Phân tích Effect Hội tụ Thông qua các hoạt động khác nhau di truyền

Phân tích Effect Hội tụ Thông qua các hoạt động khác nhau di truyền

Analysis of Convergence Effect Via Different Genetic Operations

D.F.Fam & S.P Koh & S.K Tiong & K.H Chong

Department of Electronic & Communication Engineering, Universiti Tenaga Nasional,

Km 7, Jalan Kajang-Puchong, 43009 Kajang, Selangor

se20597@uniten.edu.my,johnnykoh@uniten.edu.my,siehkiong@uniten.edu.my,chongkh@uniten.edu.my

Abstract: Genetic Algorithms (GAs), Evolution Strategies (ES), Evolutionary Programming (EP) and Genetic Programming (GP) are some of the best known types of Evolutionary Algorithm (EA)where it is

a class of global search algorithms inspired by natural evolution In this research, genetic algorithm is one of the optimization techniques used to maximize the performance of solar tracking system This paper presents analysis of convergence effect via different genetic operations used in Genetic Algorithm

as explained in the introduction and methodologies Simulation Results will demonstrate the ability of

GA to produce different solutions via different genetic operations to maximize the performance of solar tracking system

Index Terms—genetic algorithm, solar tracking, genetic operations

1 Introduction

The basic principles of GA was developed by

John Holland [1] They have since been

reviewed and the concepts have been applied

on a wider range [2],[3],[4] in today’s world

The GA is derived from Darwin’s theory of

Natural Selection A GA mimics the

reproduction behavior observed in biological

populations and employs the principal of

“survival of the fittest” in its search process

The idea is that an individual (design solution)

is more likely to survive if it is adapted to its

environment (design objectives and constraints)

Therefore, over a number of generations,

desirable traits will evolve and remain in

genome composition of the population over

traits with weaker characteristics A GA differs

from conventional optimization in many ways

It allows coding for a combination of both

discrete and continuous design variables A GA

is population based search, which results in

multiple solutions in one run, rather than only

one solution Apart from that, GA needs

objective function values and not its derivatives

(As required in gradient based methods) which may not exist in many real world applications.Literature review shows that only few researchers cited some finding regarding

GA based solar tracking system as follow: Khlaichom et al applied a closed loop control using genetic algorithm (GA) method for a two-axis (altitude over azimuth) solar tracking system A sensor fabricated from poly crystalline solar cell converts solar radiation to voltage In their algorithm the decoder and counter receive signals from an optical encoder and convert it to the current corresponding to degree-position of the axle turns Data is then transferred to a PC via an interface card for maximum tracking The system tracks the sun with +/-100 in both axes The tests and analyses explained that the solar tracking system using GA increases the output voltage to 7.084% in comparison to that with

no GA [5] Syamsiah Mashohor et al evaluated the best combination of GA parameters to optimize a solar tracking system for PV panels in terms

of azimuth angle and tilt angle Simulation

results demonstrated the ability of the proposed

GA system to search for optimal panel

positions in term of consistency and

convergence properties It also has proved the

ability of the GA-Solar to adapt to different

environmental conditions and successfully track

sun positions in finding the maximum power by

precisely orienting the PV panels.[6]

However, recent researches for GA based solar

tracking system are based on the traditional GA

algorithm structure which is shown as below:

// populations //

t=0

Step 1= Initialize P (t)

Evaluate P(t)

While (Solution NOT found OR Max

Generation NOT Reached)

Do

t= t + 1

Select P(t) from P(t-1)

Recombine P(t)

{

Do Crossover

Do Normal Mutation

}

Evaluate P(t)

If

{

P(t) = Solution;

End If

}

End

As shown in the Algorithm above, traditional

genetic algorithms are composed of four key

processing as shown below [7] :

1) initialize P(t)

2) evaluate P(t)

3) select P(t)

4) recombine P(t)

Anyhow, most population-based, reproductive,

optimization algorithms such as genetic

algorithms had a critical problem called

premature convergence problem [8, 9, 10] This

problem occurs when highly fit parents in a

population pool breed many similar offspring

in the early evolution time If the highly fit individuals are local optima areas, then newly generated offspring from the parents are also near the local optima areas

In this coming methodology section, an explanation of different genetic operations will be studied and results section will show the best genetic operations in preventing premature convergence problem

2 Methodology

Methodology part is divided into few sub sections below:

