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Differential Evolution

Hossein Talebi Hassan Nikoo

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 2 Differential Evolution

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history

 Ken Storn.

Price's attempts to solve the Chebychev Polynomial fitting Problem that had been posed to him by Rainer

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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 EAs

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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, current population it influenced by difference between individual of the

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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 evolution in beginning bigger step size (exploring) Differences are small search process (exploiting) at smaller the step end of of size

DE operators

   Mutation Crossover Selection 7 Differential Evolution

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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 vector as follow: , we make a trial

mutation (cont)

Target vector 9 Differential Evolution Weighted Differential Where:

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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 Parameters

Scaling factor

Differential Evolution    The smaller the value of step size the smaller the small enough to allow differentials to exploit tight valleys, and large enough to maintain diversity.

Empirical results suggest that provides good performance generally

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Control Parameters

Recombination 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

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2.

3.

Target vector is selection (x) Number of difference vectors used (y) How crossover points are determined (z)

20 Differential Evolution    Target vector is the best individual in current population, One differential vector is used.

Any of the crossover methods.

21 Differential Evolution    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.

22 Differential Evolution    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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2.

At list two difference vectors.

calculated from the best vector and the parent vector 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 … Differential Evolution

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References

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Computational Intelligence, an introduction,2 nd edition, Andries Engelbercht, Wiley Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces, Rainer Storn,Kenneth Price,1995 Differential Evolution, homepage http://www.icsi.berkeley.edu/~storn/code.html

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Thanks For Your Attention

Any Question?