The concept of bloat — the increase of program size without a corresponding increase in fitness — presents a significant drawback to the application of genetic programming. One approach to controlling bloat, dubbed
spatial structure with elitism
(SS+E), uses a combination of spatial population structure and local elitist replacement to implicitly constrain unwarranted program growth. However, the default implementation of SS+E uses a replacement scheme that prevents the introduction of smaller programs in the presence of equal fitness. This paper introduces a modified SS+E approach in which replacement is done under a lexicographic parsimony scheme. The proposed model,
spatial structure with lexicographic parsimonious elitism
(SS+LPE), exhibits an improvement in bloat reduction and, in some cases, more effectively searches for fitter solutions.