AN IMPROVED GENETIC ALGORITHM WITH GENE VALUE

REPRESENTATION AND SHORT TERM MEMORY FOR

SHAPE ASSIGNMENT PROBLEM

Ismadi Md Badarudin

Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Shah Alam, Selangor, Malaysia

Abu Bakar Md Sultan, Md Nasir Sulaiman, Ali Mamat

Faculty of Computer Science and Information Technology, Universiti Putra Malaysia, Serdang, Selangor, Malaysia

Mahmud Tengku Muda Mohamed

Faculty of Crop Science, Universiti Putra Malaysia, Serdang, Selangor, Malaysia

Keywords: Genetic algorithm, Specific-domain initialization, Short term memory, Shape assignment.

Abstract: The purpose in shape assignment is to find the optimal solution that combines a number of shapes with

attention to full use of area. To achieve this, an analysis needs to be done several times because of the

different solutions produce dissimilar number of items. Although to find the optimal solution is a certainty,

the ambiguity matters and huge possible solutions require an intelligent approach to be applied. Genetic

Algorithm (GA) was chosen to overcome this problem. We found that basic implementation of Genetic

Algorithm produces uncertainty time and most probably contribute the longer processing time with several

reasons. Thus, in order to reduce time in analysis process, we improved the Genetic Algorithm by focusing

on 1) specific-domain initialization that gene values are based on the X and Y of area coordinate 2) the use

of short term memory to avoid the revisit solutions occur. Through a series of experiment, the repetition of

time towards obtaining the optimal result using basic GA (BGA) and improved GA (IGA) gradually

increase when size of area of combined shapes raise. Using the same datasets, however, the BGA shows

more repetition number than IGA indicates that IGA spent less computation time.

1 INTRODUCTION

Genetic algorithm (GA) is an alternative method of

solving many design problems which are considered

as ambiguous problems and / or consists of the huge

possible solutions. The initial step is to represent a

legal solution to the problem to be solved by a string

of genes that can take on some value from a

specified finite range or alphabet. This string of

genes, which represents a solution, is known as a

chromosome. Each chromosome represents a legal

solution to the problem and is composed of a string

of genes. The binary alphabet {0, 1} is often used to

represent these genes but sometimes, depending on

the application, integers or real numbers are also

used. In fact, almost any representation can be used

that enables a solution to be encoded as a finite

length string.

The GA’s chromosome consists of groups of

variables, which are represented by groups of genes.

The initialization of these genes significantly affects

the GA’s performance, and an improper choice for

the chromosome structure will often result in poor

performance. The good representation of a

chromosome explains the power of the GA search

because they improve its efficiency and

effectiveness. The better a chromosome contribute,

the more of its genes will be preserved for the next

generation (Chen-Fang Tsai and Kuo-Ming Chao,

2007). The good coding for a chromosome

representation will ensure reduce the possible

number of proposed solutions to be analyzed.

According to Schaffer (1985) the short defining of

178

Md Badarudin I., Md Sultan A., Sulaiman M., Mamat A. and Tengku Muda Mohamed M..

AN IMPROVED GENETIC ALGORITHM WITH GENE VALUE REPRESENTATION AND SHORT TERM MEMORY FOR SHAPE ASSIGNMENT

PROBLEM.

DOI: 10.5220/0003493601780183

In Proceedings of the 13th International Conference on Enterprise Information Systems (ICEIS-2011), pages 178-183

ISBN: 978-989-8425-54-6

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

chromosome length consisting of bits which work

well together, and lead to improved performance

when incorporated into a chromosome.

The reasons using GA because of the

metaheuristic properties that are applied in GA to

reach the optimal result in term of time and quality

are better (Goldberg, 1989; Miihlenbein and

Schlierkamp, 1993; Srinivas and Patnaik, 1994).

With some properties of metaheuristic are

implemented by GA promise better solution;

however certain situations might need an

improvement of GA with several strategies to yield

an efficient time.

