Intelligent Automation & Soft Computing A

This article was downloaded by: [Uniwersytet Warszawski] On: 21 October 2014, At: 23:55 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Intelligent Automation & Soft Computing Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tasj20

A Chromosome Representation Encoding Intersection Points for Evolutionary Design of Fuzzy Classifiers a

a

Joon-Yong Lee , Joon-Hong Seok & Ju-Jang Lee

a

a

Department of Electrical Engineering, KAIST , University of Electronic Science and Technology of China , 335 Gwahangno (373-1 Guseong-dong) , Yuseong-gu Daejeon , 305–701 , Republic of Korea Published online: 01 Mar 2013.

To cite this article: Joon-Yong Lee , Joon-Hong Seok & Ju-Jang Lee (2012) A Chromosome Representation Encoding Intersection Points for Evolutionary Design of Fuzzy Classifiers, Intelligent Automation & Soft Computing, 18:3, 237-246, DOI: 10.1080/10798587.2008.10643240 To link to this article: http://dx.doi.org/10.1080/10798587.2008.10643240

PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

Intelligent Automation and Soft Computing, Vol. 18, No. 3, pp. 237-246, 2012 Copyright © 2012, TSI® Press Printed in the USA. All rights reserved

A CHROMOSOME REPRESENTATION ENCODING INTERSECTION POINTS FOR EVOLUTIONARY DESIGN OF FUZZY CLASSIFIERS

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

JOON-YONG LEE, JOON-HONG SEOK, AND JU-JANG LEE Department of Electrical Engineering, KAIST 335 Gwahangno (373-1 Guseong-dong), Yuseong-gu Daejeon, 305-701, Republic of Korea

ABSTRACT—Unlike the conventional chromosome representation to search the shape of fuzzy membership functions, a novel encoding scheme to search the optimal intersection points between adjacent fuzzy membership functions is originally presented for evolutionary design of fuzzy classifiers. Since the proposed representation contains the intersection points directly related to the boundary of classification, it is intuitively expected that redundancy of the search space is reduced and the performance is better in comparison with the conventional encoding scheme. The experimental results show that the proposed encoding scheme gives superior or competitive performance in two realworld datasets and gives more interpretable fuzzy classifiers. This short paper has provided additional explanation to the previous works introduced in the latest conference. Key Words: Fuzzy classifiers, genetic algorithms, encoding scheme, intersection points of membership functions

1. INTRODUCTION In classical data-driven fuzzy modeling, design of optimal fuzzy classifier has been commonly dealt with as a search problem [1][2]. Optimal design of fuzzy classifiers (FCs) is one of the most complex search problems since there are various feasible solutions according to the combination of fuzzy rules and membership functions (MFs). In other words, the optimal design of FCs is described as a non-convex and multimodal search problem. Besides, the high-order and large scale problems caused by the large number of rules, MFs, and input attributes also exist in the optimal design of FCs. In order to overcome these difficulties, many researchers have applied metaheuristic search methods to optimally design FCs. Among them, evolutionary algorithms (EAs) such as genetic algorithms (GAs) have been widely used in the much of the literature due to their search ability and reliability [1]-[3]. EAs are basically general-purpose population-based stochastic search algorithms which use multiple candidate solutions simultaneously and find the best solution [4]. Irrespective of the given problem, the first step in applying EAs is to encode solutions for the given problem into a set of parameters: a chromosome. Thus, to optimize fuzzy models in a framework of EAs, the first step is to represent a fuzzy model into a chromosome. For evolutionary design of FCs, an encoding scheme relevant to the given problem is also required because an encoding scheme plays an important role to decide the property of search space [1][4]. The conventional encoding methods for evolutionary design of FCs are mainly designed to find the shape of the fuzzy MFs as a center and width of a Gaussian MF and 3 or 4 edge points of a triangular or trapezoidal MF. However, recent related works [5], providing an intuitive insight for properties of fuzzy rules, argue that the boundary of classification is formed in the intersection points between two adjacent MFs. In other

