This work consists of two different, yet interrelated applications of genetic algorithms. In the first part of this work, we present a genetic algorithm designed to solve boundary value problems in conduction heat transfer. As the results show, our algorithm shows good convergence and can solve problems with a variety of boundary conditions. This is largely due to the presence of a novel "genetic engineering" local search operator that significantly increases the algorithm's accuracy. However, the performance of this operator deteriorates with increasing problem size, both in terms of accuracy and running time. Thus, in subsequent work, we improve the algorithm in two ways: First, we replace the "genetic engineering" operator with a new and far more powerful "regeneration" operator that improves accuracy even further, while maintaining its effectiveness with increasing problem size. Second, the algorithm is implemented on a parallel computer. Our parallelization strategy is the well-known "master-slave" strategy that involves distributing the fitness evaluation among several processors. The tests conducted indicate that considerable improvement in performance can be achieved for problem sizes of the order of 40,000 unknowns. More encouragingly, parallel speedup and efficiency both increase with increasing problem size, something we find very promising.; In the second major component of this work, the reverse is attempted: Genetic algorithm methodology is used in conjunction with principles of energy conservation to study evolution itself. This is done by developing a micro-analytical modeling procedure that explicitly simulates an evolving biological population at the level of individual genotypes and phenotypes. The population evolves according to the familiar genetic algorithm operators of fitness evaluation, selection, reproduction, and mutation. Our model is differentiated from previous work in this area in that fitness is not calculated on the basis of an arbitrary mathematical function, but on the mathematical formulation of the principle of energy conservation, thereby putting the model on a sound mathematical footing. The model was tested by applying it to two problems of interest: That of transgenic organism release into the wild, and the practice of genetic eugenics. Preliminary results and comparisons with other models indicate the qualitative validity of our model.
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