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Show RESULTS Results are submitted in several graphical fonns, which merit discussion. First of all is the most basic presentation, absolute perfonnance index value versus iteration. This type of graph is simply a line-plot of performance index evaluations as a function of sequential algorithm iterations. Graphs of this type are generated for both the direction-set and the genetic algorithm techniques. They answer the fundamental question for a particular run: Over time, was performance of the burner improved? These graphs are individually helpful in addressing the ideas of efficacy, or whether or not the control system completed its objective. Two or more of these graphs can be helpful in comparing the efficiency of one technique to another: Did one technique reach a high performance condition sooner than another? This type of graph is referred to as an absolute performance history curve. Another graph type is similar to the first but displays a running average performance rather than an instantaneous performance, versus iteration. This gives an indication of the burner's overall performance for a particular run, and can be used to compare the efficiency of competing optimization techniques. This type of graph is called an averaie performance history curve. The third type of result presented here is also useful in evaluating the efficacy of a particular direction-set trial. This graph is a contour plot of the performance map, overlaid by the path that a particular direction-set trial run produced. It shows where operation of the burner started, and if the region of measured high performance was indeed attained by the direction-set technique. This plot type is known as a direction history graph. The fourth graph type is similar to the direction history graph but is used for display of the genetic algorithm results. One plot of the performance map is produced for each generation, with the location of each individual in a parttcular generation denoted by a data marker. This shows whether or not, over time, the locations of the individuals converged to the region of high performance. It also shows, over several generations, how less-fit individuals are less likely to be selected for reproduction than more-fit creatures. This final graph type is referred to as a population history graph. Results from the proof-of-concept phase, and the initial exploration of the genetic algorithm, are included in the Appendix, and show the ability of the genetic algorithm to find the 8 |