Baby Steps into Genetic Programming
aerique.blogspot.com
aerique.blogspot.com
A very simple way to fight bloat is to penalize an individual's fitness value in proportion to how long it takes to find that individual's fitness value.
Then, if you bias selection such that fitter individuals are more likely to survive, then the individuals that take a shorter time to evaluate should have a slightly higher chance of surviving; and those individuals should be the very individuals that are less bloated.
Of course, the problem is determining just how much to penalize their fitness values. And, as in much else in evolutionary computation, that generally comes down to simply doing a number of runs with different penalties and see how they compare.
One down side to keep in mind when using any kind of penalty for bloat is that some research has shown that unrestricted tree growth is often required for solving larger and more complex problems. So there's a trade-off involved in reducing bloat vs allowing better solutions to evolve.
Now, as to the second problem of maintaining diversity, that is a much tougher nut to crack.
Two of the simplest techniques are using mass extinction events and separating the larger population in to a number of smaller populations (called "demes", "islands", or "subpopulations") and is generally referred to as "the island model".
Mass extinctions are very simple. Just wipe out a large portion of the population in a given number of generations (or when you've determined that the population has become too inbred) and repopulate it with random individuals. This will maintain diversity.
Of course, you usually don't want to wipe out your best individuals, so you'll spare them. But that's where the problem comes in, as the best individuals will likely quickly come to dominate the population again. But hopefully in the mean time they'll breed with some of the new random individuals and the population will get some new blood. And when the population starts to get too inbred again, or a certain number of generations pass, there could be another extinction event, etc..
In the island model, if the islands are kept totally separate and no individuals from any island are allowed to breed with individuals from any other islands, then this is obviously equivalent to simply running a number of separate smaller populations at the same time. This is might be fine for maintaining diversity, but no benefit will accrue from combining the solutions in each of the subpopulations.
So, what's usually done is to let individuals from one subpopulation breed with individuals from another subpopulation at given times during the run. Again, if they are allowed to interbreed at every generation, then this will be equivalent to just having one large population as usual. So you'll want to keep individuals on any given island from breeding with individuals from other islands for a number of generations. The longer you keep the subpopulations from interbreeding, the more diverse they'll be (or so the theory goes). At the same time, the longer you keep them from interbreeding, the slower the convergence rate (the time it takes to reach a global optimum in the search space) will be.
Unfortunately, there have been mixed results reported about the island model. Some research has suggested that it's better to just use one very large population. But on the other hand, there have also been successes reported with the island model, and reports that smaller populations outperform larger ones. So it's a mixed bag, and usually very problem dependent, as much of evolutionary computation tends to be.
Finally, there are also many, many other much more sophisticated and effective techniques for fighting bloat and maintaining diversity. But I'll leave finding those as an exercise to the reader. Just a quick tip: type "genetic programming" and "bloat" or "diversity" in to the form on this page:
Whereas with tournament selection I found that the population remained diverse.
Just my findings though, I'm no expert on GA and certainly not on GP.
Diversity of individuals in the population depends on a number of factors. The selection method is one such factor. But another factor is what individuals there are to select from in the first place.
Using the simple mass extinction event technique, you effectively limit the pool of individuals that can be selected from to those few that survive the extinction plus the new randomly created individuals that take the place of those that went extinct.
I suppose this could be considered a special rare breeding phase that combines an elitist selection method along with a 100% mutation of the remaining population.
Some other factors that influences diversity are the crossover and mutation operators that are used, along with the decisions concerning which parts of the program trees are allowed to change and where they get the replacements from.
For instance, if crossover were allowed only from or to certain parts of the tree, that could decrease (or even increase) diversity compared to the standard case of imposing no such restrictions during crossover.
Another possibility is performing crossover multiple times per generation on the same individual. The more similar a given individual is to other individuals in the population, the more crossovers could be performed on that individual, hopefully increasing the diversity in the population. Multiple mutation could similarly be employed.
Yet another factor that could affect diversity is simply the population size. Clearly, a population of one individual is minimally diverse. As the size of the population grows, so too (hopefully) does the diversity. There has been some research in to dynamically sizing the population to increase or decrease diversity as needed.
