Analysis of the Superiority of Parameter Optimization over Genetic Programming for a Difficult Object Detection Problem

We describe a progression of solutions to a di ffi cult object detection problem, that of locating landmarks in X-Rays used in orthodontic treatment planning. In our fi rst formula tion an object detector was a genetic program whose inputs were a number of attributes computed from a scanning window. We used a rich function set comprising f+; ; -; ÷ ; min; max; ifthenelseg. Experimentation with di ff erent function sets revealed that using the function set f+; g gave detectors that were almost as accurate. Such detectors are essentially a linear combination of attributes so we also implemented a parameter optimization solution with a particle swarm optimizer. Contrary to expectation, the PSO detectors are more accurate and smaller than the GP ones. Our analysis of the reasons for this reveals that (1) the PSO approach involves a considerably smaller search space than the GP approach, (2) in the PSO approach there is a 1-1 mapping between genotype and phenotype while in the GP approach this mapping is many-1 and many semantically equivalent potential solutions are evaluated, (3) the fi tness landscape for PSO is a good one for search in that solutions are distributed in areas of high fi tness that are easy to locate while the GP landscape is much more di ffi cult to characterize and areas of high fi tness more difficult to find.