- 96 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Differential Evolution' - sybill-lowe

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

Presentation Transcript

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

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

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

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

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)

DE operators

- Mutation
- Crossover
- Selection

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:

Geometrical Illustration (mutation)

Crossover

- DE crossover is a recombination of trial vector, ,and parent vector , to produce offspring, :

Methods to determine

- Exponential crossover:

Geometrical Illustration (crossover)

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

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

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

Variation of DE

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

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

- 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.

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

- 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

application

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

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

Thanks For Your Attention

Any Question?

Download Presentation

Connecting to Server..