Genetic Algorithms

Overview• Genetic Algorithms: a gentle introduction

– What are GAs

– How do they work/ Why?

– Critical issues

• Use in Data Mining– GAs and statistics

– decile performance maximization

– multi-objective models

Natural Genetics to AI

• Computational models inspired by biological evolution– survival of the fittest

– reproduction through cross-breeding

Genetic Algorithms• Population based search (parallel)

– simultaneous search from multiple points in search space– useful in complex, unstructured search spaces

(less prone to local failures)

Population members: potential solutions

• Population of solutions evolve from one generation to the next

Genetic Algorithms

• Search objective– Fitness score for population members

(fitness function)

• Survival of the fittest– selection

• Generating new solutions– “Mating” and reproduction of individuals

(crossover, mutation)

Basic OperationString1 (f1)

String2 (f2)

String3 (f3)

String4 (f4)

...

...

StringN (fN)

String1

String2

String2

String4

...

...

Stringx

Offspring1(1,4)

Offspring2(1,4)

Offspring3(2,7)

Offspring4(2,7)

...

...

OffspringN(x,y)

Selection RecombinationCrossover Mutation

Generation t Generation t+1

GAs: Parallel Search

X

X

Hill climber

Fitness

x

GAs: Basic Principles• Representation of individuals

– String of parameters (genes) : chromosome

eg. optimize a function F(p,q,r,s,t)

Population members: p q r s t

– genotype and phenotype

Binary representation?

• Population members as bit strings

F( p,q,r,s,t) as:

1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0

p q r s t

– early theory in terms of binary strings (schema

theorem)

– unnecessary perversity?

GAs: Basic Principles• Survival of the fittest (Fitness function)

– numerical “figure of merit”/utility measure of an individual

– tradeoff amongst a multiple evaluation criteria

– efficient evaluation

GAs: Basic Principles

• Iterative search– population evolves over generations

• Convergence– progression towards uniformity in population

– premature convergence?

(local optima)

Typical GA Run

Fitness

Generations

Best

Average

Operators: Selection

• Fitness proportionate selection (fi/f )

• number of reproductive trials for individuals

Selection• Roulette-wheel selection (stochastic sampling with replacement)

– wheel spaced in proportion to fitness values

– N (pop size) spins of the wheel

• Stochastic universal sampling– N equally spaced pins on wheel

– single turn of the wheel

Selection• Premature converge• Fitness scaling

f = f - (2*avg. - max.)

• Ranked fitness

• Elitism

• Steady-state selection

• Demetic grouping

Operators: Crossover

Parent 1: axpsqvqbtpihd

Parent 2: qzxxaycgbtphw crossover sites

Offspring 1: azpsavcbtpphd

Offspring 2: qxxxqyqgbtihw

(Uniform crossover)

• combining good building blocks

Operators: Mutation

• alters each gene with small probabilityx 1 y x 0 y 0 y y 0 x y x y

x 1 y x 0 y 1 y y 0 x x x y

Non-Binary Representations• Integer, real-number, order-based, rules, ...

• Binary or Real-valued? real representations give faster, more

consistent, more accurate results

• High-level representation– intuitive, can utilize specialized operators– effective search over complex spaces

Real-valued representationParent1: 3.45 0.56 6.78 0.976 2.5

Parent2: 0.98 1.06 4.20 0.34 1.8

Offspring1: 3.22 0.56 6.78 0.65 2.12

Offspring2: 1.43 1.06 4.20 0.41 1.93

(Arithmetic crossover)

High-level representationParent1:

Parent2:

Offspring1:

Offspring2:

{(1.2 x 3.4) (5.8 x 6.0) (0.2 x 0.61)}1 2 7

{( . . ) ( . . ) ( . . )23 41 36 51 51 5616 2 4 x x x

( . . ) ( . . )}03 11 22 273 9x x

{ ( . . ) ( . . )}(1.2 x 3.4)1 22 27 51 5619 4x x

{( . . ) [( . . ) ]23 41 36 516 2 x x (5.8 x 6.0)2

( . . ) }03 113x (0.2 x 0.61)7

High-level representation

{( . . ) ( . . )}03 11 22 273 9 x x

{( . . ) ( . . ) ( . . )}03 11 22 27 51 623 9 4 x x x

• Generalize/Specialize

{( . . ) ( . . )}03 11 22 273 9 x x

{( . . ) ( . . )}045 09 19 293 9 x x

Tree-structured representation (GP)

/

x 5

log

*

(x log(y))/5)

y

•Automated learning of programs (originally)parse tree expressions

•Non-linear interaction terms

•Function set : internal nodes{+,-,*,/,log}

•terminal set: leaf nodes{constants, variables}

Tree-structured representation

• Representing complex patterns

<

if

y 7

0

* y

x 2

+AND

>

x 2

If (y<7) and (x>2) then 0 else 2x+y

Genetic search: Issues• Coding scheme, fitness function critical– the “art” in GA design!– General mechanism so robust that, within reasonable margins, parameter

settings are not critical.

• Representation to match problem, domain– utilizing domain knowledge

• problem-specific crossover, mutation, selection

• Flexibility in fitness function formulation– modeling business objectives

Genetic search: Issues

• Stochastic search– initial populations, probabilistic operators

– multiple runs with different random streams

– Initializing population with known solutions– seeding initial population with solutions from multiple,

independent runs

Genetic search: Issues

• Guarantees optimality? – But...

• GAs and traditional techniques– especially useful where traditional approaches fail

– in conjunction with traditional techniques

• Parallelizable for large data– multi-processor, networked machines

Using GAs ?

• When to use a GA?

• GA and traditional techniques

• How long does it take?

• Will it perform better?

Using GAs

• population size

• mutation, crossover rates

• how many generations

• multiple runs

Is it a “black-box”?

? Huh?

• Data characteristics

• Fitness function

• GA parameters

GA Application Examples• Function optimizers

– difficult, discontinuous, multi-modal, noisy functions

• Combinatorial optimization– layout of VLSI circuits, factory scheduling, traveling

salesman problem

• Design and Control– bridge structures, neural networks, communication networks

design; control of chemical plants, pipelines

GA Application Examples• Machine learning

– classification rules, economic modeling, scheduling strategies

Portfolio design, optimized trading models, directmarketing models, sequencing of TV advertisements,adaptive agents, data mining, etc.