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Genetic Algorithms

G5BAIMArtificial Intelligence MethodsArtificial Intelligence Methods

Graham Kendallgxk@cs.nott.ac.uk ‐ http://www.cs.nott.ac.uk/~gxk

Acknowledgement: Some of these slides are based on those from Wendy Williams

Genetic Algorithms

G5BAIM Genetic AlgorithmsCharles Darwin 1809 - 1882

"A man who dares to waste an hour of life has not discovered the value of life"

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Genetic Algorithms

Classes of Search TechniquesClasses of Search Techniques

Direct methods Indirect methods

Calculus-based techniques

Evolutionary algorithms Simulated annealing

Guided random search techniques

Dynamic programming

Enumerative techniques

Search techniques

Finonacci Newton Evolutionary strategies

Centralized Distributed

Parallel

Steady-state Generational

Sequential

Genetic algorithms

Genetic Algorithms

An Abstract Example

Distribution of Individuals in Generation 0

Distribution of Individuals in Generation N

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Genetic Algorithms

Components of a GAA problem to solve, and ...

Encoding technique       (gene, chromosome)

Initialization procedure                (creation)

Evaluation function                 (environment)

Selection of parents               (reproduction)

Genetic operators    (mutation, recombination)

Parameter settings             (practice and art)

Genetic Algorithms

Genetic Algorithms• Based on survival of the fittest

• Developed extensively by John Holland in mid 70’s

• Based on a population based approach

• Can be run on parallel machines

• Only the evaluation function has domain knowledge

• Can be implemented as three modules; the evaluation module, the population module and the reproduction module.

• Solutions (individuals) often coded as bit strings

• Algorithm uses terms from genetics; population, chromosome and gene

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Genetic Algorithms

The GA Cycle

reproduction

population evaluation

modification

parents

children

modifiedchildren

evaluated children

discard

deleted members

Genetic Algorithms

Populationl ti

Chromosome Representation

Bit strings (0101 ... 1100)

Real numbers (43.2 ‐33.1 ... 0.0 89.2) 

Permutations of element (E11 E3 E7 ... E1 E15)

population

( )

Lists of rules (R1 R2 R3 ... R22 R23)

Program elements(genetic programming)

... any data structure ...

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Genetic Algorithms

Reproduction

reproduction

population

parents

children

Parents are selected at random with selection chances biased in relation to chromosome evaluations.

Genetic Algorithms

Chromosome Modification

modificationchildren

modified children

Modifications are stochastically triggeredOperators:

MutationCrossover (recombination)

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Genetic Algorithms

Evaluation

evaluation

evaluatedchildren

modifiedchildren

The evaluator decodes a chromosome and assigns it a fitness measureThe evaluator is the only link between a classical GA and the problem it is solving

Genetic Algorithms

Deletion

population

discard

discarded members

Generational GA: entire populations replacedGenerational GA: entire populations replaced with each iteration

Steady‐state GA: a few members replaced each generation

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Genetic Algorithms

A Simple Example

The Traveling Salesman Problem:

Find a tour of a given set of cities so that 

•each city is visited only once•each city is visited only once

•the total distance traveled is minimized

Genetic Algorithms

Representation

Representation is an ordered list of city

numbers known as an order‐based GA.

1) London     3) Dunedin        5) Beijing     7) Tokyo

2) Venice      4) Singapore     6) Phoenix   8) Victoria

CityList1 (3   5   7   2   1   6   4   8)

CityList2 (2   5   7   6   8   1   3   4)

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Genetic Algorithms

Mutation

Mutation involves reordering of the list:

Before:       (5   8   7   2   1   6   3   4)

After:          (5   8   6   2   1   7   3   4)

Genetic Algorithms

120

TSP Example: 30 Cities

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100

120

y

0

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0 10 20 30 40 50 60 70 80 90 100

x

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Genetic Algorithms

120

TSP30 (Performance = 941)

Solution i (Distance = 941)

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y

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0 10 20 30 40 50 60 70 80 90 100

x

Genetic Algorithms44626967 120

TSP30 (Performance = 800)

