Nguyin Thu HuyIn vd Dig Tgp chi KHOA HQC & CONG NGH$ 93(05): 75 - 79
G E N E T I C A L G O R I T H M S VARYING SIZE O F P O P U L A T I O N AND M U L T I - O B J E C T I V E O P T I M I Z A T I O N P R O B L E M S , APPLY T O S O L V E ANIMAL FEED O P T I M I Z A T I O N P R O B L E M
Neuyln Thu HuyIn', Luong SJ V'&c\ VO Mgnh XuSn^' College of information and Communication Technology - TNU
^College of Technology and Economics - TNU. ^College of Education - TNU
ABSTRACT
Population size is an important parameter in Genetic Algorithms (GAs). How population size is reasonable is a matter of concern when designing programs using GAs. Overall, population size is defined as a given parameters and unchanged in evolution processes. This paper presents research results diat GAs population size changes affecting the diversity of populations and apply to multi- objective optimization problems, specific ihe animal feed optimization problem.
Keywords; genetic algorithms, population size, diversity' of populations, animal feed optimization problem.
INTRODUCTION
In GAs, population size is an important parameter and is determined after establishing the program. Population size is how much is appropriate, it depends on the problem that we solve. Typically, population size is fixed mean number of individuals in the population is unchanged from generation to generation.
But in nature, population size is not fixed, so the study of GA is applied to the course. First, it is necessary to determine the initial population size, this number can change over generations. But changed will be what? when we increase the size? when we will increase only?... are the problems to be solved.
This paper studies and proposes an algorithm that GAs population size is not fixed. Test results are presented in multi-objective optimization problems, special the animal feed optimization problem.
The paper is structured as follows: After the preamble is proposed GAs with population size adjustment. The next section presents briefly the problem muhi-objective optimization problem and in particular animal feed optimization problem. Next, a test result as tools for solving by the proposed algorithm is compared with traditional algorithm.
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PROPOSE ALGORITHM
For comparison, we present some real-coded GAs with population size fixed and the proposed algorithm in which the population size changes during evolution, as follows:
Traditional algorithm
Encoding: Each individual is a vector of n elements; each component is a real number in the domain of the problem. Thus, a population with m individuals can be considered as a real matrix m x n level.
The genetic operators:
Crossover: Using a crossover point to generate new individual.
- Mutation is a used mutation.
Selection: Select the individual to the next generation by selective competition.
The parameters of the algorithm: population size fixed (i.e. 50 individuals), crossover probability is 1, and mutation probability is 0.1.
Proposed algorithm
For comparison, the proposed algorithm is designed similar to algorithm with population size fixed, the different of proposed algorithm and traditional algorithm is just population size parameter. Once initialized, the population size is 50 like the original algorithm above, but from the 2nd generation onwards we calculate the average adaptation of individuals with the best adapt for
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Nguyen Thu Huy^n vd Dig T^ip chf KHOA HQC & CONG N G H $ 93(05): 75 - 79 individuals with adaptabiiiiy worst iu each
generation. If the individual is born belter average adaptability, it will be selected for the next generation. Similarly, if parents (or one of the parents) have better average adaptability will be retained in the next generation, reverse the rejection. Thus, in each generation the number of individuals can be changed. Number of individuals ir.
previous generations over future generations can be 1 or 2, because in the case of a individual can also be selected born both are selected. However,' with each generation increases the population size is not good, so we limit the scope of the maximum population size is 100 individuals. This means that after some generations, if the population size grew to 100 individuals (double the initial population size), then keep that as the size on the algorithm. This algorithm is stopped after 500 steps creatures.
APPLICATION PROBLEM Multi-objective optimization problem Multi-objective optimization problem takes the following form: There are k objective ftmction fl (X), 12 (X), .,., flt (X) need to optimize (Min or Max), where X c D domain of Rn . This problem is generally no unique solution because the target is not independent of each other, sometimes conflicting. So people often consider the Pareto test of the problem and tend to be two main objectives:
Given the multiple Pareto to the user experience choices and more diverse set of this experiment possible.
With that genetic algorithms due to its features is a suitable option and there were many studies using GA solve multi-objective optimization problems. In this study, methods to choose a goal by the shortest distance to the ideal experiment. Under this method, users take out targets to be achieved for each function fi (X), of course it does not necessarily have a solution satisfying these goals. Our proposal is to set the distance to the experimental experience that the smallest possible.
