GA and SA Part of Unit4

7/29/2019 GA and SA Part of Unit4

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Genetic Algorithm


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What is a genetic algorithm?

GA part of the broadersoft computing(aka "computationalintelligence") paradigm known as evolutionary computation

First introduced by Holland (1975)

Inspired by possibility of problem solving through a process ofevolution


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What is a GA? (contd) GA mimics biological evolution to generate better solutions from

existing solutions through survival of the fittest

crossbreeding and

mutation


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What is a GA? (contd)

A GA is capable of finding solutions for many problems for which

no usable algorithmic solutions exist

GA methodology particularly suited foroptimization

Optimization searches a solution space consisting of a large number

of possible solutions

GA reduces the search space through evolution of solutions,

conceived as individuals in a population

In nature, evolution operates on populations of organisms, ensuringby natural selection that characteristics that serve the members welltend to be passed on to the next generation, while those that dont dieout


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Evolution as Optimisation

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

populations ability to survive and thus reproduce in a specificenvironment.

Evolutionary fitness - the measure of the ability to respond

adequately to the environment, is the quantity that is actuallyoptimised in natural life

Consider a normal population of rabbits. Some rabbits are naturally

faster than others. Any characteristic has a range of variation that isdue to i) sexual reproduction and ii) mutation


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How GAs work

A population of candidate solutions - mathematicalrepresentations - is repeatedly altered until an optimal

solution is found

The GA evolutionary cycle

Starts with a randomly generated initial population of solutions(1st generation)

Selects a population of better solutions (next generation) byusing a measure of 'goodness' (a fitness evaluation function)

Alters new generation population through crossbreeding andmutation

Processes of selection (step 2) and alteration (step 3) lead to apopulation with a higher proportion of better solutions


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How GAs work (contd)

The GA evolutionary cycle continues until an acceptablesolution is found in the current population,

or

some control parameter such as the maximum number ofgenerations is exceeded


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How solutions are represented

A series of genes, known as a chromosome, represents one possiblesolution

Eachgene in the chromosome represents one component of thesolution pattern

Each gene can have one of a number of possible values known asalleles

The process of converting a solution from its original form into achromosome is known as coding

The most common form of representing a solution as achromosome is a string of binary digits (aka a binary vector) eg

1010110101001Each bit in this string is a gene with two alleles: 0 and 1

Other forms of representation are also used, eg, integer vectors

Solution bit strings are decodedto enable them to be evaluatedusing a fitness measure


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If each design variable xi , i = 1, 2, . . . , n is coded in a string of length

q, a design vector is represented using a string of total length nq.

For example, (x1 = 18, x2 = 3, x3 = 1, x4 = 4):

How solutions are represented (contd..)

In general, if a binary number is given by bqbq1 b2b1b0,where bk= 0

or 1, k = 0, 1, 2, . . . , q, then its equivalent decimal number y (integer) is

given by

If a variable x bounds are given by x(l) and x(u), its decimal value can be

computed as


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GA Selection or Reproduction Selection in GA based on a process analogous to that of biological

evolutionOnly the fittest survive and contribute to the gene pool of the nextgeneration

Fitness proportional selection

Each chromosomes likelihood of being selected is proportional toitsfitness value.

Solutions failing selection are bad, and are discarded Crossover by splicing two chromosomes at a crossover point and

swapping the spliced parts

A better chromosome may be created by combining genes with

good characteristics from one chromosome with some good genesin the other chromosome

Crossover carried out with a probabilitytypically 0.7

Chromosomes not crossed over are cloned


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GA Selection or Reproduction

if Fi denotes the fitness of the ith string in the population of size n, the

probability for selecting the ith string for the mating pool (pi ) is

given by

Roulette-wheel selection scheme


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Crossover and Mutation

Mutation

A random adjustment in the genetic composition Can be useful for introducing new characteristics in a population

May be counterproductive

Probability kept low: typically 0.001 to 0.01


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Genetic Algorithm process

1. Represent the solution as a chromosome of fixed length, choose sizeof population N, crossover probability pc and mutation probability

pm.

2. Define a fitness functionffor measuring fitness of chromosomes.

3. Create an initial solution population randomly of size N:x1, x2, , xN

4. Use the fitness functionf to evaluate the fitness value of eachsolution in the current generation:

f(x1),f(x2), ,f(xN)

5. Select good solutions based on fitness value. Discard rest of thesolutions.

6. If acceptable solution (s) found in the current generation ormaximum number of generations is exceeded then stop.

7. Alter the solution population using crossover and mutation to create anew generation of solutions with population size N.

8. Go to step 4


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Genetic Algorithm process


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Advantages of GA systems

Useful when no algorithms or heuristics are available for solving aproblem

No formulation of the solution is required - only "recognition" of agood solution

A GA system can be built as long as a solution representation and anevaluation scheme can be worked out

So minimal domain expert access is required

GA can act as an alternative to - Expert Systems if

number of rules is too large or

the nature of the knowledge-base too dynamic

Traditional optimization techniques if constraints and objective functions are non-linearand/ordiscontinuous


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Advantages of GA systems GA does not guarantee optimal solutions, but produce near optimal

solutions which are likely to be very good

Solution time with GA is highly predictableDetermined by Size of the population

Time taken to decode and evaluate a solution and

Number of generations of population

GA uses simple operations to solve problems that arecomputationally prohibitive otherwise

Because of simplicity, GA software are Reasonably sized and self-contained

Easier to embed them as a module in another system

GA can also aid in developing intelligent business systems that useother methodologies, eg, Building the rule base of an expert system

Finding optimal neural networks


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Some issues related to GA based systems Level of explainability

Scalability

Data requirements Local maxima Local maxima are regions that hold good solutions relative to regions around

them, but which do not necessarily contain the best overall solutions

The region(s) that contain the best solutions are calledglobal maxima

GAs are less prone to being trapped in local maxima because of the use ofmutation and crossover

Premature convergence A GA is said to have converged prematurely if it explores a local maximum

extensively

Most significant factor leading to such convergence is a mutation rate which is

too slow Mutation interference is an effect opposite to that of premature convergence


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Simulated Annealing

Simulates the process of slow cooling of molten metal to achieve

the absolute minimum energy state. The temperature needs to be

reduced at a slow rate.

The cooling phenomenon is simulated by controlling a

temperature like parameter introduced with the concept of the

Boltzmann probability distribution.

A system in thermal equilibrium at a temperature T has its energy

distributed probabilistically according to

where k = Boltzmann constant


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Algorithm

Step 1: Initial point and termination criterion

set T = high temperature and number of iterations at T

Step2: Calculate a neighbouring point in the vicinity of current point.Step3: IfE = E(Xi+1)- E(Xi)< 0 and go to next iteration.

Else use Metropolis algorithm to accept the current point

Create a random number r in the range of (0,1).

If r exp (- E /T), accept the point according to Metropolisand go to next iteration.

Else go to step 2.

Step4: If number of iterations reached maximum, terminate the process

at T.Step5: If T is small, terminate.

Else lower T according to a cooling schedule.

New temperature = 0.5 *T , go to step 2.

GA and SA Part of Unit4

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