Determination of optimum genetic parameters for symbolic non-linear regression-like problems in genetic programming

Parametric studies have been carried out for the quartic-polynomial regression problem demonstrated in the Genetic Programming (GP) v3 toolbox of Matlab. Many classification schemes and modeling issues are polynomial based. Every possible combination originating from all available options between the two genetic parameters namely ?elitism? and ?sampling? has been analyzed while keeping all other parameters as fixed. Three performance parameters namely, execution time of a given GP run, quickness of convergence to reach the required fitness and the most important, fitness improvement factor per generation have been studied. In terms of the last mentioned performance parameter, being an indicative of diversity, it is shown that the best particular combination is ?halfelitism-sus? if naming in the general format of ?elitism-sampling? is used. On the average, this combination went on improving the fitness value (of the bestsofar individual) in more than 78% of generations as the GP simulations progressed towards the required solution. Secondly, halfelitism-roulette took, on the average, as less as 6.8 generations to complete a GP run outperforming other combinations in terms of quickness of convergence with again, halfelitism-sus as second best consuming 7.4 generations to reach at the desired quartic genre. Inspite of its promising average values, this combination showed a contrasting behavior depending upon the auto-evolution process at the start of a given GP run. Either it took on a right track and converged to the solution efficiently or it de-tracked in the very beginning and lost its performance regarding the three aforementioned parameters. Furthermore, it was found that for the combinations replace-doubletour and keepbest-doubletour giving the best two execution times (in seconds) to complete a given GP run, their results were least encouraging regarding the other performance parameters. Also, in contrast to some combinations such as, replace-tournament and rep- lace-lexictour, other combinations worked satisfactorily well in at least one of the three performances studied.