One of the nine metaheuristic properties is

strategies to guide the search process. Many of the

metaheuristic approaches rely on probabilistic

decision made during the search. But, the main

difference to pure random search is that in

metaheuristic algorithms randomness is not used

blindly but in an intelligent, biased form (Stutzle,

1999). Such strategy allows generating new starting

solutions for the local search in more an intelligent

way rather than just providing random initial

solutions. In the evolutionary computational field

(Eiben and Schippers, 1998), the process of

exploration and exploitation often refer to short term

strategy tied to randomness. According to Blum and

Roli (2003), a short term memory to escape from

local minima and to avoid cycles, this property is

often applied in simple tabu search. In addition, the

different approaches to other methods to solve

trajectory optimisation by applying the random

value with evolutionary strategy that has global

search capability and the robust characteristics (Rae-

Dong Kim et al., 2007). Nevertheless, their

efficiency has recently been criticized because the

repetition number in GA influences the length of

computation time in analysis process.

This paper focuses on the strategies of specific-

domain initialization rather in assigning value of

genes and to avoid revisit solution occurs. We divide

this paper to 5 sections. The reminder of this paper is

organized as follows, in section 2 is the overview of

application problem to be settled with the

constraints. In section 3 devotes to discussion of the

two improvement strategies that were applied in

basic GA (BGA) named by improved GA (IGA). In

chapter 4 reveals the results based on analysis of

generating solutions and followed by discussion on

the results. Finally in section 5, we discuss the

conclusion of this paper.

2 OVERVIEW OF SHAPE

ASSIGNMENT PROBLEM

Shape assignment purpose is to combine the several

of shapes to be assigned into a determined area. The

objective is to fully utilize the area, on the other

words to produce zero unused space as shown in

figure 1. The existence of many shapes can be

assigned into area therefore, possible solutions to be

analyzed will be huge. The analysis process has to

be done because of every solution produces different

number of items. Detail discussion of shape

assignment problem can be referred at previous

paper (Ismadi et al., 2010).

Figure 1: The three optimal solutions of (5,5) area

coordinate

The same size of shape but different coordinate

for instance (2,5) and (5,2) produce different number

of items. Thus, the item calculation of combined

shapes for every solution needs to be done. The

maximum number of item is considered the best, so

that the process of assigning shapes into an area will

require a repetitive analysis. However, the existence

of expected item number in the combined shapes is a

wasted time to be analyzed. For instance, the first

optimal solution as shown in figure 1 consists of the

combined shapes that are represented by

chromosome of 3, 3, 3, 2, 2, 5 of the 5, 5 area

coordinate. This means the three combined shapes

contain the three sequences of 3, 3; 3, 2 and 2, 5

coordinates, respectively. By changing the order of

shapes, the combination of shapes can be 3,3; 2,5;

3,2 or 3,2; 3,3; 2,5 or 2,5; 3,3; 3,2 or … or 2,5; 3,2;

3, 3. These all combined shapes certainly produce

the same number of items. This situation should be

avoided by ignoring the unwanted coordinate

because it contributes to the increase of computation

time in analysis process.

3 GENETIC ALGORITHM (GA)

FOR SHAPE ASSIGNMENT

PROBLEM

Shape assignment problem is considered as space

allocation problem or packing problem in which

AN IMPROVED GENETIC ALGORITHM WITH GENE VALUE REPRESENTATION AND SHORT TERM

MEMORY FOR SHAPE ASSIGNMENT PROBLEM

179

both are non-deterministic polynomial (NP)

problems. Thus, an algorithmic intelligence

techniques are required, so that the enormous

decision arise can be answered in an acceptable

time. The enormous increase in the number of

decision has led to applying heuristic algorithms

such as genetic algorithm (Stewart et al., 2004).

An analysis of clustering rectangles problem by

Burke and Kendall (1999) showed the quality of the

Simulated Annealing and Tabu Search algorithms

better than the GA. However, another analysis in

different problem domains such as TSPs (Pham and

Karaboga, 2000), showed GA outperformed the

others. Thus, the inconsistency of the efficiency and

effectiveness of the algorithms give an indication

that GA has space for improvement.

GA was applied to overcome shape assignment

problem. However the huge iterations of analysis in

GA as discussed in section 3.1 requires high

computation time. Therefore, the two improvements

of GA are identified in this issue towards reducing

the number of iteration process and as a result

diminish computation time.

3.1 Basic GA (BGA)

The common works of GA that consists of

population initiation followed by the three operators

of selection, crossover and mutation. The GA is

typically able to solve some optimisations problems;

however the computation time is always

questionable. BGA refers to two situations as

discussed below:

First situation refers the use of random number

in assigning gene value. To find the number of

possible solutions to be analyzed subjects to the

number of shapes. With four shapes for example,

means it requires eight genes of chromosome. Each

gene is randomly assigned with value between 0 and

9 that is represented by X and Y coordinates

respectively. The possible solutions in the worst case

would be 100,000,000 (10

chromosomeLength

Second situation devotes the existence of same

value of sequence genes. The repetition of optimal

shape solutions need to be compared with the

purpose of finding the maximum number of item.

