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Topic 10Evolutionary Programming, Genetic Algorithms

• Intelligence and Evolution• Evolution as Optimisation• Sexual Reproduction• Evolutionary Computation• Genetic Algorithms• Selection, Recombination & Mutation• GA Process • Example: The Travelling Salesman Problem• Advantages/Disadvantages of Genetic Algorithms

Reading: Champandard Chapter 32 Link to Evolutionary Programming on Website

Link to Genetic Algorithms on Website

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Intelligence and Evolution• One way of understanding intelligence is as the capability of a creature to

adapt itself to an ever-changing environment

• We normally think of adaptation as changes in the characteristics (including behaviours) of a single animal in response to experiences over its history

• But adaptation is also change in the characteristics of a species, over the generations, in response to environmental change

• An individual creature is in competition with other individuals of the same species for resources, mates etc.

• There is also rivalry from other species which may be a direct (predator)or indirect (food, water, land, etc.) threat

• In nature, evolution operates on populations of organisms, ensuring by natural selection that characteristics that serve the members well tend to be passed on to the next generation, while those that don’t die out

Evolution as Optimisation• Evolution can be seen as a process leading to the optimisation of a

population’s ability to survive and thus reproduce in a specific environment.

• Evolutionary fitness - the measure of the ability to respond adequately to the environment, is the quantity that is actually optimised in natural life

• Consider a normal population of rabbits. Some rabbits are naturally faster than others. Any characteristic has a range of variation that is due to i) sexual reproduction and ii) mutation

• We may say that the faster rabbits possess superior fitness, since they have a greater chance of avoiding foxes, surviving and then breeding

• If two parents have superior fitness, there is a good chance that a combination of their genes will produce an offspring with even higher fitness. We say that there is crossover between the parents’ genes

• Over successive generations, the entire population of rabbits tends to become faster to meet their environment challenges in the face of foxes

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Sexual Reproduction• The key to understanding evolution in nature lies in the basic biology of

reproduction

• The chromosome is the basic carrier of the genes, which are the units of the genetic code that control an individual’s characteristics. Each gene can take on one of a number of possible forms, called an allele

• An allele is like the value of a variable, and represents the effect that a gene will have on the physical makeup of a body

• An individual’s particular sequence of alleles is called the genotype. It determines the expression of characteristics in the individual’s body, called the phenotype

• In humans, most cells contain 23 pairs of chromosomes. But reproductive cells (spermatozoa and ova) contain 23 single chromosomes, because they must merge with their opposite number to produce a new offspring

• During fertilization of the ova by the sperm, the chromosomes from each recombine to form the 23 pairs of the new individual

Sexual Reproduction

• Selection operates as survival and choice of mates between parents• Recombination of genes is the mechanism that generates the next

generation’s characteristics • Sometimes random copying errors, called mutations, occur during the

recombination process. These are also important because they lead to new characteristics, usually useless, occasionally adaptive

Image: Osvego City School District Regents Exam Prep Center

An albino is a common mutant

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Evolutionary Computation

• Evolutionary computation simulates evolution on a computer. The result of such a simulation is a series of optimisation algorithms, usually based on a simple set of characteristics – the equivalent of a genome

• Recall that optimisation iteratively improves the quality of solutions to some problem until an optimal (or at least feasible) solution is found

• Evolutionary computation is an umbrella term that includes genetic algorithms (Holland, 1975), evolution strategies (Schwefel, 1981) genetic programming (Koza, 1994) and other methods

• A-life researchers frequently experiment with populations of simulated organisms put into artificial competition and subjected to the laws of natural selection

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Evolutionary Computation“Standard Model”

problem

apply

convert (a genotype)

feedback(fitness)

phenotype

the genome(data structure)for this species

evolution process

population of individuals, each with its owngenotype

alleles

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Image: Michael Goodin

Genetic Algorithms

• Genetic algorithms dispense with phenotypes altogether, and evolve the genotypes directly

• This is more efficient because no conversion is needed – the genotypes are applied directly to the problem at hand

• Usually the elements can be specially designed to make the process work faster and more efficiently than real evolution

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Genetic Algorithms• Genetic algorithms were introduced by John Holland (1975) with

the aim of making a computer do what nature does - find good combinations of characteristics, blindly

• He was concerned with algorithms that manipulate strings of binary digits – an artificial “chromosome”

• Each artificial chromosome consists of a number of “genes”; in the simplest case, each gene may have an “allele” of 0 or 1:

• Two mechanisms link a GA to the problem it is solving:

• Encoding is how the bits control the characteristics (incl. behaviour) of the system in the world