237

238

Intelligent Automation and Soft Computing

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

words, it indicates that the positions of the borders are determined by the points of intersection of the membership functions. Therefore, the exact shape of the fuzzy sets does not directly influence the (crisp) classification. Based on this intuitive insight, the conventional encoding schemes to search the exact shape of the fuzzy MFs have redundancy since various combinations with the different shapes enable FCs to make the same boundaries (intersection points) for the (crisp) classification. Therefore this short paper proposes the evolutionary design method for FCs using a new encoding scheme to find the intersection points of the fuzzy MFs. In other words, a novel encoding scheme is proposed to design a type-1 fuzzy classifier with an evolutionary search approach. A part of this short paper has been already introduced in the latest conference with adding a sequential encoding concept to this novel encoding scheme [13]. Hence, there is a partial overlap between the conference paper and this short paper. Especially, we tried to explain the key ideas again in more detail with concrete examples in this short paper.

2. EVOLUTIONARY DESIGN WITH INTERSECTION POINTS In this short paper, the proposed evolutionary design originally encodes the intersection points to represent the search parameter as a chromosome with grid partitioning of input space. Commonly, a chromosome represented for evolutionary design of FCs consists of two parts, such as a rule structure and the MFs’ parameters, in order to simultaneously optimize the two parts [4][6]. For encoding a rule structure, the number of fuzzy rules increases exponentially with the number of input variables and the number of MFs for each input variable under the grid-partition approach. Thus, to effectively select useful rules from all the available rules, several encoding schemes have been proposed [4][13]. For investigating the effect of a pure key idea to employ intersection points, we use the following rule-encoding method. A rule structure is encoded by real values as follows: Rf1,Rf2,…,Rfk/ m11,m12,…m1n,...,mkn/ mf11,mf12,…mf1n,...,mfkn/ C1,C2,…,Ck/ CF1,CF2,…,CFk. For every rule, a binary validity flag (Rfi) is assigned that indicates that rules with ‘1’ flag are available. mij contains the index information of the corresponding MF for the j-th input attribute in the i-th rule and mfij∈ {‘is’, ‘is NOT’, ‘don’t care’} determines the condition of the mijth corresponding MF. Ci and CFi represent output class number and certainty grade for the i-th rule, respectively. k and n describe the maximum number of selected rules and the number of input attributes, respectively. For easily understanding this representation, let us give an example. Let’s suppose that k = 3, n = 3, the number of the maximum MFs is 4, and the number of classes is 2. Then, suppose that a chromosome is generated as shown in Figure 1.

Figure 1. An exemplary chromosome for a rule structure

In Figure 1, ① means that the first rule among three selected rules is not used and the others are used. ② represents that, in the first rule, 3 input attributes are corresponding to the first, the second and the first MF among MFs for each input domain, respectively. For the second rule, 3 input attributes are corresponding to the fourth, the first and the third MF among MFs for each input domain, respectively. In the same manner, an antecedent portion of the third rule is determined. As mentioned before, ③ presents how the corresponding MF for each input attribute is applied in each rule. ‘0 1 1’ makes the antecedent part of the first rule as follows: “If x1 is 1st MF, x2 is NOT 2nd MF, x3 is NOT 1st MF.” The next ‘1 2 0’ means the antecedent part of the first

A Chromosome Representation Encoding Intersection Points for Evolutionary Design of Fuzzy Classifiers

239

rule is determined as follows: “If x1 is NOT 4th MF, x2 is ‘don’t care’, x3 is 3rd MF.” Membership degrees are calculated as Eq. (1) in terms of each condition.

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

  − ( x − c) 2   if mf ik = 0 exp 2    2σ   − ( x − c) 2   if mf ik = 1 y i = µ ( xi ) = 1 − exp 2  2σ    1 if mf ik = 2 (don' t care) 

(1)

④ and ⑤ represent the index and certainty grade of an output class for each rule, respectively. In summary, a rule structure encoded via the above exemplary chromosome is as follows: - Rule 1: If x1 is 1st MF, x2 is NOT 2nd MF, x3 is NOT 1st MF, then Class 1 with CF1 = 0.42. (No use) - Rule 2: If x1 is NOT 4th MF, x2 is ‘don’t care’, x3 is 3rd MF, then Class 1 with CF2 = 0.83. - Rule 3: If x1 is 1st MF, x2 is NOT 2nd MF, x3 is ‘don’t care’, then Class 2 with CF3 = 0.97. In order to encode MFs’ parameters, the conventional encoding scheme considers two real values such as center and width (i.e., cij and σij) to represent a Gaussian MF used in this paper. However, unlike the conventional encoding scheme, the proposed MF-encoding scheme with the intersection points is defined as follows: Af1,Af2,…,Afn/ P11,P12,…,P1s,…,Pns/ Pf11,Pf12,…,Pf1s,…,Pfns.

