Lecture 16 & 17 - Genetic Algorithms Fundamentals [Read-Only] · 2017-03-24 · GENETIC ALGORITHM Representation of Solutions: The Chromosome Rules Representation We can represent

GENETIC ALGORITHMGENETIC ALGORITHM

Introduction

A biologically inspired model of intelligence

The principles of biological evolution are applied to findsolutions to difficult problems

The problems are not solved by reasoning logically aboutthem; rather populations of competing candidate solutionsare spawned and then evolved to become better solutionsthrough a process patterned after biological evolution

1


Introduction

Less worthy candidate solutions tend to die out, while thosethat show promise of solving a problem survive andp g preproduce by constructing new solutions out of theircomponents

GA begin with a population of candidate problem solutions

Candidate solutions are evaluated according to their ability to solve problem instances: only the fittest survive and combine with each other to produce the next generation of possible

2

p g psolutions


Introduction

Thus increasingly powerful solutions. Learning is viewed as acompetition among a population of evolving candidatep g p p gproblem solutions

This method is heuristic in nature and it was introduced byThis method is heuristic in nature and it was introduced byJohn Holland in 1975

3


Basic Algorithm

beginset time t = 0;set time t 0;initialise population P(t) = {x1

t, x2t, …, xn

t} of solutions;while the termination condition is not met do

beginbeginevaluate fitness of each member of P(t);select some members of P(t) for creating offspring;produce offspring by genetic operators;replace some members with the new offspring;set time t = t + 1;

4

;end

end


Chromosome

5


Representation of Solutions: The Chromosome

Gene: A basic unit, which represents one characteristic of theindividual. The value of each gene is called an alleleg

Chromosome: A string of genes; it represents an individual i.e.a possible solution of a problem Each chromosomea possible solution of a problem. Each chromosomerepresents a point in the search space

Population: A collection of chromosomes

An appropriate chromosome representation is important for

6

pp p p pthe efficiency and complexity of the GA



The classical representation scheme for chromosomes isbinary vectors of fixed length. However, real valuedy g ,chromosomes are also possible

In binary coded chromosomes every gene has two allelesIn binary coded chromosomes, every gene has two allelesIn real coded chromosomes, a gene can be assigned any value from a domain of values

In the case of an I-dimensional search space, eachchromosome consists of I variables with each variable

7

encoded as a bit string



Example: Cookies Problem

Two parameters sugar and flour (in kgs). The range for bothis 0 to 9 kgs. Therefore a chromosome will comprise of twogenes called sugar and flourgenes called sugar and flour

5 1 Chromosome # 01

2 4 Chromosome # 02

8



Example: Expression satisfaction Problem

F = (¬a ∨ c) ∧ (¬a ∨ c ∨ ¬e)∧ (¬b ∨ c ∨ d ∨ ¬e) ∧ (a ∨ ¬b ∨ c)∧ (¬b ∨ c ∨ d ∨ ¬e) ∧ (a ∨ ¬b ∨ c)∧ (¬e ∨ f)

Ch Si bi b d f 100111Chromosome: Six binary genes a b c d e f e.g. 100111

9



Example: Model Learning

Use GA to learn the concept Yes Reaction from the FoodAllergy problem’s data

10



A potential model of the data can be represented as achromosome with the genetic representation:g p

Gene # 1 Gene # 2 Gene # 3 Gene # 4Restaurant Meal Day CostRestaurant Meal Day Cost

The alleles of genes are:

Restaurant gene: Sam, Lobdell, SarahMeal gene: breakfast, lunch

11

gDay gene: Friday, Saturday, SundayCost gene: cheap, expensive



Rules Representation

Rules are often represented by bit strings (because they canbe easily manipulated by genetic operators), but othernumerical and symbolic representations are also possiblenumerical and symbolic representations are also possible

Set of if-then rules:S ifi i f iSpecific sub-strings are allocated for encoding eachrule pre-condition and post-condition

12

Example: Suppose we have an attribute “Outlook”which can take on values: Sunny, Overcast or Rain




We can represent it with 3 bits:100 would mean the value Sunny,010 would mean Overcast &010 would mean Overcast &001 would mean Rain

110 ld S O110 would mean Sunny or Overcast111 would mean that we don’t care about its value

13

The pre-conditions & post-conditions of a rule are encodingby concatenating the individual representation of attributes




Example:If (Outlook = Overcast or Rain) and Wind = strong

then PlayTennis = Nothen PlayTennis No

can be encoded as 0111001

Another ruleIf Wind = Strong then PlayTennis = Yes

14

g y

can be encoded as 1111000




An hypothesis comprising of both of these rules can beencoded as a chromosome 01110011111010

