Evolutionary Algorithms – Directing the undirected


This is a followup to my previous post on the same topic : http://rogeralsing.com/2010/07/29/evolutionary-algorithms-problems-with-directed-evolution/

I started thinking about possible solutions after I published my last post, and I think I might have something that could work.

In order to harness the full power of evolution, we need to be able to simulate undirected evolution.
Undirected evolution requires more than one environment, so that organisms can evolve and niche into specific environments instead of just competing for the same environment.

In our case, the “environment” is the “problem” that we want to solve.
The more fit an organism is in our environment, the better it is to solve our given problem.

So far, I think everyone have been applying evolutionary/genetic algorithms on individual problems, evolving algorithms/solutions for a single purpose..
And thus, experiencing the problems of irreducible complexity.

But what if we were to introduce an entire “world” of problems?

If we have a shared “world” where we can introduce our new problems, the problem would be like an island in this world, and this island would be a new environment where existing organisms can niche into.
This way, we could see organisms re-use solutions from other problems, and with crossover we could see combinations of multiple solutions for other problems.

The solutions would of course have to be generic enough to handle pretty much every kind of algorithm, so I guess the DNA of the organisms needs to be very close to a real GPL language.
Possibly something like serialized Lisp/Clojure, running in a sandboxed environment…

By adding more and more problems to this “world”, the better it would become at solving harder problems since it can reuse existing solutions.

The structure of it all would be something like:

The “World” is the container for “Problems”.
“Problems” contains input/output sampling and “populations of organisms”, thus, each problem have its own eco system.
“organisms” evolve by mutations and genetic crossover, they can also migrate to other “problems” from time to time.

This way, an organism from the “SSH Encryption island” may migrate over to the island of “Bank authentication login code generator island” and possibly be used as a module in one of the branches of one of the organisms in there, and thus removing “irreducible complexity” from the equation here..
Evolution would be locally directed and globally undirected…

I think this could work at least to some extent, or?

//Roger

Evolutionary Algorithms – Problems with Directed Evolution


Creationists often use “irreducible complexity” as an argument against evolution.
e.g. you need all parts in place and functioning before the “whole” can do its work and thus reproduce and spread its features.

The bacteria flangellum is one such feature that have been attributed with “irreducible complexity”.
You need the “tail” and some “engine” parts in place before it can be used as a propeller and drive the bacteria forwards.

Evolutionists have however proven this wrong and shown that each of these parts have had other purposes before they were re-used/combined for propulsion, so each part was already present.

The key here is that evolution in reality is not directed to a “final goal” it simply makes organisms adapt to their current environment.
e.g. an organism might evolve a single pair of legs and later generations might get more of those legs if that is beneficial.
The front pair of legs might even later evolve into a pair of arms that allows the organisms to grab food while they eat and so on.

In short, existing features can be reused and refined in order to reach a higher fitness level in the current environment.

As far as I know, we still have not managed to accomplish this sort of “undirected evolution” in computer programs in the same sense.
If we make a program that are supposed to come up with a solution for a given problem, I would use “directed evolution” and try to breed solutions that are better and better at solving the given problem.
So if our program was supposed to come up with a propulsion system for a body, it would fail at evolving the bacteria flangellum since we experience the effects of irreducible complexity, our program is unable to evolve all the parts for other reasons than moving the body forwards.

In order to harness the full power of evolution in computer programs, we need to be able to simulate “undirected evolution” so that we can evolve all these parts that later can be re-used for other purposes.

Are there any research going on in this topic at all?

I know that the old “Tierra” simulation was sort of undirected, the only goal was to consume as much CPU as possible, but it sure could use undirected evolution to get to that goal.

But other than that, anything?

Genetic programming / Math


For those of you who are interested in evolution / GP.
Here is a small app that I made to reverse engineer blackboxed formulas.

The application is fed with a “problem domain”

The problem domain consists of multiple cases, like this:

Case1:
When X is 1 and Y is 2 I want the result to be 3
Case2:
When X is 3 and Y is 5 I want the result to be 8
Case3:
When X is 10 and Y is 10 I want the result to be 20

That was a very simple problem.
And the formula to solve the problem would be (X+Y).

Ofcourse the problems aren’t described in english, it’s code. but this is the idea behind it anyway.

Once the application is fed with a problem domain, it will create a population of “formulas”
Each formula have its own DNA, the DNA in this case is the various functions, constants and variables.

Each formula in the population will be fed with the data from each problem case and then evaluated.
Depending on how close to the goal the result is, the better the error level is.

Once each problem case have been evaluated by a formula, all the error levels per case will be summed up.
The summed error level is then used to decide what formulas are allowed to survive and breed.
(There is also a bit of crossover going on between formulas, but I won’t get into that now.)

So how fancy stuff can this application solve?

Well, here are some examples:
Problem data and result is shown on the pictures.

And no, it does not care if the result is pretty, it just strives to find a working formula.
ofcourse this could be altered so that once the solution is found, it continues to evolve and promote shorter formulas.

GenMath sample 1

GenMath sample 2

GenMath sample 3

Complex solution, the application generated a formula to convert decimal 0-15 into binary representation:

genmath41.gif

After some optimization of the final formula it came up with this:

((((int)(((((100 * ((int)(-8) & (int)(x))) - (-23 * ((int)(-4) & (int)(x)))) + x) - 2)) | (int)(7)) + 1) + x)

Not the prettiest formula in the world, but it does what it is supposed to..
Also consider that the extensive use of “(int)” is not really generated by the application,
Its my ToString implementation of binary operators that add those.

If we remove all the extra clutter which is really only part of the visual representation, we would end up with this:

(((100 * (-8 & x) - (-23 * (-4 & x)) + x) - 2) | 7) + 1 + x;

I find it quite interesting to see how evolution solves the problem, it’s far from how a human would have solved it.
Evolution also have a habit to cheat, and very much so.

Eg, if I allow the application to use the XOR binary operator, it sometimes finds XOR patterns that can be applied to the problem cases, and thus solving the problem, but not the way you might have wanted it to..

Anyway, for those interested:
The application source code (C# 2) can be downloaded here:
Genetic Math