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GeneticProgramming Maze Marchers

(ByForrestSondahl, 2005)

The applet requires Java 1.4.1 or higher. It willnot run on Windows 95 or Mac OS 8 or 9. Mac users must have OS X10.2.6 or higher and use a browser that supports Java 1.4. (Safariworks, IE does not. Mac OS X comes with Safari. Open Safari and setit as your default web browser under Safari/Preferences/General.) Onother operating systems, you may obtain the latest Java plugin fromSun'sJava site.

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Created with NetLogo* View/download model file:GeneticProgramming Maze Marchers.nlogo

View Analysis for thisModel * Back to Forrest's Final ProjectMain Page.

WHAT IS IT?

This model demonstrates the use of genetic programming to evolvewalking instructions to solve a particular maze. Genetic programming(sometimes abbreviated GP) is a technique in computer science that usesthe concepts of natural selection, genetics, and evolution to generatecomputer programs to solve a particular problem. In this case, theproblem is navigating mazes. (This model is similar to GeneticProgramming Maze Rules, but instead of evolving movement rules for theagents, this model evolves the step by step commands an agent shouldexecute to solve a particular maze.)

WHAT IS GENETIC PROGRAMMING?

In the world of biology, species evolve by means of naturalselection and the interactions of DNA. Genetic Programming takes theseideas, and applies them in the field of computer science. Given aproblem, the goal is to evolve a computer program that can solve theproblem. It starts with a population of randomly generated computerprograms. (The ingredients of these randomly generated computerprograms are chosen based on the problem that is to be solved.) Eachprogram is run, and its performance is measured by a 'fitnessfunction', which reflects how good each program is at solving theproblem. Then programs are chosen from the population to 'reproduce'.The programs are chosen randomly, but with a weighting mechanism thatmakes it more likely that the more 'fit' programs are chosen.(Analogously in the biological world, defective organisms can get luckyand pass on their DNA, but the more fit organisms have a better chanceof doing so.) There are three forms of reproduction that occur:

• Cloning (the child program is identical to its parent)
• Mutation (the child program has some of its code replaced byrandomly generated code)
• Crossover (two parent programs are chosen from the population,and the child program consists of a mixture of code from the twoparents)
  

After a full new population of programs is formed, the oldpopulation is discarded, and each of the new programs is run and theirfitness is measured. Reproduction occurs, and the cycle continues,until a program with a certain level of fitness is found -- namely, aprogram that is good enough to solve the problem given. The word'until' implies that such a state will be reached. This isn'tnecessarily true. For one thing, the problem posed might be animpossible one (e.g. 'What is the answer to life the universe andeverything?'). Or it could be solvable, but not with the ingredientsthat the programs are made from (e.g. 'What is the solution to aquadratic equation?' with programs made only of '+' and '-' operators.)But even if the solution is within the realm of possible programsgenerated by the genetic programming process, success is by no meansguaranteed. Genetic Programming is a stochastic, rather thandeterministic, approach to solving problems. Currently there are, infact, no proofs that genetic programming works -- merely empiricalevidence showing that in some situations it does. The success of thegenetic programming process is highly dependent on the choice ofingredients for the programs and a well designed 'fitness function'that 'leads' the population in the right direction toward the goal.Other important parameters include the size of the population, thelength of each program's code, and the relative probability of each ofthe reproduction mechanisms. For more information on geneticprogramming, see these web sites:
http://www.geneticprogramming.com/Tutorial/index.html
http://www.genetic-programming.com/gpanimatedtutorial.html

HOW IT WORKS

Egl _assignment1 mac os. In many NetLogo models, agents are given predetermined rules, andthen the emergent behaviors that form through the interactions of theseagents are studied. In contrast, this model is starts with a desiredbehavior (solving a maze) and works on trying to discover the code thatthe agents should execute to achieve this behavior, through use ofGenetic Programming, as described in the section above.
In this model, the maze-solving programs are represented by'codeturtles'. Codeturtles each have a piece of NetLogo code assignedto them, and it's their job to perform it. Codeturtles will then bechosen, based on their fitness, to reproduce and create anothergeneration of codeturtles.
The ingredients that make up the code are extremely simple -- onlythree commands:

• maze-turn-right (think 'rt 90')
• maze-turn-left (think 'lt 90')
• maze-forward (think 'fd 1' except if there is a wall in the way)
  

Thus, a small example program might look like:

(The internal representation of the program is actually a treestructure, since this has been often found to produce better resultsfor genetic programming. The code trees are then compiled into the formyou see above, to be run as NetLogo code.)
The fitness function, which measures each codeturtles progress, is asimple one: 'What is the geometric distance to the goal square?' Thelower this number is, the more fit a turtle is. It is easy, of course,to create mazes where this is clearly not the case (e.g. load'maze4.txt') but for many mazes, this distance measurement serves as adecent heuristic. A better (in fact, perfect) fitness function wouldcount the minimum number of open path squares that the codeturtle wouldhave to cross to reach the goal. However, if we had such a fitnessfunction, then we would already have some algorithm for computing thesolution to our maze! And if we had such an algorithm, then why wouldwe be trying to evolve codeturtles to solve it? Using the solution tofind the solution seems like a cheap trick that turns this modelentirely into a toy problem. Also, fitness is computed for eachcodeturtle after each step it takes -- not just at the end of the run.Since fitness is calculated so often, the efficiency of computingfitness is important, and this is another advantage for geometricdistance fitness, as opposed to true walking distance to goal fitness.

HOW TO USE IT

1. Set the MAZE-FILE chooser to the maze file you want to use.
2. Adjust the slider parameters (see below), or use the defaultsettings.
3. Press the SETUP button.
4A. Press the GO button to begin the simulation
4B. Press the STEP button to go through one generation at a time.
5. Watch the View, to see the codeturtles attempt to solve the mazewith their given code DNA.
6. Watch the FITNESS plot, to see how the population is doing.
7. If a codeturtle successfully gets to the end of the maze, then thesimulation will stop. To stop it earlier, press the GO button again.(It may take some time for the current generation to finish.)
8. Press the SHOW-BEST button to see the code for the current best(most fit) codeturtle.
Parameters:
MAZE-FILE: The maze file to be loaded.
POPULATION-SIZE: The number of codeturtles in each generation
INITIAL-CODE-MAX-DEPTH: The maximum depth of randomly generated codetrees, that codeturtles start with. (It also affects the size ofmutations that occur). In general, a larger number generally meanslonger programs are created.
BRANCH-CHANCE: Controls the amount of branching in the generation ofrandom code trees. Again, a larger number generally means longerprograms are created.
CLONE-CHANCE, MUTATE-CHANCE, CROSSOVER-CHANCE: These three sliderscontrol the relative probability of each genetic operation occurring,with respect to the others.
(Examples: If the sliders are set to 10, 10, 10, then there is a 1/3chance of each genetic operation happening. If the sliders are set to10, 10, 20, then there is a 25% chance of cloning, 25% chance ofmutation, and 50% chance of crossover. If the sum of these threesliders is 100, then each slider represents the percent chance of thatgenetic operation being chosen to create an offspring for the newgeneration.)
FIX-RANDOM-SEED?: If true, then RANDOMSEED is used to start theprocess. This allows a particular run to be reproduced exactly, andthus examined more closely, (provided that the parameters are thesame). If false, then RANDOMSEED is not used.
RANDOMSEED: This is the number used to seed the random numbergenerator, if FIX-RANDOM-SEED? is true, to allow for reproducibleresults.
Notes:
You cannot see the codeturtles while they are moving even if you slowdown the speed slider, because of the way their code is executed, sowhat you see on the View is their positions after they have moved forthat generation. They leave a colored trail behind them, which is notcleared between generations. This chronicles the progress of theturtles.
The best fit codeturtle (or codeturtles, when there is a tie) in eachgeneration is shown as a neutral face. If a codeturtle finds the goal,then it is shown as a smiley face.

THINGS TO NOTICE

For humans, some mazes are easier to solve than others. Likewise,some mazes are easier for this model to solve than others. Which of thefive included mazes are easiest for this model, and which are hardest?Why might 'maze4.txt' be difficult for this model, even though itappears to be a very trivial maze to our eyes? Think about the fitnessfunction, as well as other factors.
The average and best fitness values shown in the plot sometimes go upand sometimes go down. Why do you think this is? Does geneticprogramming always find a solution?
Sometimes you will see the best-fitness plot flatten out for a longtime, because the best codeturtle keeps going to the same dead-endplace which is fairly close to the goal (e.g. use RANDOMSEED=1 on'maze1.txt' for 40 generations). This is called a 'local minimum.' Thisis because the codeturtles have gotten as close as possible in theircurrent neighborhood. It is not a 'global minimum', since it is in factpossible for the codeturtles to get all the way to the solution -- butin order to get there, they first have to move to places that arefarther away from the goal before they can get closer. The concepts oflocal and global mimima are applicable to many problems in computerscience and other fields. While some algorithms have no way to escapefrom local minima, genetic programming often manages to overcome them(e.g. keep watching RANDOMSEED=1 on 'maze1.txt' until generation 112 --you will see it escape the first local minimum, and find another, untilit eventually finds the goal.) What is it about genetic programmingthat allows it to escape? What parameters in the model could be changedto better overcome local minima?
The colors of the codeturtles have some meaning. They are initiallyrandomly colored, but:
* When a codeturtle results from cloning, it has the same color as itsparent.
* When a codeturtle results from crossover, it has a color averagingits two parents.
* When a codeturtle is mutated, it has a random color.