Figure 2. An illustration of Gaussian fuzzy MFs for an input attribute.

Afi represents a feasibility flag of the i-th input attribute and Pfij also indicates feasibility of Pij (xij, yij) which represents the j-th intersection point for the i-th input attribute. All the input attributes are normalized into a range of 0 and 1. Hence, we use the x coordinates of 0 and 1 as two end points so that (s+1) MFs are obtained by s intersection points (see Figure 2). If y coordinates of intersection points for an attribute are defined as a constant, the chromosome length is reduced as much as Nmf×Nattr at least in comparison with the conventional encoding method, where Nmf and Nattr describe the maximum number of MFs for each attribute and the number of attributes (= input dimension), respectively. Besides, y coordinates for each attribute are bounded as between 0.4 and 0.6 so that the interpretability property of FCs obtained by evolutionary design is preserved without the additional measure as shown in the next section. In the same way to the rule encoding, let’s give an example of the MF encoding. Then, suppose that a chromosome is generated as follows:

240

Intelligent Automation and Soft Computing

Figure 3. An exemplary chromosome for MF parameters

As stated above, ① means the feasibility flag of each input attribute in Figure 3 so that the

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

second input attribute is not used in terms of ‘1 0 1’. ② and ③ respectively represent the x coordinates and y coordinate of the intersection points when y coordinates of intersection points for an attribute are defined as a constant for example. ④ means feasibility flags of each intersection point. Then, MFs for each input domain are illustrated in Figure 4. Here, x2 is not used in terms of the feasibility flag of input attributes. Consequently, two exemplary chromosomes illustrated in Figure 1 and Figure 3 are combined and dealt with as a real-valued chromosome in this paper.

Figure 4. MFs of an exemplar chromosome of Figure 3

As mentioned in the related works [13], the symmetric Gaussian function depends on two parameters center (c) and width (σ) as given by  − ( x − c) 2 y = µ ( x) = exp 2  2σ

  .

For example, we can derive c and σ from two intersection points P1(x1, y1) and P2(x2, y2) as follows (see Figure 2.). First, substituting two intersection points into the Gaussian MF, we get

A Chromosome Representation Encoding Intersection Points for Evolutionary Design of Fuzzy Classifiers

241

  − ( x1 − c) 2    y1 = exp 2   2σ   2  y = exp − ( x2 − c)   2σ 2   2  .

By the definition of the natural logarithm, we also get  − 2σ 2 ln y1 = ( x1 − c) 2  2 2 − 2σ ln y 2 = ( x2 − c) .

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

For x1 < c < x2 , we have

 x1 − c = −σ − 2 ln y1   x2 − c = σ − 2 ln y 2 . Hence, we can derive from the above

 − 2 ln y 2 x1 + − 2 ln y1 x 2 c = − 2 ln y1 + − 2 ln y 2   x 2 − x1 σ =  − 2 ln y1 + − 2 ln y 2  .

(2)

3. FUZZY LOGIC INFERENCE AND GA The fuzzy rule used in this paper is defined as follows [7][8]: Ri : IF x1 is m1j AND x2 is m2k AND … xn is mnl, THEN class is Ci with CFi As mentioned previously, we use the certainty factor (CF) to impose the uncertainty for a type1 fuzzy logic system. In [7], the effect of certainty grades has already investigated on the performance of fuzzy rule-based classification systems. It shows that the learning of rule weights can be equivalently replaced by the modification of the membership functions of antecedent or consequent fuzzy sets considered in type-2 fuzzy modeling. Besides, the following voting method is employed for the fuzzy logic inference as in [9][10]. Algorithm 1 describes the pseudo code to classify the given dataset with a FC and then evaluate a FC. Algorithm 1. CLASSIFICATION(FC, X)

N c : The number of classes. Si : The score of the i-th class. Nd n

k : The number of selected rules.