1) Conventional crossover and mutation 2) Crossover only

3) Clone and selective mutation

Using conventional method of having crossover and mutation in Genetic Algorithm will affect its performance One of the typical problem is Premature Convergence Problem [11,12].Most individuals in a prematurely converged situation are located at some local optimum areas and they can’t get out of the local optimum areas because the exploration power of mutation is low If we increase the exploration power by setting the mutation probability to high, then the speed of convergence to global optimum areas becomes slow As a result, it is very difficult for genetic algorithms to escape this premature convergence problem This considerably makes the performances of genetic algorithms degrade

Crossover is a genetic operator that combines two chromosomes (parents) to produce a new chromosome (offspring) The purpose of

crossover is to produce the new offspring which

is better than both of the parents if it takes the

best characteristics from each of the parents

Crossover occurs during evolution according to

a user-definable crossover probability In this

experiment, a single point crossover is used

Consider the following 2 parents which have

been selected for crossover The “|” symbol

indicates the randomly chosen crossover point

Parent 1: 11001|010

Parent 2: 00100|111

After interchanging the parent chromosomes at

the crossover point, the following offspring are

produced:

Offspring1: 11001|111

Offspring2: 00100|010

Crossover can not generate quite different

offspring from their parents because it uses

acquired information from their parents

In most function optimization problems, their

input variables are encoded into the binary

strings of individuals Since the binary strings

represent binary numbers for each variable, the

higher the bit position of string is, the larger the

bit weight has From this, it is helpful to mutate

some part of strings of individuals according to

their fitness That is, if an individual has low

fitness, then we mutate the most significant part

in order to largely change because we regard

the individual to be far from the global

optimum Otherwise, we mutate the least

significant part in order to do fine tuning

because the individual has high probability to

be near global optimum This selective

mutation can make genetic algorithms fast

approach to the global optimum and quickly get

out of premature convergence As a result, it

will increase the performances of genetic

algorithms

3 Simulation

A solar tracking has been developed to evaluate the application of genetic algorithm

as depicted in Figure 3 It would explore the intensity of sunlight at different angles and locate the highest intensity with the GA simulation The solar tracking is placed at the

origin point of (Xo=45 °, Yo=45 °) The

default base point is at the centre of the

will keep on searching the highest intensity location with GA searching method Both stepper motors controlling X and Y axis of solar tracking will receive the signals through motion controller to determine the angles of movement for both axis Highest intensity that

is absorbed by solar cell will convert the digital voltage to analogue signal to be transmitted to Visual basic program via Programmable logic controller Panasonic FPX-C14R

The simulation has been carried out using the Conventional GA given in 3 tables below, Table 1, Table 2 and Table 3 with the objectives to analyse the convergence effect

Table 1: Conventional GA simulation parameter

Maximum Generation

Population, p o

Chromosome length Selection Method

Crossover Rate, p c

No.BestChromosomes

Kept, k b

Crossover Type

50

10

8 Roulette Wheel 80%

0.025

2

1 Dynamic

Table 2: Conventional GA simulation

parameter with Crossover Only

Maximum Generation

Population, p o

Chromosome length

Selection Method

Crossover Rate, p c

No.BestChromosomes

Kept, k b

Crossover Type

50

10

8 Roulette Wheel 80%

1 Dynamic

Table 3: Conventional GA simulation

parameter with clone and selective mutation

Maximum Generation

Population, p o

Chromosome length

Selection Method

Crossover Rate, p c

Elitism Rate, E c

Selective Mutation

No.BestChromosomes

Kept, k b

Crossover Type

50

10

8 Roulette Wheel 80%

80%

0.025

1 Dynamic

Results of this implementation will be shown in

the section as below

4 Preliminary Results

This solar tracking has been performed under

on a sunny day around 11am at school field

From the first simulation parameters

requirement which publish conventional genetic

algorithm characteristic, gathered results will be

shown as graph below:

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Generation

Best: 0.018654 Mean: 0.018654

Best fitness Mean fitness

Graph 1 : Best Fitness Value- 0.018654 using conventional GA

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Generation

Average Distance Between Individuals

data1

Graph 2 : Average distance between individuals in each generation using conventional GA

