Conclusions and Future Work

The results of this test are encouraging because micro genetic algorithms show a much faster rate of convergence than standard genetic algorithms in the solution of this simple, relatively high-dimensional problem. At the very least micro genetic algorithms could be run for a few generations and use the results as starting points for gradient-based methods.

From the point of view of the genetic algorithm inversion, some lessons have been learned after extensive testing of the evolution parameters. Firstly, using a micro-genetic algorithm with uniform cross-over without mutation emerges as the best option for this problem (as opposed to a standard genetic algorithm with single-point cross-over and jump and creep mutation). Secondly, a micro-genetic-algorithm population of 5 individuals with a cross-over probability of 0.95 seems to be optimum for this problem.

An important issue to be further analyzed is that of the multi-modality of the search space. In this case it is clear that there is a single global minimum, namely recovering the original trace sample-by-sample. However, I have found that once I get close enough to this global minimum it takes a large number of iterations to escape local minima (many traces ``almost fit'' exactly the original). My present convergence criteria do not allow for checking of convergence of individual model parameters so I have to investigate alternative options.

Another important issue has to do with the convenience of working with the model parameters directly in their floating-point representation rather than the standard binary encoding used here. This approach has the advantage of not requiring a resolution limit on the model parameters.