Genetic Algorithm with Upgrading Operator

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1 Genetic Algorithm with Upgrading Operator NIDAPAN SUREERATTANAN Computer Science and Information Management, School of Advanced Technologies, Asian Institute of Technology, P.O. Box 4, Klong Luang, Pathumthani 12120, THAILAND Abstract: - In recent years, Genetic Algorithm (GA) has grown rapidly and extensively used in various fields. GA is a search method based on the paradigm of natural selection and natural genetics. With their special characteristics: a coding of parameter set, searching from a population, appropriate measure of fitness, and probabilistic transition rules, GA can perform evolving a solution for several types of problems. Although the basic operators, crossover and mutation, work so well in the vast majority of genetic algorithm implementations. However, an important problem still remains in balancing between exploration and exploitation in genetic search. This problem concerns to a selective pressure and population diversity. Selective pressure can have a decisive effect on the outcome of an evolutionary search. Higher the pressure, more speed up the convergence but perhaps on a local optimum. Conversely, lower the pressure, slower the convergence but more variation of population. Anyway, population diversity provides the raw materials for adaptation. Hence, to let different species emerge and coexist inside the evolving population for a sufficient amount of time, the new computational operators for GA are proposed in this paper. Concentrating a chance to avoid complete loss of the characters on the worst chromosomes, the upgrading operator is presented. Performance of combination of the basic GA and the proposed operator is compared with the pure basic GA. Results on the optimization functions and the real applications in feature selection problem provide valuable evidence that the proposed GA perform more robust than the basic GA. Key-Words: - Genetic Algorithm, Exploration, Exploitation, Selective Pressure, Population Diversity, Upgrading Operator 1 Introduction Genetic Algorithm (GA) introduced and developed by Holland [1], is a search algorithm to mimic the adaptive process of natural evolution. GA has proved to be a robust, domain independent [2], and efficient search method for a large space using probabilistic selection [3]. It can also avoid local minima [4]. Booker [5] described that GA strike a reasonable balance between exploration of the search space and exploitation of the best solutions currently available. He fur-

2 ther explained that the power of the algorithm comes from finding the best solution in sampling regions of the search space containing relatively high proportions of good solutions. Despite the demonstrated advantages of genetic algorithm and even though GA is widely and successfully used in many applications, there have been several problems to be considered seriously. Loss of population diversity in genetic search is one of these problems. In fact, a performance of GA is heavily dependent on the population representative. Unfortunately, there is a lack of population diversity in the gene pool, according to the limit choices of the existing operators for introducing variation into a population. Even though many selection schemes, alternative crossover and mutation were introduced (e.g. [6][7][8]). Genetic population is mainly constructed by the crossover operator, which performs material exchange between the couple of the selected chromosomes. The crossover operator itself can not reintroduce the loss of some chromosome characteristics so the operator like mutation is needed to alter the value of population chromosomes. A variety of influences can cause slight changes in the chemical structure of a living gene. Such changes are called mutations. The rate at which any particular gene undergoes mutation is ordinarily extremely low. But every individual organism has a very large number of different genes, and the total number of genes in all the individuals of a species is vast indeed. Population diversity has become an important issue in genetic search, it is a term for the degree of population variety, including the number and frequency of population in a given pool, and also the variation in genes. Generally, searching by GA has to concern with a selective pressure since it can have a decisive effect on the outcome of the genetic search. Selective pressure is a degree to which better individuals are favored whereby the higher the selective pressure, the more favored the better individuals. The worse individuals more likely tend to die off. If the selective pressure is too high, it can lead to loss of gene diversity then further to loss of population diversity. Nowadays, genetic learning algorithm is plagued with premature convergence. Even the algorithms try too hard but sometimes end up converging prematurely. According to the intuitive reason for premature convergence that the individuals in the gene pool are too alike or identical, then the chance of premature converging to a local optimum can also increase due to a lack of population diversity. On the other hand, too little selective pressure is apart from wasting time. Hence, maintaining diversity of population is needed to avoid this event. During the past several decades, there are many biological operators and mechanisms for rearranging genetic material. This context motivated the interest to investigate if any of these significantly yield new computational operators of use in artificial GA. In this study, the upgrading operator was proposed to improve genetic diversity. A comparison of performance between the proposed GA (the basic GA with upgrading operator) and the basic GA conducted on optimization functions and real applications were demonstrated. 2 Upgrading Operator The upgrading operator proposed to not only avoid complete loss of characteristics of the worst chromosome but also improve some of these characteristics. By specified selection of mating between the worst chromosome and the best chromosome, the crossing over results in the new chromosome containing part of the characteristics from the worst parent. The fitness of this new chromosome is expected to be greater than the fitness of the worst parent. Dealing with ex-