Solution j(Distance = 800)7864625442504040382135

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67606040425099

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Genetic Algorithms

120

TSP30 (Performance = 652)

Solution k(Distance = 652)

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Genetic Algorithms42383526 120

TSP30 Solution (Performance = 420)

Best Solution (Distance = 420)2135327

38464458606976

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78716967628494

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Genetic Algorithms

Issues for GA Practitionersh b lChoosing basic implementation issues:

representation

population size, mutation rate, ...

selection, deletion policies

crossover, mutation operators

T i i C i iTermination Criteria

Performance, scalability

Solution is only as good as the evaluation function (often hardest part)

Genetic Algorithms

Benefits of Genetic Algorithms

Concept is easy to understand

Modular, separate from application

Supports multi‐objective optimization

Good for “noisy” environments

Always an answer; answer gets better with time

Inherently parallel; easily distributed

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Genetic Algorithms

Benefits of Genetic Algorithms (cont.)

Many ways to speed up and improve a GA‐based application as knowledge about  problem domain is gained

Easy to exploit previous or alternate solutions

Flexible building blocks for hybrid applications

Substantial history and range of use

Genetic Algorithms

When to Use a GA

Alternate solutions are too slow or overly complicated

Need an exploratory tool to examine new approaches

Problem is similar to one that has already been successfully solved by using a GA

Want to hybridize with an existing solutionWant to hybridize with an existing solution

Benefits of the GA technology meet key problem requirements 

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Genetic Algorithms

Some GA Application TypesDomain Application Typeso a pp cat o ypes

Control gas pipeline, pole balancing, missile evasion, pursuit

Design semiconductor layout, aircraft design, keyboardconfiguration, communication networks

Scheduling manufacturing, facility scheduling, resource allocation

Robotics trajectory planning

M hi L i d i i l t k i i l ifi tiMachine Learning designing neural networks, improving classificationalgorithms, classifier systems

Signal Processing filter design

Game Playing poker, checkers, prisoner’s dilemma

CombinatorialOptimization

set covering, travelling salesman, routing, bin packing,graph colouring and partitioning

Genetic Algorithms

GA AlgorithmI iti li l ti f h• Initialise a population of chromosomes

• Evaluate each chromosome (individual) in the population

• Create new chromosomes by mating chromosomes in the current population (using crossover and mutation)

• Delete members of the existing population to make way for the new members

• E al ate the ne members and insert them into the pop lation• Evaluate the new members and insert them into the population

• Repeat stage 2 until some termination condition is reached (normally based on time or number of populations produced)

• Return the best chromosome as the solution

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Genetic Algorithms

GA Algorithm1 I iti li ti1. Initialization

2. Evaluation

3. Selection

4. Recombination

5. Mutation

6. Replacement

7 Repeat steps 2–6 until a terminating condition is met7. Repeat steps 2 6 until a terminating condition is met.

Genetic Algorithms

GA Algorithm1. Initialization

1 I iti li ti

2. Evaluation

3. Selection

4. Recombination

5. Mutation

6. Replacement

7. Repeat steps 2–6 until a terminating condition is met.

1. Initialization

The initial population of candidate solutions is usually generated randomly across the search space. However, domain‐specific knowledge or other information can be easily incorporated.

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Genetic Algorithms

GA Algorithm1. Initialization

2 E l ti

2. Evaluation

3. Selection

4. Recombination

5. Mutation

6. Replacement

7. Repeat steps 2–6 until a terminating condition is met.

2. Evaluation

Once the population is initialized or an offspring population is created, the fitness values of the candidate solutions are evaluated.

Genetic Algorithms

GA Algorithm1. Initialization

3 S l ti

2. Evaluation

3. Selection

4. Recombination

5. Mutation

6. Replacement

7. Repeat steps 2–6 until a terminating condition is met.

3. Selection

Selection allocates more copies of those solutions with higher fitness values and thus imposes the survival‐of‐the‐fittest mechanism on the candidate solutions. The main idea of selection is to prefer better solutions to worse ones, and many selection procedures have been proposed to accomplish this idea, including roulette‐wheel selection, stochastic universal selection, ranking selection and tournament selection, some of which are described in the next section.