: The number of input attributes. : The number of data. X = {( X 1 , C1 ), ( X 2 , C2 ), , ( X N , C N )} d d : Data set for classification. 1 2 n X i = {xi , xi ,  , xi } : An input pattern of the i-th datum.

Ci : A target class of the i-th datum. CR: Correction rate of FC ( % ).

242

Intelligent Automation and Soft Computing

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

1: for d = 1 to Nd do 2: CR ← 0 3: for i = 1 to Nc do 4: /* Initialize a score of each class for the d-th datum. */ 5: Si ← 0 6: end for 7: for i = 1 to k do 8: /* Calculate a score for each class. */ 9: if Rfi == 1 then n 10: µi ( X d ) ← CFi × ∏ j =1µ j ( xdj ) 11: 12:

end if SC ← SC + µi ( X d ) i

13: 14:

end for

15:

Classify

i

Cmax ← arg maxi Si

X d as the Cmax th class in this FC.

16: if Cmax == Cd then 17: CR ← CR + 1 18: end if 19: end for 20: CR ← CR/N d In GA, the fitness function for evaluating FCs consists of the correction percentage of the training data, the total number of membership functions, and the number of rules as shown in Eq. (3).

f = TrCR − wm ⋅ N m − wr ⋅ N r

(3)

TrCR represents the ratio of the correction number to the total number of training data and the Nm and Nr represent the number of membership functions and rules, respectively. TrCR is calculated by substituting a FC and train data in Algorithm 1. wm and wr are defined as the weights for Nm and Nr, respectively. In other words, the fitness function is designed to maximize the correction rate and simplify the rule structure. Algorithm 2 represents the applied GA for optimal design of a fuzzy classifier. Algorithm 2. Genetic algorithm for FC design Np: The number of individuals in a population. No: The number of offsprings. Mg: The maximum number of generations for a trial. P = {FC1, FC 2, … , FC Np}: An population. Xtrain: Train data. 1: g ← 1 2: Initialization: Randomly generate an initial population with Np individuals (a fuzzy classifier is encoded as a chromosome). 3: for i = 1 to Np do

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

A Chromosome Representation Encoding Intersection Points for Evolutionary Design of Fuzzy Classifiers

243

4: /*Evaluate an initial population*/ 5: CLASSIFICATION(FCi, Xtrain) 6: Calculate a fitness function value of FCi. 7: end for 8: while g < Mg do 9: Elitism: Employ the elitism selection for fast convergence. Among the individuals of the current population, an elite individual with the best fitness value is selected as a parent in advance. 10: Selection: Use the tournament selection [11]. First, two individuals are randomly selected in the current population. After comparing the fitness function value of one with the other, an individual that wins the competition is selected as a parent for the next generation. 11: Crossover: The arithmetic crossover [4][11] is employed. Linear combination of the two selected parents is carried out. A linear combination factor α is in the range of [0, 1] in order to search for an optimal solution in the convex region between the selected individuals. Finally, generate offsprings with No individuals. 12: Mutation: Uniform mutation is used for offsprings [11]. 13: Generate a new population by combining parents with offsprings for the next generation. 14: for i = 1 to Np do 15: /*Evaluate a new population*/ 16: CLASSIFICATION(FCi, Xtrain) 17: Calculate a fitness function value of FCi. 18: end for 19: g ← g + 1 20: end while 21: Elitism. Finally, FC encoded as a elite individual is determined as optimal design of a fuzzy classifier for train data Xtrain.

