WIT Press

The Window Algorithm


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D A Newlands & D Brain


Genetic algorithm (GAs) have long been known as effective search techniques for high dimensional spaces. Function finding attempts to discover a mathematical function that adequately describes a set of data. A standard genetic algorithm searches for all coefficients of a function concurrently, but there are difficulties in simultaneously minimising run times and maximizing accuracy. One recent improvement to GA performance is Delta Coding which searches all coefficients in parallel but increases the accuracy as the search progresses. This paper presents another method of tackling the accuracy and speed trade-offs in GAs. Instead of searching for all coefficients at the same time, a sliding window of coefficients is searched. Experiments are performed into fitting functions to data points and results indicate that good performance can be obtained with small windows. The results indicate that the window algorithm is a useful modification to the standard GA. Some insight into window sizing is presented. 1 Introduction Many mathematical techniques exist for fitting functions to data, such as collocation and osculation [Scheid, 1968] but, for example, when the domain is of very high dimensionality, when attempting to fit a non-linear function to spaces between data points or when the surface is discontinuous, mathematical techniques become computationally infeasible. It has been shown that some artificial neural networks [Ginsberg, 1993, Hecht-Nielsen, 1987] -a technique based on mathematical principles - cannot find some polynomials [Cardell et al., 1994]. Genetic algorithms [Goldberg, 1989] can search large spaces quickly and, due to their abstraction of data, have a wide