3 ploitation objective, the worst chromosome tends more likely to die off due to a selective pressure. However, the upgrading operator preserves some characteristics of the worst chromosome to improve variant in a population and yield exploration objective. 3 Experiments In this experimental studies, the crossover and mutation probabilities were set to 0.6 and 0.001, respectively. 3.1 Optimization Functions De Jong s functions [9] summarized in Table 1 (modified from [5]) are used in this Section. The performance of GA and GA U on the set of test functions were shown in Table 2. Table 1: Standard Set of Test Functions Function Bounds Search Space Resolution F 1 (x) = 3 i=1 (x i) x i 5.12 x i =0.01 F 2 (x) = 100 (x 2 1 x 2) 2 +(1 x 1 ) x i x i =0.001 F 3 (x) = 5 i=1 [x i] 5.12 x i 5.12 x i =0.01 F 4 (x) = 30 i=1 ix4 i + GAUSS(0, 1) 1.28 x i 1.28 x i =0.01 [ F 5 (x) = j=1 1 2 j+ i=1 (xi aij)6 ] x i x i =0.001 Table 2: Comparative Performance: GA vs GA U Function Minimum Value GA GA U Solution Generation Solution Generation F F F F F

4 De Jong [9] described that nicely scaled quadratic function like F1 with a low-dimensional, one can hardly do better. He addressed that F2 violates several of the assumptions made concerning the function to be minimized; it is non-convex deep parabolic valley, nonquadratic, and also badly scaled. The demonstration of performance brought out an interesting characteristic of GA U that it could achieve the minimum value faster than GA, in all cases considered here. Although none of both methods found the optimum point on F2 but the proposed GA reached the nearoptimum point in far less generation than the GA within 5000 generations. For all functions used, the execution time used by the proposed GA is more satisfactorily than which used by the basic GA (Table 3). Table 3: Execution Time Comparison on Function Optimization Function Time Required (hh:mm:ss) GA GA U F1 00:00:01 00:00:01 F2 00:00:15 00:00:08 F3 00:00:11 00:00:02 F4 00:14:09 00:14:06 F5 00:00:01 00:00:01 Total 00:14:38 00:14: Feature Selection In this study, the training sets generally contained a half of the entire data sets. Anyway for huge data sets, the training sets would be limited maximally to 500. All data sets were randomly divided into a training set, used to generate decision rules, and a testing set, used to measure the performance of the produced rules. The maximum number of generation to be run was limited to 20. A single Nearest-Neighbor (1- NN) algorithm is applied as a classifier in the experiments. The NN algorithm is based on a minimum-distance classification concept [10]. The NN algorithm has been a subject of both experimental and theoretical studies for many years ([11][12][13][14][15]). It is one of the oldest and simplest methods for performing general, nonparametric classification [16]. The NN classifier computes the Euclidean distance from an unlabeled pattern p to the prototype of each class, and assigns the pattern to the class to which it is closest. The experiments on 4 real-world data set (Soybean, Satellite, Texture, and Voting) were conducted to compare the effectiveness of the GA U to the GA for feature selection problem. A bit string with a fixed length equaling the size of the entire feature set, was used to represent the presence and absence of each of the possible features. A value of 1 in the ith bit means that the ith feature is included in the feature subset, and a value of 0 means that the ith feature is not included in the subset. Table 4-5 illustrate that GA U outperforms the basic GA in all cases considered.