However, same value of sequence genes will

produce the same number of items and thus, the

process of finding the optimal solution is a wasted

time. According to Richard (2000), without

controlling this situation usually to be revaluated

consequently spends computational effort on

evaluating fitness function far exceeds that of

genetic operator.

3.2 Improved GA (IGA)

The two situations in BGA for this domain problem

therefore, we developed the two strategies with

intention to reduce iteration process in analysis

process and eventually the processing time will be

probably reduced.

First strategy is to assign possible shapes into

the area randomly with specific-domain in

initialization process. This strategy focuses to

randomly assign the value of genes that are derived

from the X and Y coordinates of area as shown in

figure 2. For example, the X and Y of area coordinate

represent 4 and 5 respectively. Thus the odd spaces

of chromosome the number can be assigned is

between 1 and 4, similar to even spaces where the

number between 1 and 5 is allowed.

Figure 2: Chromosome by gene value that assigned

randomly.

The possible solutions are based on the formula

of (X areaCoordinate

chromosomeLength/2

* Y

areaCoordinate

chromosomeLength/2

). Thus, the number of

possible solutions by (4, 5) area coordinate

is160,000 (4

* 5

) in the worst case.

Second strategy, the optimal shape assignment

solution is not necessary the best solution as long as

it does not achieve the maximum number of items.

The process of obtaining the maximum item might

need to be done iteratively. Therefore, the same

optimal solution might occur. To avoid that, a

control in GA by short term memory approach was

employed. The short term memory is cleared at the

start of each new generation and so can only store

information about the current. The use of short term

memory is to check whether an individual is a

duplicate of one encountered earlier in the current

generation (Jason and Chris, 2003).

Some cases the use of priori knowledge is

applicable for feasible solution and protecting the

same chromosome to be frequently revaluated will

probably reduces the computation time. There are

two possible matters will occurs in generating

optimal solutions which are 1) the current result and

previous result is same 2) The block combination of

current and previous result is same but different

location place. These matters promote same number

of items.

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The creation of database is to collect all previous

successful optimal results. The optimal solution will

be compared with the available previous optimal

solution in database. The existence of same

combination of shapes will be rejected and

regenerate to another optimal solution, otherwise the

next process to calculate item and find the maximum

item will be implemented. This comparison process

is repeated until meeting a defined evaluation

number. This control is expected reduce time

because of a calculating of items for combined

shapes can be skipped when the existence of same

optimal between the current and previous solutions.

The flowchart in figure 3 shows the overall

processes of finding the best solution of shape

assignment.

Figure 3: Processes of finding the best shape assignment.

4 RESULT AND DISCUSSION

The three experiments with different datasets were

used for the comparisons between BGA and IGA in

terms of computation time usage. The purpose of the

first experiment is to find the number of

chromosome to find optimal solution and the

number of iteration. Second experiment focuses on

number of negative value and number of positive

value that both were generated by BGA and IGA.

The third experiment is to obtain the number of

repetition when the execution of short term memory.

4.1 Experiment 1: Iteration of Genome

to Produce the Successful Shape

Assignment

Table 1 shows the same dataset was used in BGA

and IGA. The chromosome value and gene iteration

of both BGA and IGA were stated.

Table 1: Different Area Coordinate, Same Number of

Shape.

The graph in figure 4 shows, both BGA and

IGA generated a consistent increase of iteration

number when the X and Y area coordinate raise.

However, the iteration number of BGA is higher

than IGA at all levels of the area coordinate;

therefore the computation time taken by IGA less

than BGA.

Figure 4: Iteration number of both BGA and IGA.

4.2 Experiment 2: Analysis of Positive

and Negative Value of Fitness

Status

The fitness status can be positive of negative value.

