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Evolutionary Intelligence

Genetic Algorithms

Genetic Programming

http://math.hws.edu/xJava/GA/

Definition of Intelligence

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More general definition of intelligence

Not based on 'human' intelligence

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On 1 July 1858, On 1 July 1858, Charles DarwinCharles Darwin presented his theory presented his theory of evolution before the Linnean Society of London. of evolution before the Linnean Society of London. This day marks the beginning of a revolution in This day marks the beginning of a revolution in biology. biology.

Darwin’s classical Darwin’s classical theory of evolutiontheory of evolution, together with , together with Weismann’s Weismann’s theory of natural selectiontheory of natural selection and and Mendel’s concept of Mendel’s concept of geneticsgenetics, now represent the neo-, now represent the neo-Darwinian paradigm.Darwinian paradigm.

Natural evolutionNatural evolution

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Questions for Machine Intelligence?

Can intelligence be connected with evolution?

Can evolution be connected with understanding?

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Intelligence and Evolution

• Intelligence can be defined as Intelligence can be defined as the capability of the capability of a system to adapt its behaviour to ever-a system to adapt its behaviour to ever-changing environment (to evolve)changing environment (to evolve)

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Intelligence and Evolution

• Evolutionary computation simulates evolution Evolutionary computation simulates evolution on a computer.on a computer.

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According to Alan Turing, According to Alan Turing, the form or appearance of a the form or appearance of a system is irrelevant to its intelligencesystem is irrelevant to its intelligence. .

The result of a simulated evolutionary process is a The result of a simulated evolutionary process is a series of optimisation algorithms, usually based on a series of optimisation algorithms, usually based on a simple set of rules. Optimisation iteratively improves simple set of rules. Optimisation iteratively improves the quality of solutions until an optimal, or at least the quality of solutions until an optimal, or at least feasible, solution is found.feasible, solution is found.

Can evolution be intelligent?Can evolution be intelligent?

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The behaviour of an individual organism is an The behaviour of an individual organism is an inductive inference about some yet unknown aspects inductive inference about some yet unknown aspects of its environment. If, over successive generations, of its environment. If, over successive generations, the organism survives, we can say that the organism survives, we can say that this organism this organism is capable of learning to cope with changes in its is capable of learning to cope with changes in its environment.environment.

Evolution as Learning

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Evolutionary Computation

• The evolutionary approach is based on The evolutionary approach is based on computational models of natural selection and computational models of natural selection and genetics. We call them genetics. We call them evolutionary evolutionary computationcomputation, an umbrella term that combines , an umbrella term that combines genetic algorithmsgenetic algorithms,, evolution strategiesevolution strategies andand genetic programminggenetic programming..

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Neo-DarwinismNeo-Darwinism is based on processes of is based on processes of reproduction, mutation, competition and selection. reproduction, mutation, competition and selection. The power to reproduce appears to be an essential The power to reproduce appears to be an essential property of life. The power to mutate is also property of life. The power to mutate is also guaranteed in any living organism that reproduces guaranteed in any living organism that reproduces itself in a continuously changing environment. itself in a continuously changing environment.

Processes of Processes of competition and selection normally take competition and selection normally take place in the natural world, where expanding place in the natural world, where expanding populations of different species are limited by a finite populations of different species are limited by a finite space.space.

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Evolution can be seen as a process leading to the Evolution can be seen as a process leading to the maintenance of a population’s ability to survive and maintenance of a population’s ability to survive and reproduce in a specific environment. This ability is reproduce in a specific environment. This ability is called called evolutionary fitnessevolutionary fitness..

Evolutionary fitness can also be viewed as a measure Evolutionary fitness can also be viewed as a measure of the organism’s ability to of the organism’s ability to anticipate changes in its anticipate changes in its environment. environment.

Evolutionary Fitness

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Optimization

The The fitnessfitness, or the quantitative measure of the , or the quantitative measure of the ability to predict environmental changes and ability to predict environmental changes and respond adequately, respond adequately, can be considered as the can be considered as the quality that is optimised in natural lifequality that is optimised in natural life..

