EVOLVING A SOLUTION:

DEVELOPMENTAL PLASTICITY IN EVOLUTIONARY COMPUTATIONURS Presentation – April 17th,

2009

Sara Lahr

Some problems are difficult to solve They may have many factors They may have a solution that is always in

fluxPredicting Financial MarketsDiscovering the Contagiousness of Diseases

Two excellent tools: Evolutionary ComputationGenetic Programming

THE BIG PICTURE

Background TermsEvolutionary ComputationGenetic Programming

N-gram GP The Problem: Definition and Solution Incremental Fitness Development Results Conclusion

OUTLINE

Evolutionary Computation is a field of Artificial Intelligence that uses growth and development of a population of individuals to find solutions to a given problem.

EVOLUTIONARY COMPUTATION

You have a problem that you don’t know how to solve.

You can recognize a good solution if you see

it.

HOW DOES IT WORK?

HOW DOES IT WORK? Generate a population of random solutions

1– ADBCE 2– ACBDE

3– ADEBC 4- ABCED

Find the better individuals and generate a new population based on them. Repeat.

Evolutionary Computation is a field of Artificial Intelligence that uses growth and development of a population of individuals to find a solution to a given problem.

Genetic Programming is a subset of EC where each individual is an actual computer program.

GENETIC PROGRAMMING

Evolutionary Computation is a field of Artificial Intelligence that uses growth and development of a population of individuals to find a solution to a given problem.

Genetic Programming is a subset of EC where each individual is an actual computer program.

N-gram GP is an extension of GP where the programs are linear sequences of instructions generated based on probabilities learned over time.

N-GRAM GP

A N-gram is a group of n consecutive elements in a sequence. def and efg are both 3-grams of defg.

Each item in the N-gram is an instruction. d may be ADD, e SUB, etc.

A matrix holds the probability of a given instruction appearing. Given instruction d followed by instruction e: the

matrix determines the next instruction based on evolved probabilities.

Existing good program: dedededef Building a new program: de_

d – 0.75 f – 0.25

N-GRAM GP

THE SYMBOLIC REGRESSION PROBLEM

GOAL: Find a function that maps to a given set of data points.

STAGE 1

STAGE 2

STAGE 3

STAGE 4

STAGE 5

STAGE 6

ConvergenceThe system makes a specific instruction

consistently dominant

Inflexibled may be important early, but f may vital to the

program later

Not ModularCreates large loops of converged instructions.

N-GRAM GP WEAKNESSES

A technique we developed for N-gram GP.

A block of instructions is generated by the probability matrix and appended to the end of the program. If the fitness of the extended program gets worse, the block is thrown away, and a new block is generated.

INCREMENTAL FITNESS DEVELOPMENT

INCREMENTAL FITNESS DEVELOPMENT

A B C

Original Program

Original Program

New Block

INCREMENTAL FITNESS DEVELOPMENT

Original Program

Original Program

C D B

C D B

New Block

Kept Block

New Block

A B CDiscarded Block

A E B

Versus Incremental Fitness Development Convergence

IFD is a more meticulous searcher; it maps out local possibilities

Inflexible IFD is more flexible; it is able to find the less

probable instructions

Not Modular IFD is able to split the function into valuable

portions

N-GRAM GP WEAKNESSES

PROBLEM N-gram GP* IFD*x + x2 + x3 + x4 + x5 100 100-x - 2x2 + x3 100 1001.009 + 1.419x + x2 61 1006 + x2 + 3x3 + 8x5 0 06 100 1006 + x2 10 946 + x2 + 3x3 0 18x5 100 1003x3 + 8x5 51 100x2 + 3x3 + 8x5 7 80sin(x) 1 63

RESULTS

*Number of successful runs out of 100 independent trials

Theoretical work necessary for improving existing tools.

Incremental Fitness Development is a successful extension of N-gram GP

The more successful the system, the more reliable the solutions

The more reliable the solutions the more useful they are in application

CONCLUSIONS

J. R. Koza. Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, USA, 1992.

N. F. McPhee, E. Crane, S. E. Lahr, R. Poli. Developmental Plasticity in Linear Genetic Programming. GECCO '09: Proceedings of the 11th annual conference on Genetic and evolutionary computation. Montreal. 2009.

R. Poli and N. McPhee. A linear estimation-of-distribution GP system. In M. O’Neill, L. Vanneschi, S. Gustafson, A. I. Esparcia Alcazar, I. De Falco, A. Della Cioppa, and E. Tarantino, editors, Proceedings of the 11th European Conference on Genetic Programming, EuroGP 2008, volume 4971 of Lecture Notes in Computer Science, pages 206–217, Naples, 26-28 Mar. 2008. Springer.

R. Poli, W. B. Langdon, and N. F. McPhee. A field guide to genetic programming. Published via http://lulu.com and freely available at http://www.gp-field-guide.org.uk, 2008. (With contributions by J. R. Koza).

REFERENCES

QUESTIONS?

ACKNOWLEDGEMENTSThanks to the Morris Academic Partnership program and to all who

helped me in this work, especially Nic McPhee, Ellery Crane (UMM ‘06), and Riccardo Poli

Romeo and Juliet – Shakespeare“JULIET If I do I drink to thee Had I it written I

would not let us forth So that my father that went hence so fast ?”

Wikipedia: Genetic Programming and N-gram“In addition because of the best parsers of

English currently in existence are roughly of this idea often say this approach is overly broad in scope .”

Declaration of Independence“We hold these truths to be totally dissolved and

that all political connection between them and the state remaining in the meantime exposed to all the dangers of invasion from without and convulsions within .”

N-GRAM GP TEXT GENERATIONS

MODULARITY

Program using Incremental Fitness Development. >More Modular

Program using standard N-gram GP. >Less modular

A matrix holds the probability of a given instruction appearing.

InstructionStartREAD_IN: Reg1READ_IN: Reg2ADD: Reg2MULT: Reg1SWAP

Answer: 2x2

N-GRAM GP

Register 1 Register 20 0x 0x xx 2xx 2x2

2x2 x