self introduction applied fractional calculus workshop series n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Self-Introduction Applied Fractional Calculus Workshop Series PowerPoint Presentation
Download Presentation
Self-Introduction Applied Fractional Calculus Workshop Series

Loading in 2 Seconds...

play fullscreen
1 / 47

Self-Introduction Applied Fractional Calculus Workshop Series - PowerPoint PPT Presentation


  • 69 Views
  • Uploaded on

Self-Introduction Applied Fractional Calculus Workshop Series. Zhigang, Lian/Link MESA (Mechatronics, Embedded Systems and Automation) Lab School of Engineering, University of California, Merced E : zlian2@ucmerced.edu Phone: 2092598023 Lab : CAS Eng 820 ( T : 228-4398).

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Self-Introduction Applied Fractional Calculus Workshop Series' - satinka-herrera


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.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
self introduction applied fractional calculus workshop series

Self-IntroductionApplied Fractional Calculus Workshop Series

Zhigang, Lian/Link

MESA (Mechatronics, Embedded Systems and Automation)Lab

School of Engineering,

University of California, Merced

E: zlian2@ucmerced.edu Phone:2092598023

Lab: CAS Eng 820 (T: 228-4398)

Jun 30, 2014. Monday 8:00-18:00 PM

Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMercedu

outline

1

2

HCSPSO search

3

New Cuckoo search

4

Experiment

Random distribution

Outline
slide4

Slide-4/1024

1. Random distribution

1.1 L’evy distribution

A Lévy flight is a random walk in which the step-lengths have a probability distribution that is heavy-tailed. The "Lévy" in "Lévy flight" is a reference to the French mathematician Paul Lévy.

In probability theory and statistics, the Lévy distribution, named after Paul Lévy, is a continuous probability distribution for a non-negative random variable. 

AFC Workshop Series @ MESALAB @ UCMerced

slide5

Slide-5/1024

Broadly speaking, flights is a random walk by step size follows distribution, and walking direction is uniform distribution. CS algorithm used Mantegna rule with distribution to choose optional step vector.

In the Mantegna rule, step size s design as:

The   ,   follows normal distribution, i.e

,

here, ,

AFC Workshop Series @ MESALAB @ UCMerced

AFC Workshop Series @ MESALAB @ UCMerced

slide6

Slide-6/1024

Le´vy stable distributions are a rich class of probability distributions and have many intriguing mathematical properties. The class is generally defined by a characteristic function and its complete specification requires four parameters:

Stability index:

Skewness parameter:

Scale parameter:

Location parameter with varying ranges:

AFC Workshop Series @ MESALAB @ UCMerced

slide7

The  Curve of L’evy distribution

AFC Workshop Series @ MESALAB @ UCMerced

slide8

Slide-8/1024

1.2 The Mittag-Leffler distribution

Pillai (1990) introduced the Mittag-Leffler distribution in terms of Mittag-Leffler functions. A random variable with support over is said to follow the generalized Mittag-Leffler distri-bution with parameters and if its Laplace transform is given by:

The cumulative distribution function (c.d.f.) corresponding to above is given by  

AFC Workshop Series @ MESALAB @ UCMerced

slide9

Slide-9/1024

1.3 Other distribution

AFC Workshop Series @ MESALAB @ UCMerced

slide10

Slide-10/1024

2. HCSPSO search

1)A Hybrid CS/PSO Algorithm for Global Optimization

Iterative equation:

AFC Workshop Series @ MESALAB @ UCMerced

slide11

Slide-11/1024

2) The pseudo-code of the CS/PSO is presented as bellow:

AFC Workshop Series @ MESALAB @ UCMerced

slide13

Slide-13/1024

3) Hybrid CSPSO flow

The algorithm flow:

AFC Workshop Series @ MESALAB @ UCMerced

slide15

Slide-15/1024

3.New Cuckoo search

3.1 New Cuckoo Search method

based on the obligate brood parasitic behavior of some cuckoo species in combination with the L´evy flight behavior of some birds and fruit flies, at the same time, combine particle swarm optimization (PSO), evolutionary computation technique.

AFC Workshop Series @ MESALAB @ UCMerced

slide16

Slide-16/1024

3.2 New Cuckoo Search(Lian and Chen)

1) Iterative equation:

2)The pseudo-code of the CS/PSO is presented as bellow

AFC Workshop Series @ MESALAB @ UCMerced

slide17

Slide-17/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide18

Slide-18/1024

3) New CS with the L´evy and Mittag-Leffler distritution

AFC Workshop Series @ MESALAB @ UCMerced

slide19

Slide-19/1024

4. Experiment

4.1 Experiment function

AFC Workshop Series @ MESALAB @ UCMerced

slide20

Slide-20/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide21

Slide-21/1024

4.2 Experiment with large size

1) Simulation data

AFC Workshop Series @ MESALAB @ UCMerced

slide22

Slide-22/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide23

Slide-23/1024

2) The Graph of Convergence

AFC Workshop Series @ MESALAB @ UCMerced

slide24

Slide-24/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide25

Slide-25/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide26

Slide-26/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide27

Slide-27/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide28

Slide-28/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide29

Slide-29/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide30

Slide-30/1024

4.3 Experiment with different distributions

1) Improve test functions

The above test function , have same characteristic of optimization solution , which is their imperfection. In the experimental process, we found algorithm with high probability random coefficient generation mode close to 0, it is easy to make  close to 0, so it is easy to converge to 0. This caused problem is algorithm search performance surface phenomena is ‘powerful’, in fact this false appearance is mad by the defects test function cause algorithm make strong fake image.

AFC Workshop Series @ MESALAB @ UCMerced

slide31

Slide-31/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide32

Slide-32/1024

2) Test

To fund the best performance of algorithm with different random coefficient generate by L´evy and Mittag-Leffler distribution. We will take the main random coefficients with different distribution generate, in which and from 0 to 2 with 0.1 step changes, research and analysis the performance of different distribution random parameters how to influence algorithm.

AFC Workshop Series @ MESALAB @ UCMerced

slide33

Slide-33/1024

AFC Workshop Series @ MESALAB @ UCMerced

slide34

we find the algorithm with random coefficient generated by Mittag-Leffler distributionand approximately equal 1 and 1 is efficient, and by L´evy distribution and approximately equal 0.8 and 1.2 is efficient. Again verify, the PSO algorithm is based on Uniform distribution, c1 and c2 approximately equal 1.8 and 1.6 is efficient.

slide35

The PSO, CS HCSPSO and NCS algorithm with random generate of different Uniform, L´evy and Mittag-Leffler distributions and solve the test function, in which and from 0 to 2 with 0.1 step changes, and for the X axis,  for Y axis, the optimal value as Z axis, the three-dimensional graphics are as following.

slide44

Slide-44/1024

4.4 Solution

Descine one efficient optization tool;

Find test function have big imperfection;

Find Uniform,L´evy and Mittag-Leffler distribution effective used in different algortihm.

AFC Workshop Series @ MESALAB @ UCMerced

slide45

Slide-45/1024

Future work

Base on the NCS, look for more efficient optimization?

The NCS and FC like the combination of optimization tools, looking for more efficient?

The application of NCS in the new object, solving other optimization problems?

AFC Workshop Series @ MESALAB @ UCMerced