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How is a population with increasing fitness How is a population with increasing fitness generated?generated? Let us consider a population of rabbits. Some rabbits Let us consider a population of rabbits. Some rabbits

are faster than others, and we may say that these rabbits are faster than others, and we may say that these rabbits possess superior fitness, because they have a greater possess superior fitness, because they have a greater chance of avoiding foxes, surviving and then breeding.chance of avoiding foxes, surviving and then breeding.

If two parents have superior fitness, there is a good If two parents have superior fitness, there is a good chance that a combination of their genes will produce chance that a combination of their genes will produce an offspring with even higher fitness. Over time the an offspring with even higher fitness. Over time the entire population of rabbits becomes faster to meet their entire population of rabbits becomes faster to meet their environmental challenges in the face of foxes.environmental challenges in the face of foxes.

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All methods of evolutionary computation simulate All methods of evolutionary computation simulate natural evolution by natural evolution by creating a population of creating a population of individuals, evaluating their fitness, generating a new individuals, evaluating their fitness, generating a new population through genetic operations, and repeating population through genetic operations, and repeating this process a number of timesthis process a number of times. .

Simulation of natural evolutionSimulation of natural evolution

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John Holland introduced the concept of genetic John Holland introduced the concept of genetic algorithms in Computer Sciencealgorithms in Computer Science

His aim was to make computers do what nature does. His aim was to make computers do what nature does. Holland was concerned with Holland was concerned with algorithms that algorithms that manipulate strings of binary digitsmanipulate strings of binary digits..

Genetic AlgorithmsGenetic Algorithms

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Chromosomes

Each artificial “chromosomes” consists of a Each artificial “chromosomes” consists of a number of “genes”, and each gene is number of “genes”, and each gene is represented by 0 or 1:represented by 0 or 1:

1 10 1 0 1 0 0 0 0 0 1 0 1 10

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Nature has an ability to adapt and learn without being Nature has an ability to adapt and learn without being told what to do. In other words, nature finds good told what to do. In other words, nature finds good chromosomes blindly. GAs do the same. Two chromosomes blindly. GAs do the same. Two mechanisms link a GA to the problem it is solving: mechanisms link a GA to the problem it is solving: encodingencoding and and evaluationevaluation..

Encoding and Evaluaton

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Crossover and Mutation

The GA uses a measure of fitness of individual The GA uses a measure of fitness of individual chromosomes to carry out reproduction. chromosomes to carry out reproduction.

As reproduction takes place, the crossover As reproduction takes place, the crossover operator exchanges parts of two single operator exchanges parts of two single chromosomes, and the mutation operator chromosomes, and the mutation operator changes the gene value in some randomly changes the gene value in some randomly chosen location of the chromosome. chosen location of the chromosome.

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Step 1Step 1:: Represent the problem variable domain as a Represent the problem variable domain as a chromosome of a fixed length, choose the size of a chromosome of a fixed length, choose the size of a chromosome population chromosome population NN, the crossover probability , the crossover probability ppcc and the mutation probability and the mutation probability ppmm..

Step 2Step 2:: Define a fitness function to measure the Define a fitness function to measure the performance, or fitness, of an individual chromosome performance, or fitness, of an individual chromosome in the problem domain. The fitness function in the problem domain. The fitness function establishes the basis for selecting chromosomes that establishes the basis for selecting chromosomes that will be mated during reproduction.will be mated during reproduction.

Basic genetic algorithmsBasic genetic algorithms

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Step 3Step 3: : Randomly generate an initial population of Randomly generate an initial population of chromosomes of size chromosomes of size NN::xx11, , xx22, . . . , , . . . , xxNN

Step 4Step 4: : Calculate the fitness of each individual Calculate the fitness of each individual chromosome:chromosome:f f ((xx11), ), f f ((xx22), . . . , ), . . . , f f ((xxNN))

Step 5Step 5:: Select a pair of chromosomes for mating from Select a pair of chromosomes for mating from the current population. Parent chromosomes are the current population. Parent chromosomes are selected with a probability related to their fitness.selected with a probability related to their fitness.