Something else that has been proposed for increasing diversity is segregating highly fit individuals from very unfit individuals. This way the highly fit individuals won't come to dominate the very unfit individuals, and thereby hopefully preserve diversity. This could be done with an island model, and as higher fit individuals on a certain island evolve, they can be transferred out of the islands of lower fitness to other islands of higher fitness.
And there are probably dozens if not hundreds of other ways of trying to influence diversity, as it is a critical aspect of genetic programming.
One last thing I should mention (maybe I should have mentioned it first) is that a lot of this depends on exactly how you measure diversity (yet another important field of research).
Is it enough to call a population diverse if every individual is different from every other individual? Well, what if they are but they differ only in ways that don't affect fitness? Or what if they do differ in ways that affect fitness, but with only minor variations from individual to individual? And what about structure differences? It's possible to have two individuals with the same fitness value but different structures. And there are many other measures as well.
So, depending on how you measure diversity (and when you do so, and to which members of the population), you could come up with different approaches to trying to influence it.
http://www.genetic-programming.com/humancompetitive.html
That list is kind of dated, though, and in no way representative or exhaustive.
I tried copying and pasting the stuff in here: [http://www.genetic-programming.org/gplittlelisp.html] into a file and loading it into clisp but it throws a bunch of syntax errors.
anyone know where you can grab a working copy of it? (I have never used lisp before, so I am probably not the best person to debug by hand...)
http://www.amazon.com/Genetic-Programming-Computers-Selectio...
This is one of my most prized computer books, perhaps the most prized book I have. Even though I wasn't a Lisper when I started reading this book, I ended up building (without realizing it at first) a little Lisp inside Python for exploring the concepts.
If you thought Koza's old website is inspiring, consider getting this book. It's huge and expensive, but to me it feels like one of the 3 books I'd want to bring with me to a desert island or through the destruction of civilization.
The problem with genetic programming is that as soon as you start a approaching a program of reasonable complexity, even small mutations start wreaking havoc to whole program logic. If we make a biological analogy, it is like evolving an elephant from an ape-like ancestor. Evolution in real world isn't so drastic.
Remember that elephants (and all other life on this planet) evolved from single-celled organisms (and even from non-life), which are far more different from elephants than even apes are. So drastic evolutionary changes do happen in the real world. But they just take a very long time.
The problem is that not only do we not have millions or even billions of years to evolve our artificial organisms, but that the environments in which our artificial organisms grow, their representation, and the operations performed on them during their "lifetime" and during breeding are incredibly restricted and simplified compared to what happens in the real world.
It's very difficult to model even a tiny fraction of that (see the supercomputer time dedicated to creating a detailed model of even a single neuron, for instance). And, as for the programs that are evolved via GP, it's rare for them to be allowed to create completely arbitrary code. Their instruction sets are usually very limited so as to reduce the search space. They are also usually given quite limited data to work with, are modified very little during their lifetimes (if at all), and the sorts of things that can happen during breeding are similarly curtailed. So it's really no wonder that their existence and evolution is not always so spectacular as what nature has been able to achieve over the millenia.
Now, the problem you mention regarding the disruptive nature of mutation (crossover can also have this effect) is also important. The attempts to solve it have generally focused to finding ways to reduce this disruption (usually by making the crossover or mutation less random). I recommend searching Citeseer for "destructive crossover" to see examples of some proposed solutions.
Some of his work has even created patentable inventions! (I'm on my phone and cooking so no links.)
Given that most later GP implementations have been done in other languages (from C to Java to Python), it's good to finally see it come full circle back to Lisp once more.
http://homepages.sover.net/~nichael/nlc-publications/icga85/
The term "Genetic Programming" may have been coined by Hugo de Garis.
As to GP implementations. In the research world, there are probably four major ones. I'll list them in the order I think they're presently used:
1. ECJ. Java. [I wrote it, hehe].
2. OpenBEAGLE. C++.
3. EO. C++.
4. lil-gp. C. lil-gp is still quite serviceable but a bit long in the tooth now. I used lil-gp very heavily before writing ECJ, and in fact many things in ECJ were inspired by it.