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Show The optimization technique employed in this demonstration is known as a direction-set technique. Any technique which works from an initial point in a given search space and then optimizes along each of a set of directions within that space can be classified as a direction-set technique. What distinguishes individual techniques within this classification is the process by which those directions are chosen. The method of steepest descent is one popular direction-set technique. This method is considered a first order technique because it involves calculating or measuring the local gradient and then optimizing along the line in the direction of steepest descent (or ascent). Upon optimization in one direction, the gradient is again determined and optimization proceeds in the new direction. Although powerful, the time-consuming process of measuring the gradient at each turning point prevented exploration of this method in the current research. The direction-set technique used in the proof-of-concept stage is known as Powell's method, a zero order technique, because it does not require calculation of a gradient. The approach and results of the proof-of-concept demonstration are included in the Appendix. Following success of this initial demonstration, more practical studies were undertaken. First, a more advanced optimization method, known as the genetic algorithm, was incorporated and applied to the same problem, and same burner geometry, addressed in the proof-of-concept. The results from this study appear in a previous work [S1. John and Samuelsen, 1994] and are presented here in the Appendix. Genetic algorithms represent a radical departure from traditional forms of optimization, such as the direction-set class of search methods. Based on natural selection mechanics, the description of this method requires language borrowed from that field of study. The process starts with a population of individuals. The fitness of each individual is evaluated and a new population is produced based on the previous generation's fitness. Individuals are selected for reproduction according to each one's fitness: individuals with higher fitness have a better chance of reproduction. Each individual selected for reproduction can be represented by a character string and functions as a chromosome. Each chromosome may undergo crossover with its mate based on a finite probability that crossover will occur. In addition, each allele-represented by a single character in an individual's chromosome (string)-has a small probability of mutating [Goldberg, 1989]. 6 |