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Step 6Step 6:: Create a pair of offspring chromosomes by Create a pair of offspring chromosomes by applying the genetic operators applying the genetic operators crossovercrossover and and mutationmutation..

Step 7Step 7:: Place the created offspring chromosomes in the Place the created offspring chromosomes in the new population.new population.

Step 8Step 8:: Repeat Repeat Step 5Step 5 until the size of the new until the size of the new chromosome population becomes equal to the size of chromosome population becomes equal to the size of the the initial population, initial population, NN..

Step 9Step 9:: Replace the initial (parent) chromosome Replace the initial (parent) chromosome population with the new (offspring) population.population with the new (offspring) population.

Step 10Step 10:: Go to Go to Step 4Step 4, and repeat the process until the , and repeat the process until the termination criterion is satisfied.termination criterion is satisfied.

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GA represents an iterative process. Each iteration is GA represents an iterative process. Each iteration is called a called a generationgeneration. A typical number of generations for . A typical number of generations for a simple GA can range from 50 to over 500. The entire a simple GA can range from 50 to over 500. The entire set of generations is called a set of generations is called a runrun..

Because GAs use a stochastic search method, the fitness Because GAs use a stochastic search method, the fitness of a population may remain stable for a number of of a population may remain stable for a number of generations before a superior chromosome appears. generations before a superior chromosome appears.

Genetic algorithmsGenetic algorithms

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Termination

• A common practice is to terminate a GA after a A common practice is to terminate a GA after a specified number of generations and then specified number of generations and then examine the best chromosomes in the examine the best chromosomes in the population. If no satisfactory solution is found, population. If no satisfactory solution is found, the GA is restarted.the GA is restarted.

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Genetic algorithmGenetic algorithm

1 01 0X1i

Generation i

0 01 0X2i

0 00 1X3i

1 11 0X4i

0 11 1X5i f = 56

1 00 1X6i f = 54

f = 36

f = 44

f = 14

f = 14

1 00 0X1i+1

Generation (i + 1)

0 01 1X2i+1

1 10 1X3i+1

0 01 0X4i+1

0 11 0X5i+1 f = 54

0 11 1X6i+1 f = 56

f = 56

f = 50

f = 44

f = 44

Crossover

X6i 1 00 0 01 0 X2i

0 01 0X2i 0 11 1 X5i

0X1i 0 11 1 X5i1 01 0

0 10 0

11 101 0

Mutation

0 11 1X5'i 01 0

X6'i 1 00

0 01 0X2'i 0 1

0 0

0 1 111X5i

1 1 1 X1"i1 1

X2"i0 1 0

0X1'i 1 1 1

0 1 0X2i

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A simple example will help us to understand how a A simple example will help us to understand how a GA works. Let us find the maximum value of the GA works. Let us find the maximum value of the function (15function (15xx xx22) where parameter ) where parameter xx varies between 0 varies between 0 and 15. For simplicity, we may assume that and 15. For simplicity, we may assume that xx takes takes only integer values. Thus, chromosomes can be built only integer values. Thus, chromosomes can be built with only four genes:with only four genes:

Genetic algorithms: case studyGenetic algorithms: case study

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Suppose that the size of the chromosome population Suppose that the size of the chromosome population NN is is 6, the crossover probability 6, the crossover probability ppcc equals 0.7, and the equals 0.7, and the

mutation probability mutation probability ppmm equals 0.001. The fitness equals 0.001. The fitness

function in our example is defined byfunction in our example is defined by

ff((xx) = ) = 15 15 xx xx22

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The fitness function and chromosome locationsThe fitness function and chromosome locations

x

50

40

30

20

60

10

00 5 10 15

f(x)

(a) Chromosome initial locations.

x

50

40

30

20

60

10

00 5 10 15

(b) Chromosome final locations.

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In natural selection, only the fittest species can In natural selection, only the fittest species can survive, breed, and thereby pass their genes on to the survive, breed, and thereby pass their genes on to the next generation. GAs use a similar approach, but next generation. GAs use a similar approach, but unlike nature, the size of the chromosome population unlike nature, the size of the chromosome population remains unchanged from one generation to the next.remains unchanged from one generation to the next.