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Animal feed optimization problem Animal feed optimization problem is expressed as follows: Thai Nguyen feed joint stock company needs to produce a feed for pigs to market to consumers. The production of feed for pigs-standard TCVN 1547-1994 Vietnam; 1kg feed production should meet the following nutritional standards:
Protein crude fiber
Lipit
0.6
Raw materials for feed production include:
northern red glutinous maize, bran rice milling machine type I, soybean V74, dryoil, meal fish 60% lighter. In particular, the proportion of the nutrients of the raw material is shown in the following table:
Maize Bran rice soybean Dryoil Meal fish
Protein 10.20 11.90 39.00 45.34 61.49
C r u d e nber 1.20 8.10 5.90 6.12 0.74
Ca 0.08 0.20 0.19 0.35 5.39
P 0.05
1.17 0.15 6.51 2.05
LipIt 2.60
12J5 15.00 6.03 4.0S Model the problem as follows: The symbol of the raw materials Pk in an feed unit is y^.
Then, x^ must satisfy the following constraints:
• C|iX, +C|2\2+...-C|nXn>d|
C . , \ i +C22X2+....C:nXn>d3
(1)
CnlXi +C„2X2+....C„„X„>d„
X|,X2 Xn> 0 Price function f2= aiXjH-a2X2+ anX^ need minimum.
The symbol Xn+i is the number of units produced food. When the external conditions (1) we need additional condition (2):
XiX„+,<b|
X2Xn+l<b2 (2) XnXn+l<bn
Nguyin Thu Huyk va Dtg T^p chi KHOA HQC & CONG NGH$ 93(05): 75 - 79 Thus, the problem can be stated is necessary
to define x, such that:
Function of number.'// = x„.i -> max.
Price function: / ; = ^a^Xj^ -> min
;=l
In there:
For the fypes of materials:
+ Market price is a^ (d / kg)
+ Quantity in stock existing as bk (kg) + The proportion of nutrients in raw materials:
Crude Protein: Cik Crude fiber content: Cik Calcium: Cs^
Concentration of P: C4k Lipid content: Cst
- For food: The food will be inspected to ensure quality if minimum standards:
Crude Protein: d|
Crude fiber content: d2 Calcium: dj Concentration of P: d4 Lipid content: ds
The goal set for the problem is to produce food for pigs to reach quality standards (standard TCVN 1574-1994-Vietnam) with the lowest prices and the number is as much as possible These are two objectives problem. The question here is to produce as much as possible (with the number of materials available in stock by entering data) with the lowest prices.
Apply propose algorithm to solve animal feed optimization problem
We proceed to problems with using GAs as follows:
Encoding: Each individual is a five- dimensional vector, each component to the value of a variable. For easy to follow and by the small dimensions can be used to add two more components denote the objective fiinction value corresponding to the last section presents the deviation from the standard input objective fiinction. Thus, each individual is a real vector space R8. In the
first part corresponding to the values of the variables, the following two components respectively corresponding to the value function fl, f2, the final component is the deviation,
- Initial population is 50 individuals.
- The evolutionary process is as follows: Two parents are selected individual (random) to conduct a crossover point to create two new individuals. Individuals are born to compete with their parents. For the genetic algorithm with population size is fixed, in four individuals (father, mother and two children) two instances in which you are better adapted it is centered in the population in the next generation. Otherwise, be eliminated. Number of individuals will not change during evolution. As for the genetic algorithm with population size changes, we calculate the average adaptation of individuals with the best adapted to the individual adaptability is the worst in each generation. If the child is born with better average adaptability, the child (or children) will be selected on the next generation. Similarly, if parents (or one of the parents) have better average adaptability will be retained in the next generation, reverse the rejection. Thus, in each generation the number of bodies can be changed.
- Times of creation is 500 times, i.e. after 500 generations for the resuUs and compare the results of two algorithms with each other on which to draw conclusions.
Test results
We have compiled and tested two algorithms running on Madab language version 7.6.0.324. In particular, we ran each algorithm 10 times and checked out the program the worst and the best results to compare the two algorithms together.
The diversify of the population in this case we calculate the distance between individuals with the lowest level appropriate for individuals with high adaptabilify. At 500 generations of each run, we selected individuals with low adaptabilify and highest at the same time the distance between them.
Here are the specific results:
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Nguyin Thu Huy^n vd Dtg T^p chl KHOA HQC & C 6 N G N G H $ 93(05): 75-79 We import the data input is X| = 0.18359; X2 =
0.53919; \ , '- 0.065169; x., = 0.059175; x, = 0,15288 and tabic I are the results so that the deviation between individual adaptabilify highest and lowest after 10 run by the genetic algorithm with fixed population size (algorithm 1) and population size changes (algorithm 2).
After thai, the deviation of both the two adaptive algorithms, we continue to run the program and see the results of two goals on the problem. From there, we can assess whether temporary deviation function adapted values affect the final results of the objective function or not. Objective function results in both two algorithms are shown in Table 2.
Comments
The results in table 1 shows that in 10 different running times of each algorithm, the adaptive value deviations highest and lowest individuals of the two superior algorithm (table I) this means that the diversify of algorithm 2 higher algorithm 1. Thus, population size changes to effect better animal feed optimization problems to increase
the diversify of populations. Also, from table 2, we see value both f| and f2 objective function of the proposed algorithm has better traditional algorithm with a fixed size.
