On October 9, 1997 I successfully defended my thesis and completed my master's degree in Mathematical Sciences. The topic of my research involved Genetic Algorithms and their application in curve-fitting and function optimization.
Genetic Algorithms are computational models which simulate the behavior of natural systems, like biological reproductive systems. Their structure is likened to Darwin's theory of Evolution, where 'survival of the fittest' in candidate solution strings takes over and the best fit candidates dominate the population. Through iteration this eventually leads to the optimal solution (at least this is the hope).
The topic of my research dealt with applying GAs to two very distinct problems:
Altimeter data collected by the satellite tends to be contaminated with the mean Gulf Stream topography. Using the above equation to estimate the contamination and then remove it has been shown to be a successful approach.
I have modified existing GA software to find these coefficients A -> G based on the satellite data in surprisingly little computation time. The results obtained with my GA are comparable to results obtained by the Naval Remote Sensing Branch.
Although my GA does find the optimal solution consistently, the estimated convergence time is not satisfactory. Possible solutions to this were illustrated and the research provided a good starting point for anyone looking to optimize the procedure to be a suitable method for solving the problem for any population size.
Genetic Algorithms work suitably well at solving both of these problems in competitive computation times. If GAs sound interesting to you be sure to check out the comp.ai.genetic newsgroup.