4. EXPERIMENTAL RESULTS 4.1 Experimental Setting

The proposed encoding scheme focused on the intersection points is verified by two experiments (glass and pima-Indians-diabetes dataset [12]) performed under the same optimization tool and the same fuzzy operators, but with different ways of encoding. In other words, for investigating only the effect of the proposed encoding scheme, the other conditions of these experiments are exactly the same. Table I shows the experimental condition. These results were obtained by 50 independent runs. As mentioned in Table I, we performed 10-fold cross validation (CV). The maximum number of function evaluations is determined as 100×max {Lc, Lp}, where Lc and Lp represent the chromosome lengths of the conventional encoding scheme and the proposed encoding scheme, respectively. Glass dataset has 214 Instances, 9 attributes (excluding an identification number), and 7 classes. 9 attributes of Glass dataset contain a refractive index, and the weight percents of several main chemical substances. Pima Indians diabetes dataset has 768 instances, 8 attributes, and 2 classes. The diagnostic is investigated as whether the patient shows signs of diabetes according to World Health Organization criteria. In particular, all patients here are females at least 21 years old of Pima Indian heritage.

244

Intelligent Automation and Soft Computing

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

Table I. Experimental Parameter Settings Parameters

Values

wm

0.001

wr

0.1

Crossover rate

0.75

Mutation rate

0.015

Population size

60

Offspring size

30

Max. number of generations

200

Max. number of MFs for each attributes

10

Max. number of Rules

10

Number of fold for CV

10

4.2 Results

Glass dataset and Pima Indians diabetes dataset are well known and widely used to test the classification methods. It is relatively hard to classify these datasets due to multivariate characteristics. Table II shows that the proposed encoding scheme outperforms in the glass and Pima Indians diabetes dataset. As shown in Table II, the proposed encoding scheme is superior to the conventional one with respect to the better CR for the training data and the smaller number of the input attributes and rules. As mentioned previously, the chromosome length is also reduced in the proposed encoding scheme. It is expected that the good performance is caused by the reduction of search space and its redundancy. These results are similar to the results of the previous works [13] and since the interpretable performance is also similar to [13], we do not report the results again in this short paper.

5. CONCLUSION This short paper presents an encoding scheme using the intersection points for evolutionary design of a FC. Namely, the proposed encoding approach in this short paper aims to find the intersection points of each input attribute directly related to the border of classification instead of the shape of membership functions. As addressed in the previous works, we also carried out experiments with two well-known real-world datasets in order to investigate the effects of the proposed encoding scheme. The experimental results also show that the proposed encoding scheme generally provides superior and competitive FCs in terms of the correction rate and complexity of rule structure due to the reduced search space in comparison with the conventional encoding scheme. The relatively interpretable FCs are obtained without additional computation to measure the interpretable degree for every chromosome. As a further work, we consider a new encoding scheme relevant to an evolutionary programming for a type-2 fuzzy logic system design in order to improve the convergence speed and performance.

A Chromosome Representation Encoding Intersection Points for Evolutionary Design of Fuzzy Classifiers

245

Table II. Experimental Results (CR describes the correction rate.)

Data

Results

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

Glass

Pima Indians Diabetes

Conventional encoding

Fitness value

61.3

Standard deviation 7.1

Training CR (%)

62.1

Testing CR (%) Num. of Attributes Num. of MFs

Proposed encoding

65.3

Standard deviation 5.6

7.3

65.6

5.1

54.1

8.5

57.1

6.2

4.2

1.5

3.9

0.9

21.2

7.2

19.8

7.1

Num. of Rules

10.8

2.1

9.1

1.6

Chromosome length

559

Fitness value

79.3

1.1

79.1

1.4

Training CR (%)

75.7

1.2

78.1

1.5

Testing CR (%)

74.4

2.6

72.9

2.2

Num. of Attributes

4.4

1.3

4.2

1.8

Num. of MFs Num. of Rules Chromosome length

22.0 8.9 285

7.1 2.8

23.3 9.7 205

7.3 1.6

Mean

Mean

469

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.