The positive is given when some hard constraints

have been fully fulfilled. While fail to do so the

negative value will be assigned. The below

procedure shows how the fitness status is given as

follow:

Control

Mechanism

AN IMPROVED GENETIC ALGORITHM WITH GENE VALUE REPRESENTATION AND SHORT TERM

MEMORY FOR SHAPE ASSIGNMENT PROBLEM

181

Area Size Æ areaX * areaY ---- (a)

Size of combined shape

∑

i=1

((shapeX)

* (shapeY)

)

---- (b)

if (b) <= (a)

fitness status = “positive”

Else if (b) > (a)

fitness status = “negative”

The positive values of chromosomes mean there

are tendencies to assign all combined shapes into an

area but the space is not necessarily fully utilized.

However, at the next generation, these chromosomes

have opportunity to reach optimal solution. Whereas

the negative value of chromosomes are stated when

a possibility of at least one of shapes fail to be

assigned into the area. These chromosomes will be

rejected for the next generation.

Table 2 shows the repetition number of positive

and negative value for both BGA and IGA using the

same dataset.

Table 2: Comparing possibility number of negative value

in BGA and IGA.

The result of negative and positive value of

both BGA and IGA were analyzed and the result is

illustrated by graph as shown in figure 5. At 4, 4

and 5, 5 areas coordinate of BGA produce 70 and 57

percent of negative values respectively, and then the

values tremendously plunge to 10 percent at the next

coordinate of areas. While IGA shows the negative

value of all areas is not much difference between 7

to 10 percent.

Figure 5: Percentage of repetition number of negative

value.

The 4, 4 and 5, 5 area coordinate of BGA

produced high percentage of negative value and it

give a justification of the 0 to 9 gene values

representation is not applicable. The higher gene

values than area coordinates produce more

unsatisfied conditions. We can conclude based on

the overall result that the BGA produces more

repetition number of negative value than IGA, so

that insignificant chromosomes lead to time increase

and affect to quality of result. Therefore, the

undefined specific initialization in BGA becomes

the possibility of chromosomes to violate the hard

constraints are higher. These insignificant

chromosomes have possibility to be used in

processes of crossover and mutation. Therefore use

of awful chromosome for producing new offspring

consequently gives more time to find the optimal

solution.

4.3 Experiment 3: Repetition Number

of Same Solution Optimal Solution

Basically, the larger area coordinates will produce

higher number of possible solutions. Refer to table

3, the area coordinates of analysis number 1 and 3

generated possible results with 4,096 (4

* 4

) and

110,592 (6

* 8

) respectively, as the result of

analysis number 3 required more analysis time.

Refer to experiment 3, there were three same

solutions as shown in table 3. As a comparison, by

BGA, the process of calculating tree number and

determining the best line-direction and required

15,575 (

bS=N

∑

bS=1

(ItNum * OS)

) iterations, while IGA

required only 9203 (

bS=N

∑

bS=1

ItNum

) iterations.

The overall time taken is based on the

accumulation of time in all repetition processes.

Small areas coordinates have higher tendency to

occurrence of the repetitive optimal shape solution.

The different computation time of both BGA and

Table 3: Analysis of the Same Optimal Shape Solution.

IGA increases consistently when more repetition

number of same optimal solution. However, when

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the evaluation number is small (refer to figure 3), the

possibility of repetition number might not happen,

thus computation time of both will be same.

From our observation the taken time for each

experiment was inconsistent at certain time but it

infrequently happen is a challenge. A justification on

this matter is a probabilistic algorithm with a

randomness strategy applied in GA, therefore the

number of repetitions and iterations and hardly

expected.

5 CONCLUSIONS

IGA possibly reduces number of repetition by

focussing on assigning values to genes and

controlling the repetition of optimal solution. The

gene value is based on an area coordinate will be

more significant when the area coordinate increases.

Besides that, the less number of negative values in

obtaining the optimal solution will reduce

computation time because of the awful

chromosomes will be diminished. Meanwhile,

controlling mechanism in obtaining the best optimal

reduce computation time by looking at the number

of iteration.

ACKNOWLEDGEMENTS

This research is registered in the Fundamental

Research Grant Scheme (FRGS) and it is fully

funded by Ministry of Higher Education (MOHE),

Malaysia. Authors express our highly appreciation

and thanks to MOHE, Malaysia and Universiti

Teknologi MARA, Malaysia for sponsoring one of

the authors in PhD level. Authors also wish to thank

the Universiti Putra Malaysia that provides facilities

and conducive environments for carrying out this

research.

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MEMORY FOR SHAPE ASSIGNMENT PROBLEM

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