THINGS TO TRY

Try changing the POPULATION-SIZE slider. With a small population,each generation moves by more quickly, but it generally takes moregenerations to find a solution. Also, small populations mean increasedinbreeding. What affect does this have on the process? How low can thepopulation go such that the process still finds a solution on a fairlycomplicated maze such as 'maze0.txt' for instance? What does the plotlook like when you have a population size of just 1 or 2?
Try changing the INITIAL-CODE-MAX-DEPTH and the BRANCH-CHANCE. Notethat if the codeturtles' code gets long, then the codeturtles run moreslowly. Try starting with a very short code length (e.g.INITIAL-CODE-MAX-DEPTH 4, BRANCH-CHANCE .80). After one generation, thebest-fit codeturtle's code may be only 6 lines long. It will take manymore commands than this simply to walk the distance to the goal. Doesit take longer for genetic programming find a solution, when startingwith code fragments that are far too inadequate? How does the code growin size?
Crossover is usually the driving force of genetic programming. Trymoving the genetic operations sliders around, and run the model. Whathappens if you only allow cloning, and no mutation or crossover? Onlymutation? Only crossover?

EXTENDING THE MODEL

There is a model called Genetic Programming Maze Maker, which can beused to create maze files. Create several interesting maze files, andadd them to the MAZE-FILE chooser. What types of mazes does this modeldo well with? What types of mazes are hard for the model to handle? Arethere mazes that humans can solve that this model can't?
Sometimes the codeturtle with the best fitness in a given generationdoesn't make it into the next generation. The probability is in itsfavor, but nothing is guaranteed. Some implementations of GeneticProgramming DO guarantee that the best program so far is always clonedto the new generation. This would mean that the 'best fitness' plotwould be strictly non-increasing. Think of a situation where this couldlead to poor results. Make changes to the GP Library framework, suchthat the best codeturtle is always cloned. (Or better yet, make it sothat it's a switch that can be set.) Use BehaviorSpace to decide if itimproves results or not.
This maze is built on a rectangular grid. Instead of thinking of it asa grid, imagine that each open floor square is a small closed room,connected to other rooms by teleport devices. In the current model, theteleport devices can only connect to adjacent squares. But supposeinstead, that any room could be connected to any other room in the mazeby teleportation. Enough preamble -- try to build a generalized versionof this model in which codeturtles are traveling along the edges of anetwork, trying to find a goal node, instead of a goal square.

NETLOGO FEATURES

The NetLogo feature on which this whole model stands is the abilityto take a string of text, and run it as NetLogo code. This is achievedthrough the 'run' primitive.
Extensive use of recursion and lists has been employed, especially todeal with the tree structures which codeturtles use to store code.Since trees are not natively supported in NetLogo, they have beenimplemented as nested lists.
It is also interesting to note that this model is built from two parts.The first part is the 'GP Library for NetLogo', which consists of aframework of procedures that are useful for any model that is usinggenetic programming. The second part consists of procedures that arespecific to this model. Since NetLogo doesn't support any formalconcept of code libraries, this separation is largely achieved throughpositioning of the code, naming conventions, and comments.

RELATED MODELS

'Genetic Programming Maze Rules' - The brother model to this one.
'Genetic Programming Maze Maker' - A tool for loading/saving maze filesthis model uses.

'Genetic Programming Demo' - A simple model demonstrating how to usethe GP Library.
Start here if you want to build your own genetic programmingmodel.
There are also several models out there that work with GeneticAlgorithms, which are closely related to Genetic Programming. See:
'Echo' under Biology
'ARS-Genetics' and 'BinaryGA' by Thomas Hills, in the User CommunityModels.

CREDITS AND REFERENCES

Author: Forrest Sondahl
Date: November 28, 2005
Project Web Page: http://cs.northwestern.edu/~fjs750/netlogo/final/
Part of the Genetic Programming Library for NetLogo project, whichconsists of a library of code that makes it easier to write geneticprogramming models, as well as several sample models that demonstratethe use of the library.
Created for the course CS 460 Multi-Agent Modeling, at NorthwesternUniversity.

Back to Forrest's FinalProjectMain Page.

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