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Differential Evolution

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. history.

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Differential Evolution

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  1. Differential Evolution HosseinTalebi Hassan Nikoo

  2. 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

  3. history • Ken Price's attempts to solve the Chebychev Polynomial fitting Problem that had been posed to him by Rainer Storn.

  4. 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

  5. Difference of DE with other EAs • mutation is applied first to generate trial vectors, then cross over is applied to produce offspring • mutation step size are not sampled from prior know PDF, it influenced by difference between individual of the current population

  6. 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)

  7. DE operators • Mutation • Crossover • Selection

  8. 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:

  9. mutation (cont) Where: Target vector Weighted Differential

  10. Geometrical Illustration (mutation)

  11. Crossover • DE crossover is a recombination of trial vector, ,and parent vector , to produce offspring, :

  12. Methods to determine • Binomial crossover: Problem dimention

  13. Methods to determine • Exponential crossover:

  14. Geometrical Illustration (crossover)

  15. 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

  16. General DE Algorithm

  17. Control Parameters Scalingfactor • 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

  18. 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

  19. Variation of DE • Target vector is selection (x) • Number of difference vectors used (y) • How crossover points are determined (z)

  20. Target vector is the best individual in current population, • One differential vector is used. • Any of the crossover methods.

  21. 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. is randomly selected • The closer is to 1, the more greedy the search process • Value of close to 0 favors exploration.

  23. 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/binshows good convergence characteristics

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

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

  26. Thanks For Your Attention Any Question?

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