7. Genetic Programming and Emergent Order GP-Seminar 신수용

2 Contents u Introduction u Evolution of Structure and Variable Length Genomes u Iteration, Selection, and Variable Length Program Structures u Evolvable Representations u The Emergence of Introns, Junk DNA, and Bloat u Introns in GP defined u Why GP Introns Emerge u Effective Fitness and Operator u Why Introns Grow Exponentially u The Effects of Introns u What to Do about Introns

3 7.1 Introduction u This chapter focuses on emergent properties arising from GP’s freedom of representation of the problem space u Two important properties of GP  GP’s ability to search the space of the problem representation  The problem of introns or bloat u emergence -> variable length genotype 때문

4 7.2 Evolution of Structure and Variable Length Genomes u The capability to evolve a representation of the problem depends on the ability of a learning algorithm to modify the structure of its own solutions u By evolving structure, a variable length genotype may be able to learn not only the parameters of the solution, but also how many parameters there should be, what they mean, and how they interrelate u The variable length genotype is perhaps GP’s most radical practical innovation compared to its EA roots

5 7.3 Iteration, Selection, and Variable Length Program Structures u The essence of evolution  iterative insofar as generation after generation of populations are assigned reproduction opportunities  selective, insofar as the better performing variants get a better chance to use these opportunities u Dawkins called this aspect cumulative selection  the effects of selection acting on one generation are inherited by the next

6 7.4 Evolvable Representations u Problem representation  most ML paradigm: a fairly constrained problem representation (Boolean, threshold, decision trees, etc) u Constraints  advantage: making the traversal of the solution space more tractable as long as the solution space is well tailored to the problem domain u GP search space  the problem space + the space of the representation of the problem

7 7.4 Evolvable Representation (2) u Ignoring Operators or Terminals  system should magnify the exploration of sections of the representation space that produce better results u Finding Solutions of the Correct length  GP can find a short or a long solution where a fixed length representation cannot u Modularization and Meta-Learning  표현방법 탐색 공간에 대한 연구  Modularization (chap 10)  Meta-Learning l information about the problem representation from one GP run is used to bias the search in later GP runs

8 7.5 The Emergence of Introns, Junk DNA, and Bloat u Angeline  the first GP researcher to associate this emergent “extra code” in GP with the concept of biological introns  “occasional occurrence” u Tackett  GP bloat was caused by blocks of code in GP individuals u A body of research has established that GP bloat is, in reality, caused by GP introns  introns are a persistent and problematic part of the GP process

What Can We Learn from Biological Introns u 생물학적 개념의 introns 과 GP 의 introns 은 거의 동일한 개념  phenotype 에 아무런 직접적 영향을 주지 않음  play some role in protecting good building blocks against destructive crossover  have indirect effect on survivability, the nature of the effect is different

Introns in GP Defined u Introns in GP  A feature of the genotype that emerges from the process of the evolution of variable length structures  does not directly affect the survivability of the GP individual u properties  introns are emergent and they do not directly affect the fitness of the individual u artificially inserted introns: artificial intron equivalents u Global  introns for every valid input to the program u local  only for the current fitness cases and not necessarily for other valid inputs

Why GP Introns Emerge u While introns do not affect the fitness of the individual, they do affect the likelihood that the individual’s descendents will survive u effective fitness  survivability of an individual’s offspring  The fitness of the parent. The fitter the parent, the more likely it is to be chosen for reproduction  the likelihood that genetic operators will affect the fitness of the parent’s children u introns emerge principally in response to the frequently destructive effects of genetic operators

Effective Fitness and Crossover u Complexity of the program  length or size of the program measured with a method that is natural for a particular representation u absolute complexity  total size of the program or block u effective complexity  the length of the active parts of the code within the program

(2) u Using fitness-proportion selection, block exchange crossover C j e : the effective complexity of program j C j a : the absolute complexity of program j p c : probability of crossover p j d : probability of destructive crossover f j : the fitness of the individual bar f t : average fitness of the population  the proportion of copies of a program in the next generation is the proportion produced by the selection operator minus the proportion of program destroyed by crossover

(3) u Rewrite u effective fitness  increase its effective fitness by lowering its effective complexity

Effective Fitness and Other Operator u Generalization to include the effects of other operator

Why Introns Grow Exponentially u Introns can provide very effective global protection against destructive crossover u 최적해에 근접한 개체는 fitness 를 증가시키는 것은 매우 힘들어지고, 최소한 현상태를 유지시키기 위해서 Effective fitness 를 증가시키는 방향을 선택한다.  Introns 증가 한계가 주어지지 않는다.

The Effects of Introns u introns may benefit evolution vs. introns almost always result in poor evolution and extended computation u issues about introns  Introns may have differing effects before and after exponential growth of introns begins  Different systems may generate different types of introns with different porbabilities  The extent to which genetic operators are destructive in their effect is likely to be a very important initial condition in intron growth  mutation and crossover may affect different types of introns differently

Problems Caused by Introns u Run stagnation, poor results, and a heavy drain on memory and CPU time  run stagnation: mutation 으로 해결 l intron 을 의미있는 코드로 변화시킴  poor results: introns 의 확장을 제한함

Possible Beneficial Effects of Introns u To promote parsimony in the real code  a high probability of destructive crossover  some introns in the population  a system that makes it relatively easier to reduce the amount of effective code than to add more introns u Structural protection against crossover

What to Do about Introns u Reduction of destructive effects  problem of bloat may be viewed in a more general way as the absence of homology in GP u Parsimony  the effect of parsimony pressure is to attach a penalty to the length of programs  see next slide u Changing the fitness function  the fitness function become variable -> GP individuals might find ways to improve their fitness

(2) u The effect of parsimony