5 Table 4: Performance Evaluation of GA on Feature Selection Problem Data (Feature: Accuracy) Selected Feature Accuracy Execution Time (hh:mm:ss) Satellite (36: 78.1) :08:12 Soybean (35: 81.84) :02:54 Texture (40: 76.55) :12:02 Voting (16: 89.2) :00:02 Table 5: Performance Evaluation of GA U on Feature Selection Problem Data (Feature: Accuracy) Selected Feature Accuracy Execution Time (hh:mm:ss) Satellite (36: 78.1) :04:39 Soybean (35: 81.84) :01:42 Texture (40: 76.55) :11:29 Voting (16: 89.2) :00:02 4 Conclusion In this study, we proposed the upgrading operators for genetic algorithms. It was originated for survival opportunity of the worst individual. The main conclusions are: The upgrading operator could speed up the convergence of GA on the function optimizations GA with the crossover, mutation, and upgrading operator achieved in real applications dealing with feature selection problem; the overall performance was more satisfactorily than GA without the upgrading operator Conserving genes on the worst chromosome, from complete loss by the selective pressure, could produce variation in genetic search and also improve search performance References [1] J. H. Holland. Outline for a Logical Theory of Adaptive Systems, Journal of the Association for Computing Machinery, Vol. 3, 1962, pp [2] D. E. Golberg. Genetic Algorithms in Search, Optimization, and Machine Learning, New York: Addison Wesley, [3] H. Vafaie and K. De Jong. Robust Feature Selection Algorithms, In Proceedings of the Fifth IEEE International Conference on Tools for Artificial Intelligence, Boston, MA: IEEE Press, [4] S. K. Halgamuge and M. Glesner. Input Space Segmentation with a Genetic Algorithms for Generation of Rule Based Classifier Systems, Practical Handbook of Genetic Algorithms, New York: CRC Press, [5] L. Booker. Improving Search in Genetic Algorithm, Genetic Algo-

6 rithm and Simulated Annealing, San Mateo, California, USA: Morgan Kaufmann, 1987, pp [6] P. Franti, J. Kivijarvi, T. Kaukoranta, and O. Nevalainen. Genetic Algorithms for Large Scale Clustering Problems, The Computer Journal, Vol. 40, No. 9, 1997, pp [7] P. J. B. Hancock. Methods for Evolutionary Algorithms, Practical Handbook of Genetic Algorithms, Vol. 2, 1995, pp [8] P. Larranaga, C. M. H. Kuijpers, R. H. Murga, and Y. Yurramendi. Learning Bayesian Network Structures by Searching for the Best Ordering with Genetic Algorithms, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, Vol. 26, No. 4, 1996, pp [9] K. A. De Jong. An Analysis of the Behavior of a Class of Genetic Adaptive Systems, Ph.D. Thesis. Michigan: University of Michigan, [10] J. T. Tou and R. C. Gonzalez. Pattern Recognition Principles, United States of America: Addison Wesley, [11] T. Cover and P. Hart. NN Pattern Classification, IEEE Transactions on Information Theory, Vol. 13, 1967, pp [12] P. A. Devijver. An Overview of Asymptotic Properties of NN Rules, Pattern Recognition in Practice, New York: Elsevier Publishers B. V., 1980, pp [13] L. Devroye. Automatic Pattern Recognition: A Study of the Probability of Error, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 10, No. 4, 1988, pp [14] E. F. Fix and J. Hodges. Discriminatory Analysis: Small Performance, Technical Report Project , Rep. No. 11, Randolph Field, Tex: USAF School of Aviation Medicine, [15] S. Salzberg and A. L. Delcher. Best-Case Results for Nearest- Neighbor Learning, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 17, No. 6, June, [16] S. D. Bay. Combining Nearest Neighbor Classifier through Multiple Feature Subsets, Proceedings of the Fifteenth International Conference on Machine Learning, Madison, Wisconsin, USA: Morgan Kaufmann, 1998.

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