Continuous Genetic Algorithm

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THE

CONTINUOUS GENETICALGORITHM

by:

Victoria Marcela Albacete

Rey Mark CasaquiteJeannette Supeda


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CONTINUOUS GENETIC ALGORITHM-

or better known as a real-valued GA

An algorithm used to solve a problem where the

values of the variables are continuous

Represented by floating-point numbers


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CONTINUOUSG.AVS. BINARYG.A Binary GA

- is applicable if the variables are naturally

quantized

- its precision limited by the binary representation of

variables

Continuous GA

- more logical to use when the variables are

continuous

- by using floating point numbers, it easily allows

representation to the machine precision


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Continuous GA requires less storage compare to

Binary GA.

Continuous GA is inherently faster compare to Binary

GA.

The primary difference is that the variables are no

longer represented by bits of zeros and ones but

instead by floating-point numbers.


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COMPONENTSOFA CONTINUOUS GA

The flowchart below provides a big picture overview of acontinuous GA

Define costfunction, cost,variables, SelectGA parameters

Generate initialpopulation


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Find cost for eachchromosome

Select mates

Mating

Mutation

Convergencecheck


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With this Algorithm our goal is to

solve the optimization problem

where we search for an

optimal(minimum) solution in terms

of the variable problems.


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WEBEGINBY:

- EXAMPLE VARIABLE and COST FUNCTION

Defining a chromosome as an array of variable values to be

optimized

Supposing that the chromosome has variables given bythen the chromosome is written as an array with

Then we can have

Thus each cost is found by evaluating the cost function which is

var

N

var,....,, 21 Nppp var1 N

var,...,, 21 Npppchromosome

var,...,,)(cos 21 Npppfchromosomeft


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Determine the initial population denoted by

Natural selection

- the time to decide which chromosomes in the

population are fit enough to survive and possibly

reproduce an offspring in the next generation

Among the chromosomes in a given generation

only the are kept for mating and the rest are

discarded to make room for the new offspring.

popN

popN

keepN


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Example initial population of 8 random chromosomes and

their corresponding cost


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Surviving chromosomes after a 50% selection rate


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Pairing and mating process of single- point crossoverchromosome family binary string cost


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Pairing

- in this process the most-fit chromosomes

form a mating pool. Two mothers and two fathers pair

in some random fashion

Mating - in this process the Blending Method is used

by finding the ways to combine variable values from

the two parents into a new variable values in the

offspring. A single offspring variable value can be

computed as:

Random number between 0 and 1

Nth variable in the mother chromosome

Nth variable in the father chromosome

4keepN

newp

dnmnnew ppp )1(

dn

mn

p

p


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The Linear Crossover Method is a simple

extrapolation which is a case of generating three

offspring from two parents and is given by

Heuristic Crossover is a variation where a random

number is chosen on the interval [0,1] and the

variable of the offspring is defined by

dnmnnew

dnmnnew

dnmnnew

ppp

ppp

ppp

5.15.0

5.05.1

5.05.0

3

2

1

mndnmnnew pppp )(


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Then Blend CrossoverMethod chooses a parameterthat determines the distance outside the bounds ofthe two parent variables that the offspring variable maylie.

The combination of an extrapolation with a crossovermethod begins by a randomly selecting a variable inthe first pair of parents to be the crossover point

Then the selected variables are combined to form newvariables that will appear in the children. Finally, the

crossover is completed with the rest of thechromosomes as before.

}*{ varNrandomroundup


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Mutations

to avoid the problem of overly fast

convergence, the routine is force to explore otherareas of the cost surface by randomly introducing

changes ormutations in some of the variables.

The mutation rate is chosen to be 20%. Then it ismultiplied to the total number of variables that can be

mutated in the population.

The random numbers are chosen to select the rowand columns of the variables to be mutated. The

mutated variable is replaced by a new random

variable.


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An added normally distributed random number to

the variable selected for mutation is given by

= standard deviation of a normal distribution

= standard normal distribution (mean=0 and

variance=1)

)1,0(' nnn Npp

)1,0(nN


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Mutating the population


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Contour plot of the cost function with the population after

the first generation


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Contour plot of the cost function with the population

after the second generation


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Contour plot of the cost function with the population

after the third and final generation


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The final step is to check the convergence or finding the

minimum cost in the given number of generations.


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END

Continuous Genetic Algorithm

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