Genetic Programming - GeoComputation - page 194

TABLE 8.10
Summary of Sum of Squares Error for Spatial Interaction Models

Conventional Spatial
Interaction Model Initial GP Model Simplified Model

Development Testing Model Type Development Testing Development Testing

Volume 156 (Equation 8.8) 25 205 (Equation 8.10) 28

261 8

Probabilistic 137 (Equation 8.9) 15 126 (Equation 8.11) 8

The Durham journey-to-work case study shows that GP is capable of evolving a spatial interac-
tion model. Importantly, the probabilistic GP model did better than the volume GP model, and
neither model performed better than the conventional model on the test data set - suggesting no
overall gains from the use of GP. Simplification of the GP volume model, unfortunately, in all cases
produced an even poorer fit, confirming that the far more complicated original version was actually
a superior product. Simplification of the probabilistic GP model, in contrast, produced an improved
generalisation in all cases suggesting that the far more complicated original product was in some
way overfitted. These, nevertheless, were early demonstration runs, which were designed to test and
explore the potential benefits on offer from GP. There was a steep learning curve involved and, as
ever, it would have benefitted from further refinement. The author of this original pioneering case
study, many years ago, clearly recognised and accepted that additional investigations were subse-
quently required in order to extend the initial findings and develop a truly global model, one that
was superior to conventional methodologies, and also performed well on out-of-sample test data
(Diplock, 1998). Finally, it is also clear from such initial GP solutions (Equations 8.8 and 8.9) that
raw equations derived from GP modelling in the mid-late 1990s were especially large, complex and
cumbersome products, making them difficult to rationalise and interpret. The requirement to code
the GP program from scratch, coupled with the necessary computing resources that were required
to run it effectively, made the technique more accessible to computer scientists and mathematicians
than the discerning geographer.

8.5 FUTURE DIRECTIONS
The first edition of this chapter succeeded in drawing a line in the sand which marked the end of the
first development era for GP. In the first edition, Diplock (2000) discussed the technical background
and implementation issues associated with coding a GP in Fortran. He successfully showed how
GP can be implemented and he speculated about the direction of research for the following decade.
Problems highlighted with processing speed have since been resolved with the advent of new com-
puting technology, which itself has been accompanied by accessible innovations in software, such
that one can now expect to use GP to analyse a data set on a home computer within a few hours of
data acquisition. Research papers are regularly reporting that GP solutions perform better than tra-
ditional statistical techniques, at least in terms of goodness-of-fit metrics. Arguably, the question of
whether GP actually works has been answered and we should now be focusing on how well it works,
stimulating a debate about whether GP is now coming of age.
This leads us towards ever-deeper philosophical questions and, by analogy, to the concept of a
scary two-headed monster: something that will need to be battled against over the next 10 years!
Two major challenges face GP - and, like Orthus , in Greek mythology, a two - headed hellhound,
serpent-tailed dog, with sharp edged teeth that was slain by Heracles - both must be defeated simul-
taneously. Indeed, defeating one or other head or factor, in isolation, is clearly insufficient since it
will not on its own deliver that which is required, and it is difficult to know where to start and/or how
to progress since they appear to operate in conjunction with each other and support one another!