Note that even if an attribute does not appear in a rule, wereserve its place in the chromosome, so that we can havefi d l th hfixed length chromosomes

15


Fitness Function

16


Fitness Function

Also called “evaluation function”

It is used to determine the fitness of a chromosome

Creating a good fitness function is one of the challengingCreating a good fitness function is one of the challengingtasks of using GA

17


Fitness Function

Example: Cookies Problem

Two parameters sugar and flour (in kgs). The range for bothis 0 to 9 kgs. Therefore a chromosome will comprise of twogenes called sugar and flourgenes called sugar and flour

5 1

2 4

18

The fitness function for a chromosome is the taste of theresulting cookies; values can be from 1 to 100


Fitness Function

Example: Expression satisfaction Problem

F = (¬a ∨ c) ∧ (¬a ∨ c ∨ ¬e)∧ (¬b ∨ c ∨ d ∨ ¬e) ∧ (a ∨ ¬b ∨ c)∧ (¬b ∨ c ∨ d ∨ ¬e) ∧ (a ∨ ¬b ∨ c)∧ (¬e ∨ f)

Ch Si bi b d f 100111Chromosome: Six binary genes a b c d e f e.g. 100111

Fitness function: Number of clauses having truth value of 1

19

ge.g. 010010 has fitness 2


Fitness Function


Use GA to learn the concept Yes Reaction from the data

The fitness function can be the score of the classificationThe fitness function can be the score of the classificationaccuracy of the rule-set over a set of provided trainingexamples (number of training samples correctly classified by

h )a chromosome)

Often other criteria may be included as well, such as the

20

ycomplexity of the rules or the size of the rule set


Reproduction Operators

21


Reproduction Operators

Genetic operators are applied to chromosomes that areselected to be parents, to create offspringp , p g

Basically of two types: Crossover and Mutation

Crossover operator create offspring by recombining thechromosomes of selected parents

Mutation is used to make small random changes to achromosome in an effort to add diversity to the population

22

y p p


Reproduction Operators: Crossover

Crossover operation takes two candidate solutions anddivides them, swapping components to produce two new, pp g p pcandidates

23



Figure illustrates crossover on bit string patterns of length 8

The operator splits them and forms two children whose initialsegment comes from one parent and whose tail comes fromthe otherthe other

Input Bit Strings1 1 # 0 1 0 1 # # 1 1 0 # 0 # 1

Resulting Strings

24

g g1 1 # 0 # 0 # 1 # 1 1 0 1 0 1 #



Two genes sugar and flour (in kgs)Crossover operation on chromosomesp

5 1 5 45 1 5 4

2 4 2 1

25



The place of split in the candidate solution is an arbitrarychoice. This split may be at any point in the solutionp y y p

This splitting point may be randomly chosen or changedsystematically during the solution processsystematically during the solution process

Crossover can unite an individual that is doing well in onedi i ith th i di id l th t i d i ll i thdimension with another individual that is doing well in theother dimension

26


Reproduction Operators: Crossover (Important Similarities)

Suppose we have these chromosomes and their fitness values

A) 01101 169B) 11000 576C) 01000 64C) 01000 64D) 10011 361

If l th t i hi h h hi h fit l h b th t thIf we analyze the strings which have high fitness value, we have observe that theyboth have a 1 in the 1st column, whereas the low fitness strings have a 0. Inthe second column we have a 1 in B and 0 in D, and 1 in the low fitnessstrings. We wonder that if 1 in the 2nd column is associated with low fitness, so

27

gwe may improve the score of B by putting a 0 in place of 1 in the 2nd column


Problem solving through GA

Optimize value of ( )f x x( ) sin= π2 6 over 0 255≤ ≤xOptimize value of ( )f x( ) sin= 256 over 0 255≤ ≤x

where x is restricted to integers.The maximum value of 1 occurs at x = 128.


Problem solving through GA

• One variable• Use binary alphabet

g g

• Use binary alphabet• Therefore, represent each individual as 8-bit binary

string• Set number of population members to (artificially

low) 8• Randomize populationp p• Calculate fitness for each member of (initialized)

population


References

Engelbrecht Chapter 8 & 9

30

Documents

Lecture 16 & 17 - Genetic Algorithms Fundamentals [Read-Only] · 2017-03-24 · GENETIC ALGORITHM Representation of Solutions: The Chromosome Rules Representation We can represent