From the point of view of the genetic algorithm inversion some lessons have been learned after extensive parameter testing: use of a micro-genetic algorithm with uniform cross-over and no mutation emerges as the best option for this problem (as opposed to a standard genetic algorithm with single-point cross-over and jump mutation). A micro-genetic-algorithm population of 5 or 7 individuals with a cross-over probability of 0.9-0.95 seems to be optimum for this problem. The micro-genetic algorithm in this case converges to a reasonable solution after about 4000 generations (20000 function evaluations) in 10 seconds on a single-processor Linux PC.

An important issue to be further analyzed is that of the multi-modality of the search space. It is clear in this case that there is a single global minimum, namely matching the original trace sample-by-sample. This, however, does not guarantee a similar sample-to-sample match in the original log, which is a consequence of the non-linearity of the problem.

I have found that once I get close enough to this global minimum it takes a large number of iterations to scape local minima (many traces match ``almost exactly'' the original). My present convergence criteria do not allow for checking of convergence of individual parameters so I have to investigate alternative options. Another issue is the convenience of using the floating point representation of the model parameters directly for the inversion rather than their binary representation. This may increase the resolution of the model parameters and make the inversion overall more robust.

11/11/2002