The last column in Table shows the ratio of the The last column in Table shows the ratio of the individual chromosome’s fitness to the population’s individual chromosome’s fitness to the population’s total fitness. This ratio determines the chromosome’s total fitness. This ratio determines the chromosome’s chance of being selected for mating. The chance of being selected for mating. The chromosome’s average fitness improves from one chromosome’s average fitness improves from one generation to the next.generation to the next.

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Roulette wheel selectionRoulette wheel selectionThe most commonly used chromosome selectionThe most commonly used chromosome selection techniques is the techniques is the roulette wheel selectionroulette wheel selection..

100 0

16.5

36.743.149.5

75.2

X1: 16.5%X2: 20.2%X3: 6.4%X4: 6.4%X5: 25.3%X6: 24.8%

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Crossover operatorCrossover operator

In our example, we have an initial population of 6 In our example, we have an initial population of 6 chromosomes. Thus, to establish the same population chromosomes. Thus, to establish the same population in the next generation, the roulette wheel would be in the next generation, the roulette wheel would be spun six times.spun six times.

Once a pair of parent chromosomes is selected, the Once a pair of parent chromosomes is selected, the crossovercrossover operator is applied. operator is applied.

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First, the crossover operator randomly chooses a First, the crossover operator randomly chooses a crossover point where two parent chromosomes crossover point where two parent chromosomes “break”, and then exchanges the chromosome parts “break”, and then exchanges the chromosome parts after that point. As a result, two new offspring are after that point. As a result, two new offspring are created.created.

If a pair of chromosomes does not cross over, then the If a pair of chromosomes does not cross over, then the chromosome cloning takes place, and the offspring are chromosome cloning takes place, and the offspring are created as exact copies of each parent.created as exact copies of each parent.

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X6i 1 00 0 01 0 X2i

0 01 0X2i 0 11 1 X5i

0X1i 0 11 1 X5i1 01 0

0 10 0

11 101 0

CrossoverCrossover

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Mutation represents a change in the gene. Mutation represents a change in the gene. Mutation is a background operator. Its role is to Mutation is a background operator. Its role is to

provide a guarantee that the search algorithm is not provide a guarantee that the search algorithm is not trapped on a local optimum.trapped on a local optimum.

The mutation operator flips a randomly selected gene The mutation operator flips a randomly selected gene in a chromosome. in a chromosome.

The mutation probability is quite small in nature, and The mutation probability is quite small in nature, and is kept low for GAs, typically in the range between is kept low for GAs, typically in the range between 0.001 and 0.01.0.001 and 0.01.

Mutation operatorMutation operator

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MutationMutation

0 11 1X5'i 01 0

X6'i 1 00

0 01 0X2'i 0 1

0 0

0 1 111X5i

1 1 1 X1"i1 1

X2"i0 1 0

0X1'i 1 1 1

0 1 0X2i

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The genetic algorithm cycleThe genetic algorithm cycle

1 01 0X1i

Generation i

0 01 0X2i

0 00 1X3i

1 11 0X4i

0 11 1X5i f = 56

1 00 1X6i f = 54

f = 36

f = 44

f = 14

f = 14

1 00 0X1i+1

Generation (i + 1)

0 01 1X2i+1

1 10 1X3i+1

0 01 0X4i+1

0 11 0X5i+1 f = 54

0 11 1X6i+1 f = 56

f = 56

f = 50

f = 44

f = 44

Crossover

X6i 1 00 0 01 0 X2i

0 01 0X2i 0 11 1 X5i

0X1i 0 11 1 X5i1 01 0

0 10 0

11 101 0

Mutation

0 11 1X5'i 01 0

X6'i 1 00

0 01 0X2'i 0 1

0 0

0 1 111X5i

1 1 1 X1"i1 1

X2"i0 1 0

0X1'i 1 1 1

0 1 0X2i

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Class ExerciseClass ExerciseSuppose it is desired to find the maximum of the Suppose it is desired to find the maximum of the function of two variables:function of two variables:

where parameters where parameters xx and and yy vary vary between between 3 and 3.3 and 3.

