on genetic algorithms is now so huge that it is beyond my ability to compile a decent reasonable review. For years, there has been an urgent and growing demand for guidelines to operate a genetic algorithm on a practical problem. On the theoretical side, progress is quite slow and somehow disappointing for practitioners. The theoretical works often deal with a simple toy problem, otherwise the behavior of the genetic algorithm is too complex to be amenable to rigorous mathematical analysis. Here I propose a simple heuristic in order to control efficiently the genetic algorithm, based on speculations coming from statistical mechanics and the conjectured existence of critical states. Although it is quite simple, I have not been able to locate this heuristic in the literature, and I hope it will be useful. Apart from my own belief, it is supported by several empirical studies, the most notable one being the work of Ochoa [13], and it is in accordance with several conclusions and ideas appearing in the work of van Nimwegen and Crutchfield [17]. Error threshold. The fundamental notion on which the heuristic is based is the notion of error threshold, introduced by Manfred Eigen in 1971 [6]. Eigen analyzed a simple system of replicating molecules and demonstrated