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Genetic Algorithms

Objectives

To provide a background and understanding of basic genetic

algorithms and some of their applications.

a basic genetic algorithmthe basic discussion

the applications of the algorithm

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Genetic Algorithms

1859

Origin of the Species

Survival of the Fittest

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Genetic Algorithms

1975

Genetic Algorithms

Artificial Survival of the Fittest

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Genetic Algorithms

Terms

Biological GA Terms

Chromosome StringGene Feature, character

Genomes Guesses, solutions, collection of genes

Genetic algorithms are search procedures based onthe mechanics of genetics and natural selection.

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Genetic Algorithms

Numerous techniques and algorithms have beendeveloped to assist the engineer in the creation ofoptimum development strategies.

These procedures quickly converge to optimal

solutions after examining only a small fraction of thesearch space and have been successfully appliedto complex engineering optimisation problems.

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Genetic Algorithms

Evolution in the animal world allows developingspecies to thrive in particular environments.

Genetic algorithms are capable of solving othertypes of problems, using genetic operatorsabstracted from nature, they form a mechanismsuitable for a variety of search problems.

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Genetic Algorithms

Genetic algorithms try to imitate the Darwinianevolution process in computer programs.

Conceivable solutions are represented, the 'fittest'will have the greatest chance of reproducing.

Successful properties will therefore be favourablyrepresented within the population of solutions.The population is the successively 'optimised' after a

number of generations.

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Genetic Algorithms

In evolutionary systems, populations evolve byselective pressures, mating between individuals, andalterations such as mutations.

In genetic algorithms, operators duplicate,

recombine and change solutions in the currentpopulation to create a new population, simulatingsimilar effects.

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Genetic Algorithms

A genetic algorithm simulates Darwinian theory ofevolution using highly parallel, mathematicalalgorithms that, transform a set (population) ofmathematical object (typically strings of 1's and 0's)into a new population, using operators such as:

reproduction, mutation and crossover.

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Genetic Algorithms

The initial population is selected at random, whichcould be the toss of a coin, computer generated orby some other means, and the algorithm willcontinue until a certain time or a certain condition ismet.

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Genetic Algorithms

Determine the initial population of creaturesDetermine the fitness of the populationReproduce the population using the fittest parentsof the last generationDetermine the crossover point, this can also be

randomDetermine if mutation occurs and if so on whichcreature(s)

Repeat from step 2 with the new population until

condition (X) is true

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Genetic Algorithms

Such algorithms differ from traditional search andoptimisation methods in that they

use codings of the control parametersadapt solutions themselves

process successive generationsuse randomised operators.

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Genetic AlgorithmsEncoding the Solutions

The decision variables of a problem arenormally encoded into a finite length string

This could be a binary string or a list of integersFor example :

or0 1 1 0 1 1 0 1 0 2 3 4 11 45

We could also representnumbers as coloured boxes

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Genetic AlgorithmsEncoding the Solutions

Initial populationEvaluations on the population

Breeding (iteratively)Choose suitable parentsProduce two offspringMutation

Evaluation function - Domain knowledge

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Generate InitialPopulation

PopulationGeneration 'n'

Reproduce

Population

CrossoverPopulation

MutatePopulation

n = n + 1

n = 1

n < 20

Final

Population

n = 20

Genetic AlgorithmsFlowchart (20 generations)

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Reproduction

Genetic Algorithms

1

2

3

1

2

3

Solutions are carriedforward to the next

stage based onweighted probability.

Some will survive (1)Some will reproduce (2)

Some will die out (3)

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Parent selection

Genetic Algorithms

Roulette WheelSelection

Sum the fitnesses of all thepopulation members, TF

Generate a random number, m,between 0 and TFReturn the first population memberwhose fitness added to the preceding

population members is greater than orequal to m

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Crossover

Genetic Algorithms

A percentage of thepopulation is selected forbreeding and assignedrandom mates.

A random crossoverpoint is selected and apair of new solutionsare produced

1

2

1

2

Crossover

One Point Crossover inOne Point Crossover in

Genetic AlgorithmsGenetic Algorithms

Graham Kendall

[email protected]

http://cs.nott.ac.uk/~gxkAdapted from Dr Graham Kendalls G5BAIM lecture example

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Mutation

In a small percentage ofthe population random

changes are made.

Genetic Algorithms

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Genetic Algorithms

Each iteration of the loop is called a generation, fitnesscan be gauged in several different ways depending on theapplication of the algorithm.

Reproduction and crossover play the primary role in artificialgenetic search. Reproduction emphasises highly fit strings(or good solutions), and crossover recombines these selected

solutions for new, potentially better solutions.

Mutation plays a secondary role in the search by providingdiversity in the population.