• Evaluation is working out the fitness conferred by an artificial chromosome by testing in the world

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Selection, Recombination & Mutation• Populations of artificial chromosomes will be generated over a

number of generations

• This involves selection, recombination and mutation

• The chromosomes’ fitness is used to select them in pairs for mating

• As recombination takes place, a crossover operator exchanges parts of the two single chromosomes from the mated individuals

• A mutation operator flips genes value in some randomly chosen location of the chromosome at some rate set by a parameter

• Chromosomes can actually be arbitrarily complex data structures:- bit strings (1011010000010101)- real numbers (43.2, -33.1, ... , 0.0, 89.2)- set permutations (E11, E3, E7, ... , E1, E15)- lists of rules (R1, R2, R3, ... , R22, R23)- program elements (genetic programming)- really, any data structure

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Basic Genetic Algorithm• Step 1. Represent the problem domain as a chromosome of fixed

length n, choose the size of population of chromosomes N, a crossover probability pc and a mutation probability pm

• Step 2. Define a fitness function f to measure the performance (fitness) of an individual chromosome in the problem domain. The fitness function is the basis for selecting chromosomes that will be mated during reproduction

• Step 3: Randomly generate an initial population of chromosomes of size N: x1, x1, ... ,xN

• Step 4: Calculate the fitness of each individual chromosome: f(x1), f(x2), ... , f(x)N

• Step 5: Select a pair of chromosomes for mating from the current population. Parent chromosomes are selected with a probability related to their fitness (eg by Roulette wheel, tournament, ranking, random walk or remainder methods)

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Basic Genetic Algorithm

• Step 6. From those parents, create a pair of offspring chromosomes by applying the genetic operators crossover and mutation

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

• Step 8: Repeat from Step 5 until the new population size equals the old population size

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

• Step 10: Go to Step 4, and repeat the process until some termination (or optimisation) criterion is satisfied

• Note: the best individuals from the final population should now perform above the criterion level

• Iterative process: each iteration is a generation. Typical run is anywhere from 50 to > 500 iterations

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Genetic Algorithm Process

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Example: Travelling Salesman Problem• Find a tour of a given set of cities so that 1) each city is visited only

once 2) the total distance traveled is minimised

• Representation is an ordered list of city numbers (known as order-based GA):

1) London 3) Dunedin 5) Beijing 7) Tokyo2) 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)

• Recombination uses i) crossover and ii) mutation by inversion:

Parent1(3 5 7 2 1 6 4 8)Parent2(2 5 7 6 8 1 3 4)

Child (2 5 7 2 1 6 3 4)

crossover

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Example: Travelling Salesman Problem• Mutation involves reordering of the list: eg flip elements 3 and 6

• * *

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

• Now consider 30 unnamed cities on a grid, each with (x,y) coordinates

mutation

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Example: Travelling Salesman Problem

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Example: Travelling Salesman Problem

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Example: Travelling Salesman Problem

In 1987, Martin Groetschel and Olaf Holland found an optimal tour of 666 interesting places in the world. Source: http://www.tsp.gatech.edu//index.html

The Travelling Salesman Problem

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Pros and Cons of Genetic Algorithms• GAs are a flexible, widely applicable optimisation process

• Unlike NNs, GAs tend to avoid local minima, and find the global solution (if you are not in a hurry) because search is not restricted to a single part of the problem space

•

• Can optimise a lot of parallel measures simultaneously (multi-objective)

• Operators can be customised to take advantage of regularities or constraints in a particular domain to improve speed or quality of convergence

But... • Abstractions about the problem itself such as mathematical simplifications can’t be

used

• Difficult to predict how long convergence will take – randomness in the process means this might vary widely

• Because it requires representation and processing on a sizable population of genotypes, it could be expensive in terms of memory and computation – very complex problems could be infeasible

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GAs can be used when...• Alternative solutions are too slow or overly complicated

• Need an exploratory tool to examine new approaches

• Need an “anytime” algorithm – always a solution, only improves

• Want to make a hybrid with another system

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

GAs are now used to optimise the design parameters of complexmachines, such as jet engines

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References• Holland, John H. Adaptation in Natural and Artificial System. Ann

Arbor: The University of Michigan Press, 1975.

• Koza, J.R. Genetic Programming II: Automatic Discovery of Reusable Programs. Cambridge, Mass.:MIT Press, 1994.

• Negnevitsky, M., Artificial Intelligence: A Guide to Intelligent Systems, Harlow, Essex: Addison Wesley, Pearson Education Limited, 2002. Chapter 7.

• Schwefel, H.P. Numerical Optimisation of Computer Models. Chichester: John Wiley & Assoc., 1981.