Well, it seems that there is some difference between gene expression programming (GEP) and cartesian genetic programming (CGP or what I view as classic genetic programming), but the difference might be more hyped up than it really ought to be. Please note that I have never used GEP, so all of my comments are based on my experience with CGP.
In CGP there is no distinction between genotype and a phenotype, in other words- if you're looking at the "genes" of a CGP you're also looking at their expression. There is no encoding here, i.e. the expression tree is the gene itself.
In GEP the genotype is expressed into a phenotype, so if you're looking at the genes you will not readily know what the expression is going to look like. The "inventor" of GP, Cândida Ferreira, has written a really good paper and there are some other resources which try to give a shorter overview of the whole concept.
Ferriera says that the benefits are "obvious," but I really don't see anything that would necessarily make GEP better than CGP. Apparently GEP is multigenic, which means that multiple genes are involved in the expression of a trait (i.e. an expression tree). In any case, the fitness is calculated on the expressed tree, so it doesn't seem like GEP is doing anything to increase the fitness. What the author claims is that GEP increases the speed at which the fitness is reached (i.e. in fewer generations), but frankly speaking you can see dramatic performance shifts from a CGP just by having a different selection algorithm, a different tournament structure, splitting the population into tribes, migrating specimens between tribes, including diversity into the fitness, etc.
Selection:
- random
- roulette wheel
- top-n
- take half
- etc.
Tournament Frequency:
- once per epoch
- once per every data instance
- once per generation.
Tournament Structure:
- Take 3, kill 1 and replace it with the child of the other two.
- Sort all individuals in the tournament by fitness, kill the lower half and replace it with the offspring of the upper half (where lower is worse fitness and upper is better fitness).
- Randomly pick individuals from the tournament to mate and kill the excess individuals.
Tribes
A population can be split into tribes that evolve independently of each-other:
- Migration- periodically, individual(s) from a tribe would be moved to another tribe
- The tribes are logically separated so that they're like their own separate populations running in separate environments.
Diversity Fitness
Incorporate diversity into the fitness, where you count how many individuals have the same fitness value (thus are likely to have the same phenotype) and you penalize their fitness by a proportionate value: the more individuals with the same fitness value, the more penalty for those individuals. This way specimens with unique phenotypes will be encouraged, therefore there will be much less stagnation of the population.
Those are just some of the things that can greatly affect the performance of a CGP, and when I say greatly I mean that it's in the same order or greater than Ferriera's performance. So if Ferriera didn't tinker with those ideas too much, then she could have seen much slower performance of the CGPs... especially if she didn't do anything to combat stagnation. So I would be careful when reading performance statistics on GEP, because sometimes people fail to account for all of the "optimizations" available out there.