O. Cordon, F. Gomide, F. Herrera, F. Hoffmann, and L. Magdalena, “Ten years of genetic fuzzy systems: current framework and new trends,” Fuzzy Sets and Systems, 141, (1), pp. 5–31, 2004. E. Zhou and A. Khotanzad, “Fuzzy classifier design using genetic algorithms,” Pattern Recognition, 40, (12), pp. 3401–3414, 2007. L.I. Kuncheva, “Fuzzy classifier design,” Springer, Physica-Verl., Heidelberg, 2000. M.-S. Kim, C.-H. Kim, and J.-J. Lee, “Evolving compact and interpretable Takagi-Sugeno fuzzy models with a new encoding scheme,” IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics, 36, (5), pp. 1006–1023, 2006. A. Klose and A. Nurnberger, “On the properties of prototype-based fuzzy classifiers,” IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics, 37, (4), pp. 817–835, 2007. M.-S. Kim and J.-J. Lee, “Design of a Fuzzy Logic Controller with Evolutionary QLearning,” International Journal of Intelligent Automation and Soft Computing, Vol. 5, December, 2005. H. Ishibuchi and T. Nakashima, “Effect of Rule Weights in Fuzzy Rule-Based Classification Systems,” IEEE Transactions on Fuzzy Systems, 9, (4), pp. 506-515, 2001. H. Ishibuchi, T. Nakashima, and T. Morisawa, “Voting in fuzzy rule-based systems for pattern classification problems,” Fuzzy Sets and Systems, 103, (2), pp. 223-238, 1999.

246

9.

10.

11.

Downloaded by [Uniwersytet Warszawski] at 23:55 21 October 2014

12. 13.

Intelligent Automation and Soft Computing

S. Y. Ho, H. M. Chen, S. J. Ho, and T.K. Chen, “Design of accurate classifiers with a compact fuzzy-rule base using an evolutionary scatter partition of feature space,” IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics, 34, (2), pp. 1031–1044, 2004. A. Fernandez, M. Calderon, E. Barrenechea, H. Bustince, and F. Herrera, “Solving multiclass problems with linguistic fuzzy rule based classification systems based on pairwise learning and preference relations,” Fuzzy Sets and Systems, 161, (23), pp. 3064-3080, 2010. Z. Michalewicz, “Genetic algorithms+data structures = Evolution Programs,” Springer, 1996. A. Asuncion and D.J. Newman, “UCI Machine Learning Repository [http://www.ics.uci.edu/~mlearn/MLRepository.html],” Irvine, CA: University of California, Department of Information and Computer Science, 2007. J.-Y. Lee, J.-H. Seok, Y.-J. Kim, and J.-J. Lee, “Evolutionary Design of Fuzzy Classifiers Using Intersection Points,” Industrial Informatics (INDIN), 2010 8th IEEE International Conference on , pp. 98-101, 2010

ABOUT THE AUTHORS J.-Y. Lee received the B.S. degrees in Electrical Engineering from Ajou University, Suwon, Korea in 2002 and the M.S. degrees in Electrical Engineering from the Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea. He is currently working toward Ph. D. degree in the Department of Electrical Engineering in Korea Advanced Institute of Science and Technology (KAIST). His current research interests evolutionary computation and intelligent control. J.-H. Seok received the B.S. degrees in Electrical Engineering from Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Korea. He is currently working toward Ph. D. degree in the Department of Electrical Engineering in Korea Advanced Institute of Science and Technology (KAIST). His current research interests artificial intelligent, evolutionary algorithms and mobile robot path planning. J.-J. Lee (M’86-SM’98) received the B.S. and M.S. degrees, both in electrical engineering, from Seoul National University in 1973 and 1977, respectively and the Ph.D. degree in electrical engineering from the University of Wisconsin in 1984. He joined the Department of Electrical Engineering, KAIST, Korea in 1984, where he is currently a professor. In 1987, he was a visiting professor at the Robotics Laboratory of Imperial College Science and Technology, London, U.K. From 1991 to 1992, he was a visiting scientist at the Robotics Institute of Carnegie Mellon University, Pittsburgh, PA. His research interests are in the areas of intelligent control of mobile robot, service robotics for the disabled, space robotics, evolutionary computation, variable structure control, chaotic control system, electronic control units for automobiles, and power system stabilizers. He is a Fellow of IEEE, SICE, and ICROS and a member of the IEEE Robotics and Automation Society, the IEEE Evolutionary Computation Society, and the IEEE Industrial Electronics Society. In 2005, he was the President of the Institute of Control, Robotics, and Systems (ICROS) in Korea and a director of SICE in Japan.