differential evolution

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Differential EvolutionHossein TalebiHassan Nikoo

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Outline History Introduction Differences of DE with other Eas Difference vector Mutation Cross over Selection General DE Parameter control Variation of DE Application References Hassan’s parts

Differential Evolution

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history Ken Price's attempts to solve the

Chebychev Polynomial fitting Problem that had been posed to him by Rainer Storn.


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Introduction The original DE was developed for

continuous value problems

Individuals are vectors

Distance and direction information from current population is used to guide the search process


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Difference of DE with other EAs1. mutation is applied first to generate

trial vectors, then cross over is applied to produce offspring

2. mutation step size are not sampled from prior know PDF, it influenced by difference between individual of the current population


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Difference Vector Positions of individuals provide valuable

information about fitness landscape. At first, individuals are distributed and over

the time they converge to a same solution Differences large in beginning of

evolution bigger step size (exploring)

Differences are small at the end of search process smaller step size (exploiting)


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DE operators

Mutation Crossover Selection


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mutation Mutation produces a trial vector for each

individual This trial vector then will be used by

crossover operator to produce offspring For each parent , we make a trial

vector as follow:


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mutation (cont)

Where:

Target vector

Weighted Differential


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Geometrical Illustration (mutation)


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Crossover DE crossover is a recombination of trial

vector, ,and parent vector , to produce offspring, :


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Methods to determine

Binomial crossover:

Problem dimention


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Methods to determine Exponential crossover:


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Geometrical Illustration (crossover)


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Selection selecting an individual to take part in

mutation to make the trial vector. Random selection

select a target vector. Random or Best individual selection between parent and offspring

to spring. Better survive


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General DE Algorithm


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Control ParametersScaling factor

The smaller the value of the smaller the step size

small enough to allow differentials to exploit tight valleys, and large enough to maintain diversity.

Empirical results suggest that generally provides good performance


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Control ParametersRecombination probability

The higher the more variation is introduced in the new population

Increasing often results in faster convergence, while decreasing increases search robustness


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Variation of DE

1. Target vector is selection (x)2. Number of difference vectors used (y)3. How crossover points are determined

(z)


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Target vector is the best individual in current population,

One differential vector is used. Any of the crossover methods.


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Any method for Target vector selection more than one difference vector Any of the crossover methods

the larger the value of , the more directions can be explored per generation.


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is randomly selected The closer is to 1, the more greedy

the search process Value of close to 0 favors exploration.


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At list two difference vectors.1. calculated from the best vector and the

parent vector2. while the rest of the difference vectors

are calculated using randomly selected vectors

Empirical studies have shown DE/current-to-best/2/bin shows good convergence characteristics


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application Multiprocessor synthesis Neural network learning Synthesis of modulators Heat transfer parameter estimation Radio network design …


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References1. Computational Intelligence, an introduction,2nd

edition, Andries Engelbercht, Wiley2. Differential Evolution - A simple and efficient

adaptive scheme for global optimization over continuous spaces, Rainer Storn,Kenneth Price,1995

3. Differential Evolution, homepage http://www.icsi.berkeley.edu/~storn/code.html


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Thanks For Your Attention

Any Question?


differential evolution

Documents

differential vector

parent vector

recombination of trial

target vector selectionmore

crossover methods

variation of detarget

exponential crossover

binomial crossover