Parametric Regression Through Genetic Programming. Banks, E. R., Hayes, J., & Nunez, E. In Late Breaking Papers at the 2004 Genetic and Evolutionary Computation Conference, Seattle, Washington, USA, 26 July, 2004.
Parametric Regression Through Genetic Programming [pdf]Paper  abstract   bibtex   
Parametric regression in genetic programming can substantially speed up the search for solutions. Paradoxically, the same technique has difficulty finding a true optimum solution. The parametric formulation of a problem results in a fitness landscape that looks like an inverted brush with many bristles of almost equal length (individuals of high fitness), but with only one bristle that is very slightly longer than the rest, the optimum solution. As such it is easy to find very good, even outstanding solutions, but very difficult to locate the optimum solution. In this paper parametric regression is applied to a minimum-time-to-target problem. The solution is equivalent to the classical brachistochrone. Two formulations were tried: a parametric regression and the classical symbolic regression formulation. The parametric approach was superior without exception. We speculate the parametric approach is more generally applicable to other problems and suggest areas for more research.

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