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Genetic Algorithm Example I

Maximise f(x) = x3 - 60 * x2 + 900 * x +1000

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Generating random initial population

chromosome binary string x f(x)

P1 11100 28 212P2 01111 15 3475

P3 10111 23 1227

P4 00100 4 2804Total 7718

Average 1929.50

Maximise f(x) = x3 - 60 * x2 + 900 * x +100 (0

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Choose two parents (roulette selection)

Roulette wheel Parents4116 P3

1915 P2

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One point crossover (random position 1)

1 0 1 1 10 1 1 1 1

P3P2

1 1 1 1 1

0 0 1 1 1

C1

C2

0 0 1 0 00 1 1 1 1

P4P2

0 0 1 1 1

0 1 1 0 0

C3

C4

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New generation

chromosome binary string x f(x)

P1 11111 31 131P2 00111 7 3803

P3 00111 7 3803

P4 01100 12 3889Total 11735

Average 2933.75

Maximise f(x) = x3 - 60 * x2 + 900 * x +100 (0

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chromosome binarystring

x f(x)

P1 11100 28 212

P2 01111 15 3475

P3 10111 23 1227

P4 00100 4 2804

Total 7718

Average 1929.50

chromosome binarystring

x f(x)

P1 11111 31 131

P2 00111 7 3803

P3 00111 7 3803

P4 01100 12 3889

Total 11735

Average 2933.75

Two generations

Mutation

Maximise f(x) = x3 - 60 * x2 + 900 * x +100 (0

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Genetic Algorithm Example II

Traveling Salesman Problema number of citiescosts of traveling between cities

a traveling sales man needs to visit all thesecities exactly once and return to the startingcity

Whats the cheapest route?

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Traveling Salesman Problem

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Initial generation

5 8 1 84 32 27 54 67P1

78 81 27 9 11 7 44 24P2

8 1 7 9 16 36 24 19P30

6.5

7.8

6.0

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Choose pairs of parents

78 81 27 9 11 7 44 24P2

8 1 7 9 16 36 24 19P30 6.0

7.8

Crossover

78 81 27 9 16 36 24 19C2

8 1 7 9 11 7 44 24C1 5.9

6.2

13

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Next generation

78 81 27 9 16 36 24 19P2

8 1 7 9 11 7 44 24P1 5.9

6.2

7 8 2 5 10 76 4 79P2 6.0

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Traveling Salesman ProblemNo. of cities: 100Population size: 30

Cost: 6.37Generation: 88 Cost: 6.34Generation: 1100

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Genetic Algorithms

Genetic algorithms by their very nature consider awide range of the search space for a particularproblem.

Unlike other techniques they search from a populationof points not from a single point, they are thereforeless likely to become trapped on false optimisationpeaks.

Using simple operations, genetic algorithms are ableto rapidly optimise design parameters after examining

only a small fraction of the search space.

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Genetic AlgorithmsThere are many diverse applications of genetic algorithms,but there are proviso's. They are best suited to problemswhere the efficient solutions are not already known. Ifthey are applied to these solvable problems then they will

be easily out-performed by the efficient known, standardcomputing method.

The strength of GA's is their ability to heuristically search

for solutions when all else fails. But before one can usethe algorithm you must be able to represent the solutionsto the problem in a suitable format, such as a series of 1'sand 0's. If you can do this then the GA will do the rest.

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ApplyingGenetic Algorithms

to Personnel Scheduling

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Personnel Scheduling

Personnel scheduling in healthcare

is usually a very complex operationwhich has a profound effect upon theefficient usage of expensive resources.

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A number of nursesA number of shifts each dayA set of constraints

shift coverageone shift per day

resting timeworkload per month

consecutive shiftsworking weekends


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Genetic Algorithm-Initial population

-construct rosters-repair infeasible ones

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Genetic Algorithm-Select parents-Recombine rows in the two rosters

-repair infeasible ones

+

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Genetic Algorithm-Mutation-Local optimiser

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Testing Scheme

Population SizeCrossover ProbabilityMutation ProbabilityLocal Optimiser

500.7

0.001ON

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Future Development

Improving Efficiency Parameter tuning

Crossover operators

Local optimiser

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Conclusions

GA approach is feasible and practical

Heuristic Can produce better results

Not guaranteed Flexible

Fitness (evaluation) function

Independent of GA engine

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Conclusions

Predictions have been made that advances inmathematics, fuzzy logic, chaos and fractals willpromote and enhance the work currently being

undertaken by GA's.

The future will bring forth new applications ofgenetic algorithms and new techniques which will

allow GA's to be fully exploited.

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Conclusions

Survival of the fittest, the most fit of a particulargeneration (the nearest to a correct answer) are usedas parents for the next generation.

The most fit of this new generation are parents for thenext, and so on. This eradicates bad solutions andeliminates bad family lines, bad parents don't have

opportunity to produce bad children.

This facilitates the progression towards an answer tobe onwards and upwards.

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Conclusions

As we have seen Genetic algorithms are a verypowerful tool, allowing searching for solutions whenthere are no other feasible means to do so.

The algorithm is easy to produce and simple tounderstand and enhancements easily introduced. Thisgives the algorithm much flexibility, which increases

it's value.

But, exploitation of the algorithm has still much morework to be done.

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