Although this is only a test problem, but we sec prospects are very positive.
CONCLUSION
On the basis of research results on the effects of population size adjustment to the diversity of the population by applying selected two genetic algorithms with population size change and fixed in the animal feed optimization problem, we conclude that the population size changes have strong impact to the diversify of the population, but we could not confirm this with the other classes. So, there should be plenfy of time and tested on many other problem to conclude a general way the effects of changing population size.
Also it can be combined with the determination of "age" of the evolution of individual participants to decide to increase or decrease population size is also a natural development.
Table 1: Deviation values of the individual adaptation of the algorithm 1 and2 Run times
1"
2nd 3^
<•
S*
6*
7*
8*
gih 10*
Run times 1"
2"' V' 4"<
'5*
S"
7*
8*
9*
10*
deviation values of the individual adaptation of the algorithm 1
Table 2:
189.386 164.3541 231.7356 3.5167 194.3505
158.085 181.3933 175.4536 204.4504 198.2796
deviation values of the individual adaptation ofthe algorithm 2
260.986 180.9935 237.7880 155.5861 233.5421 223.8807 238.3915 222.0801 207.0624 204.4119 lvalue of two fund ions by Ihe algorithm 1 and 2 F, value of Ihe F2 value of the
algorithm 4.0473 4.5713 4.4768 5.3573 7.0483 4.2589 3.1492 3.7639 4.5823 4.2578
\
algorithm I 92.7324 90.4783 91.7845 95.4839 92.3284 91.7492 90.2383 94.2384 90.3732 91.7392Fl value of the 1 algorithm
3.9743 3.7613 4.1278 4.7358 5.6382 4.0154 3.0192 3.1239 4 2523 4.0325 2
Fi value of the algorithm 2
95.4145 93.7835 91.0845 97.3907 93.3814 92.7624 92.9831 95.2435 91.3248 92.7923
Nguyin Thu Huyen vd Dtg Tap chi KHOA HQC & CONG NGH$ 93(05): 75 - 79 REFERENCES [4]. Back etal., (2000 a,b)," Evolutionary [1]. Anyong Qing (2009), "Differential Evolution: Computation 2: Advanced Algorithms and Fundamentals and Applications in Electrical Operators" Institute of Physics Publishing, Engineering" Wiley-Blackwell (an imprint of John Bristol, UK.
Wiley & Sons Ltd), USA. [5]. Cervantes et al (2008), "A dynamic [2]. Arabas et al, (2006). "GAVaPS - a Genetic population steady-state genetic algorithm for the Algorithm with Varying Population size", resource constrained project scheduling problem".
International Conference on Evolutionary , i c o . ,- • j r-i .. • P . „ . •' Journal of Systems Engineering and Electronics, [ 3 r ' B o d i f i ' r " " ( 2 0 0 4 ) , "Genetic Algorithms: ^P™^^' - ^"'"'"S ^^'•"" "e'deberg
Theory and Applications", Journal of Genetic [^]- Thomas Weise (2009), "Genetic Algorithms", Algorithms, Springer. University of Kassel, Gemamy.
TOM TAT
G L \ I T H U A T DI TRUYEN V 6 l KICH CO QUAN T H E THAY © 6 l , AP DUNG GIAI BAI TOAN T 6 I UtJ DA MUC TIEU
VE KHAU PHAN THtTC AN GIA SUC
Nguyin Thu Huyen', Lu-ong sy Udc^ VQ Manh Xuan'"*
'Truong DQI hoc Cong nghe thong tin vd Iruyen thong- DH Thdi Nguyen
^Tru&ng Cao ddng Kinh le - Ky thudi - DH Thdi Nguyen Truong Dgi hac Sir pham- DH Thai Nguyen Kich CO quan the \i mpt tham sd quan trpng trong giai thuat di truyen (GAs - Genetic Algorithms).
Kich c& quan the the nao la hop ly Id van de can quan tam khi thiet ke chuang trinh sii dyng GAs.
Noi chung kich cO qukn thi duoc x&c dinh \k mdt tham s6 cho trudc \h khdng ddi trong qua trinh tien hoa. B^i hko ndy trinh bdy kit qua nghi6n ciru GAs md kich cd quan the thay doi dnh hudng tdi tinh da dang cua qudn thi va ap dung vdo bdi toan tdi uu da muc tieu, cu the 1^ bdi todn tdi uu khau phan thiic in gia sue.
Tir khda: Gidi thudt di iruyen, Kich cd qudn the, linh da dgng cua qudn the, toi iru khdu phdn ihirc dn gia siic
Ngdy nhgn bdi; 18/4/2012, ngdy phdn bien: 14/5/2012, ngdy duy?t ddng: 12/6/2012