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Genetic Algorithms

GA Algorithm1. Initialization

4 R bi ti

2. Evaluation

3. Selection

4. Recombination

5. Mutation

6. Replacement

7. Repeat steps 2–6 until a terminating condition is met.

4. Recombination

Recombination combines parts of two or more parental solutions to create new, possibly better solutions (i.e. offspring). There are many ways of accomplishing this (some of which are discussed in the next section), and competent performance depends on a properly designed recombination mechanism. The offspring under recombination will not be identical to any particular parent and will instead combine parental traits in a novel manner.

Genetic Algorithms

GA Algorithm1. Initialization

5 M t ti

2. Evaluation

3. Selection

4. Recombination

5. Mutation

6. Replacement

7. Repeat steps 2–6 until a terminating condition is met.

5. Mutation

While recombination operates on two or more parental chromosomes, mutation locally but randomly modifies a solution. Again, there are many variations of mutation, but it usually involves one or more changes being made to an individual’s trait or traits. In other words, mutation performs a random walk in the vicinity of a candidate solution.

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Genetic Algorithms

GA Algorithm1. Initialization

6 R l t

2. Evaluation

3. Selection

4. Recombination

5. Mutation

6. Replacement

7. Repeat steps 2–6 until a terminating condition is met.

6. Replacement

The offspring population created by selection, recombination, and mutation replaces the original parental population. Many replacement techniques such as elitist replacement, generation‐wise replacement and steady‐state replacement methods are used in GAs.

Genetic Algorithms

GA Algorithm - Evaluation

• Responsible for evaluating a chromosome

• Only part of the GA that has any knowledge about the problem.

The rest of the GA modules are simply operating on (typically) bit

strings with no information about the problem

• A different evaluation module is needed for each problem

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Genetic Algorithms

GA Algorithm - Population Module

• Responsible for maintaining the population

• Initilisation

– Random

– Known Solutions

Genetic Algorithms

GA Algorithm - Population Module• Deletion

– Delete-All : Deletes all the members of the current population and replaces

them with the same number of chromosomes that have just been created

– Steady-State : Deletes n old members and replaces them with n new

members; n is a parameter

But do you delete the worst individuals, pick them at random or delete the

chromosomes that you used as parents?

– Steady-State-No-Duplicates : Same as steady-state but checks that no

duplicate chromosomes are added to the population. This adds to the

computational overhead but can mean that more of the search space is

explored

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Genetic Algorithms

GA Parent Selection - Roulette Wheel•Sum the fitnesses of all the population members, TF

•Generate a random number, m, between 0 and TF

•Return the first population member whose fitness added to the preceding population members is

Chromosome 1 2 3 4 5 6 7 8 9 10Fitness 12 18 15 17 3 136 12 15 20 15

Running Total 12 30 45 62 65 201 213 228 248 263

1 2 3 4 5 6 7 8 9 10

Random Number 213 90 120 43 11 104 176 245 47 124

Chromsome Chosen 8 6 6 3 #N/A 6 6 9 4 6

NotesPress F9 to regenerate random numbersNotice how C6 tends to dominate due to its dominant fitness

Roulette Wheel Selection

preceding population members is greater than or equal to m

Genetic Algorithms

GA Parent Selection - Tournament• Select a pair of individuals at random. Generate a random

number, R, between 0 and 1. If R < r use the first individual as

a parent. If the R >= r then use the second individual as the

parent. This is repeated to select the second parent. The value of

r is a parameter to this method

• Select two individuals at random. The individual with the

highest evaluation becomes the parent. Repeat to find a second

parent

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Genetic Algorithms

GA Fitness Techniques• Fitness-Is-Evaluation : Simply have the fitness of the

chromosome equal to its evaluation

• Windowing : Takes the lowest evaluation and assigns each

chromosome a fitness equal to the amount it exceeds this

minimum.

