Differential Evolution
description
Transcript of Differential Evolution
![Page 1: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/1.jpg)
1
Differential EvolutionHossein TalebiHassan Nikoo
![Page 2: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/2.jpg)
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
Differential Evolution
![Page 3: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/3.jpg)
3
history Ken Price's attempts to solve the
Chebychev Polynomial fitting Problem that had been posed to him by Rainer Storn.
Differential Evolution
![Page 4: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/4.jpg)
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
Differential Evolution
![Page 5: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/5.jpg)
5
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
Differential Evolution
![Page 6: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/6.jpg)
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)
Differential Evolution
![Page 7: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/7.jpg)
7
DE operators
Mutation Crossover Selection
Differential Evolution
![Page 8: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/8.jpg)
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:
Differential Evolution
![Page 9: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/9.jpg)
9
mutation (cont)
Where:
Target vector
Weighted Differential
Differential Evolution
![Page 10: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/10.jpg)
10
Geometrical Illustration (mutation)
Differential Evolution
![Page 11: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/11.jpg)
11
Crossover DE crossover is a recombination of trial
vector, ,and parent vector , to produce offspring, :
Differential Evolution
![Page 12: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/12.jpg)
12
Methods to determine
Binomial crossover:
Problem dimention
Differential Evolution
![Page 13: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/13.jpg)
13
Methods to determine Exponential crossover:
Differential Evolution
![Page 14: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/14.jpg)
14
Geometrical Illustration (crossover)
Differential Evolution
![Page 15: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/15.jpg)
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
Differential Evolution
![Page 16: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/16.jpg)
16
General DE Algorithm
Differential Evolution
![Page 17: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/17.jpg)
17
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
Differential Evolution
![Page 18: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/18.jpg)
18
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
Differential Evolution
![Page 19: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/19.jpg)
19
Variation of DE
1. Target vector is selection (x)2. Number of difference vectors used (y)3. How crossover points are determined
(z)
Differential Evolution
![Page 20: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/20.jpg)
20
Target vector is the best individual in current population,
One differential vector is used. Any of the crossover methods.
Differential Evolution
![Page 21: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/21.jpg)
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.
Differential Evolution
![Page 22: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/22.jpg)
22
is randomly selected The closer is to 1, the more greedy
the search process Value of close to 0 favors exploration.
Differential Evolution
![Page 23: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/23.jpg)
23
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
Differential Evolution
![Page 24: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/24.jpg)
24
application Multiprocessor synthesis Neural network learning Synthesis of modulators Heat transfer parameter estimation Radio network design …
Differential Evolution
![Page 25: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/25.jpg)
25
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
Differential Evolution
![Page 26: Differential Evolution](https://reader035.fdocuments.net/reader035/viewer/2022070407/568142df550346895daf3e35/html5/thumbnails/26.jpg)
26
Thanks For Your Attention
Any Question?
Differential Evolution