0 5 10 15 20 25 30 35 40 45 50

0

1

2

3

4

5

6

7

8

9

10

11

Generation

crossover children mutation children

Graph 3 : genealogy of each individual across

the generations using conventional GA

Graph 3 : Best, worst and mean score for each

generation using conventional GA

0 0.5 1 1.5 2 2.5 3 3.5 4

Individual

state.Selection

Graph 4 : Number of children that is produced

by each individual using conventional GA

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Generation

Best: 0.018079 Mean: 0.018079

Best fitness Mean fitness

Graph 5 : Best Fitness Value- 0.018019 using conventional GA with Crossover only

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Generation

Best, Worst, and Mean Scores

Best Score Median Score

Worst Score

5 10 15 20 25 30 35 40 45 50

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Generation

Average Distance Between Individuals

data1

Graph 6 : Average distance between individuals

in each generation using conventional GA

without crossover only

0

1

2

3

4

5

6

7

8

9

10

11

Generation

crossover children mutation children

Graph 7 : genealogy of each individual across

the generations using conventional GA with

crossover only

Graph 8 : Best, worst and mean score for each generation using conventional GA with crossover only

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Selection Function

Individual

state.Selection

Graph 9 : Number of children that is produced

by each individual using conventional GA with crossover only

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

Generation

Best, Worst, and Mean Scores

best scores mean scores

worst scores

0 5 10 15 20 25 30 35 40 45 50

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

Generation

Best: 0.017131 Mean: 0.017131

Best fitness Mean fitness

Graph 10 : Best Fitness Value- 0.017131 with

clone and selective mutation

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Generation

Average Distance Between Individuals

data1

Graph 11 :Average distance between

individuals in each generation using

conventional GA with clone and selective

mutation

0 1 2 3 4 5 6 7 8 9 10 11

Generation

Graph 12 : genealogy of each individual across the generations using conventional GA with clone and selective mutation

Graph 13 : Best, worst and mean score for each generation using conventional GA with clone and selective mutation

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Generation

Best, Worst, and Mean Scores

best score

mean score worst score

1 2 3 4 5 6 7 8

0

0.5

1

1.5

2

2.5

3

Selection Function

Individual

state.Selection

Graph 14: Number of children that is produced

by each individual using conventional GA with

clone and selective mutation

5 Discussion

From the result, graph 1, 5 and 10 shows 3

different fitness value which are 0.018654,

0.018019 and 0.017131 that could be achieved

via 3 different genetic operation as below:

Genetic

operations

Fitness Value

Voltage

Conventional

GA

0.01863 10.024

Conventional

GA with

crossover

only

0.018019 10.035

Conventional

GA with

clone and

selective

mutation

0.017131 10.050

Obviously, it shows genetic operation-

Conventional GA with cloning of best

chromosome and selective mutation could

achieve the best fitness value with its ultimate

voltage value at 50th generation

Graph 2,6 and 11 display the average distance between individuals for each generation is

generation onwards Conventional GA with normal process indicates that convergence starts much faster than other 2 genetic

conventional GA with clone and mutation and

crossover only

Graph 7,8 and 13 shows the best, mean and worst score for 3 different genetic operations where it correlates to the distance between individuals across 50 generation where global minimum value is approached at an earlier stage for conventional genetic algorithm With the earliest convergence and achieving the best fitness value at its ultimate voltage, it means that physical solar tracking could track the best intensity location controlled by output

of genetic algorithm through controlling both motors X and Y movement

Graph 3,7 and 12 indicates genealogy for each individual across 50 generation for 3 different genetic operations Generally, mutation and crossover children are produced indicated by both red and blue colours lines respectively Mapping for each individual to the consecutive individual is linked to show the relationship between parent and children

Graph 4,9 and 14 shows number of children that is produced by each individual in a set of population for 3 different genetic operations Each set of individual produces different number of children which is the sum of all 50 generation

6 Conclusion

This research paper has significantly analyzes convergence effects of 3 different genetic operations that will affect the speed and efficiency of solar tracking system to reach the highest intensity location under the sunlight coverage The fitness value has identified the global minimum value for conventional GA

with cloning and selective mutation method

which is the most performing method as

compared to other 2 methods The proposed

method improves search speed, good accuracy

and approximate solution with the fitness value

0.017131 and 10.05V

6 Reference

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artificial systems, Michigan: The University of

Michigan Press, 1975

[2] Mitchell, M An Introduction to Genetic

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Programming of Computers by Means of

Natural Selection Cambridge: The MIT Press,

1992

[4] Whitley An Overview of Evolutionary

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Software Technology 2001;43 : 817-831

[5] Khlaichom P, Sonthipermpoon K

Optimization of solar tracking system basedon

genetic algorithms; 2006

http://www.thaiscience.info/

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Algorithm based Solar Tracking System for

Photovoltaic Panels; ICSET,2008

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