2222 )()1(),( 33)1(2 yxyx eyxxexyxf

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Steps to solve to a Problem using a Genetic Algorithm you must decide on the following -

How do you represent a solution as a bit string?How many bits are needed?What is the fitness function?How do you construct the initial population?What is the crossover operationWhat is the mutation operation?What probabilities should you use?How will you know when to stop?

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2222 )()1(),( 33)1(2 yxyx eyxxexyxf

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Representing the Solution as a bit string

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We also choose the size of the chromosome We also choose the size of the chromosome population, for instance 6, and randomly generate an population, for instance 6, and randomly generate an initial population.initial population.

The next step is to calculate the fitness of each The next step is to calculate the fitness of each chromosome. This is done in two stages. chromosome. This is done in two stages.

First, a chromosome, that is a string of 16 bits, is First, a chromosome, that is a string of 16 bits, is partitioned into two 8-bit strings:partitioned into two 8-bit strings:

Then these strings are converted from binary (base 2) Then these strings are converted from binary (base 2) to decimal (base 10):to decimal (base 10):

1 00 0 1 10 0 0 10 1 1 10 1and

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Now the range of integers that can be handled by 8-bits, Now the range of integers that can be handled by 8-bits, that is the range from 0 to (2that is the range from 0 to (288 1), is mapped to the 1), is mapped to the actual range of parameters actual range of parameters xx and and yy, that is the range , that is the range from from 3 to 3:3 to 3:

To obtain the actual values of To obtain the actual values of xx and and yy, we multiply their , we multiply their decimal values by 0.0235294 and subtract 3 from the decimal values by 0.0235294 and subtract 3 from the resultsresults

0235294.01256

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1 00 0 1 10 0 0 10 1 1 10 1and

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Using decoded values of Using decoded values of xx and and yy as inputs in the as inputs in the mathematical function, the GA calculates the fitness of mathematical function, the GA calculates the fitness of each chromosome.each chromosome.

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Fitness

To find the maximum of the “peak” function, we will To find the maximum of the “peak” function, we will use crossover with the probability equal to 0.7 and use crossover with the probability equal to 0.7 and mutation with the probability equal to 0.001. mutation with the probability equal to 0.001.

As we mentioned earlier, a common practice in GAs is As we mentioned earlier, a common practice in GAs is to specify the number of generations. Suppose the to specify the number of generations. Suppose the desired number of generations is 100. That is, the GA desired number of generations is 100. That is, the GA will create 100 generations of 6 chromosomes before will create 100 generations of 6 chromosomes before stopping.stopping.

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Chromosome locations on the surface of the Chromosome locations on the surface of the “peak” function: initial population “peak” function: initial population

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Chromosome locations on the surface of the Chromosome locations on the surface of the “peak” function: first generation “peak” function: first generation

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Chromosome locations on the surface of the Chromosome locations on the surface of the “peak” function: local maximum “peak” function: local maximum

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Chromosome locations on the surface of the Chromosome locations on the surface of the “peak” function: global maximum “peak” function: global maximum

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Performance graphs for 100 generations of 6 Performance graphs for 100 generations of 6 chromosomes: chromosomes: local maximumlocal maximum

pc = 0.7, pm = 0.001

G e n e r a t i o n s

BestAverage

80 90 10060 7040 5020 30100-0.1

0.5

0.6

0.7

F i

t n

e s s

0

0.1

0.2

0.3

0.4

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Performance graphs for 100 generations of 6 Performance graphs for 100 generations of 6 chromosomes: chromosomes: global maximumglobal maximum

BestAverage

100G e n e r a t i o n s

80 9060 7040 5020 3010

pc = 0.7, pm = 0.011.8

F i

t n

e s s

00.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

50

pc = 0.7, pm = 0.001

BestAverage

20G e n e r a t i o n s

16 1812 148 104 620

F i

t n

e s s

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Performance graphs for 20 generations of 60 Performance graphs for 20 generations of 60 chromosomeschromosomes