• Linear Normalization : The chromosomes are sorted by

decreasing evaluation value. Then the chromosomes are

assigned a fitness value that starts with a constant value and

decreases linearly. The initial value and the decrement are

parameters to the techniques

Genetic Algorithms

GA Population Module - Parameters

• Population Size

• Elitism

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Genetic Algorithms

GA Reproduction - Crossover OperatorsOperators

One Point Crossover inOne Point Crossover inGenetic AlgorithmsGenetic Algorithms

© Graham Kendall

gxk@cs.nott.ac.uk

http://cs.nott.ac.uk/~gxk

Uniform Crossover inUniform Crossover inGenetic AlgorithmsGenetic Algorithms

© Graham Kendall

gxk@cs.nott.ac.uk

http://cs.nott.ac.uk/~gxk

Partially MatchedPartially MatchedCrossover (PMX) inCrossover (PMX) inGenetic AlgorithmsGenetic Algorithms

© Graham Kendall

gxk@cs.nott.ac.uk

http://cs.nott.ac.uk/~gxk

Order Based Crossover

Cycle Crossover

Genetic Algorithms

GA Example• Crossover probability, PC = 1.0p y,• Mutation probability, PM = 0.0• Maximise f(x) = x3 - 60 * x2 + 900 * x +100• 0 <= x >= 31• x can be represented using five binary digits

0 100

1 9412 16683 22874 28045 32256 35567 38038 39729 4069

10 4100 4500

Max : x = 10

f(x) = x^3 - 60x^2 + 900x + 100

10 410011 407112 398813 385714 368415 347516 323617 297318 269219 239920 210021 180122 150823 122724 96425 72526 51627 34328 21229 12930 100

0

500

1000

1500

2000

2500

3000

3500

4000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37

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Genetic Algorithms

GA Example• Generate random individuals

Chromosome Binary String x f(x) P1 11100 28 212 P2 01111 15 3475 P3 10111 23 1227

P4 00100 4 2804 TOTAL 7718 AVERAGE 1929.50

Genetic Algorithms

GA Example• Choose Parents, using roulette wheel selection• Crossover point is chosen randomly

Roulette Wheel Parent Chosen Crossover Point 4116 P3 N/A 1915 P 11915 P2 1

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Genetic Algorithms

GA Example - Crossover

1 0 1 1 1

0 1 1 1 1

P3

P2

1 1 1 1 1C1

0 0 1 0 0

0 1 1 1 1

P4

P2

0 0 1 1 1C3

0 0 1 1 11

C2 0 1 1 0 03

C4

Genetic Algorithms

GA Example - After First Round of BreedingBreeding

• The average evaluation has risen• P2, was the strongest individual in the initial population. It was

chosen both times but we have lost it from the current population• We have a value of x=7 in the population which is the closest

value to 10 we have foundChromosome Binary String x f(x)

P1 11111 31 131 P2 00111 7 3803 P3 00111 7 3803 P4 01100 12 3998 TOTAL 11735 AVERAGE 2933.75

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Genetic Algorithms

GA Example - Question?

• Assume the initial population was 17, 21, 4 and 28. Using the same GA methods we used above (PC = 1.0, PM = 0.0), what chance is there of finding the global optimum?

Genetic Algorithms

GA Example - Mutation

• A method of ensuring premature convergence does not occur• Usually set to a small value• Dynamic mutation and crossover rates

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Genetic Algorithms

Try Previous Exam Question

• Question and answer are available from the course web site

Genetic Algorithms

Representation Examples

• Jakobs S. (1996) On Genetic Algorithms for the Packing of Polygons, European Journal of Operational Research, 88:165-181

• Hart E., Ross P. and Nelson J.A.D. (1999) Dynamic Scheduling chicken catching – An investigation into the success of a genetic algorithm on a real-world scheduling problem, Annals of Operations Research 92:363–380Operations Research, 92:363 380

• Both of these papers are available on the course web site

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Genetic Algorithms

G5BAIMArtificial Intelligence MethodsArtificial Intelligence Methods

Graham KendallEnd of Genetic Algorithms