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Keywords: grammatical evolution, two-dimensional chromosome, function identification problem.

Summary

Grammatical evolution (GE) is one of the evolutionary computational methods. The aim of the algorithm is to find the function and the program or the program segment which satisfies the desired objective. Although GE is designed for the same objective as genetic programming (GP), the algorithms are different. Genetic programing represents computer programs as tree structures and then, evolves the tree structures toward the programs or functions desired by applying genetic operators. The genetic operators in the GP often generate the tree structures which are invalid in the syntax meaning of functions or programs. To overcome this difficulty, GE uses the translation rules defined in the Backus Naur Form (BNF). The original GE starts from the definition of the BNF syntax definition which translates chromosomes to functions or programs. Chromosome in a binary number is translated to that in a decimal number for every bit. The rules are selected from the BNF syntax list according to the remainder of the decimal numbers with respect to the total number of candidate rules. The traditional grammatical evolution still has one difficultly. When, in the case of a discontinuous function such as a step function, the function should be defined with the help of the conditional sentences, the original GE cannot keep explicitly the construction of the conditional sentences in the genotype during the search process. The use of the genetic operators destroys the good schemata in the population and therefore, the GE convergence property is not good for the problems. To overcome this difficulty, we adopt the two-dimensional chromosome. The conditional sentence is composed of the conditional statements and the executing statements. In the two-dimensional chromosome, the conditional statements, the executing statements and their numbers are defined in the different rows of the two-dimensional structure. The present algorithm is applied to the function identification problem of the step function in order to discuss the effectiveness of the algorithm.

The remaining part of this paper is as follows. The original GE and the improved GE are explained then numerical results are given. Finally, the discussion is summarized.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 103 PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON SOFT COMPUTING TECHNOLOGY IN CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING Edited by: Y. Tsompanakis Paper 17 Improvement of Chromosome Definition in Grammatical Evolution H. Sugiura¹, Y. Wakita¹ and E. Kita^1,2 ¹Nagoya University, Nagoya, Japan. ²Kobe University, Kobe, Japan doi:10.4203/ccp.103.17 purchase the full-text of this paper Full Bibliographic Reference for this paper H. Sugiura, Y. Wakita, E. Kita, "Improvement of Chromosome Definition in Grammatical Evolution", in Y. Tsompanakis, (Editor), "Proceedings of the Third International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 17, 2013. doi:10.4203/ccp.103.17 Keywords: grammatical evolution, two-dimensional chromosome, function identification problem. Summary Grammatical evolution (GE) is one of the evolutionary computational methods. The aim of the algorithm is to find the function and the program or the program segment which satisfies the desired objective. Although GE is designed for the same objective as genetic programming (GP), the algorithms are different. Genetic programing represents computer programs as tree structures and then, evolves the tree structures toward the programs or functions desired by applying genetic operators. The genetic operators in the GP often generate the tree structures which are invalid in the syntax meaning of functions or programs. To overcome this difficulty, GE uses the translation rules defined in the Backus Naur Form (BNF). The original GE starts from the definition of the BNF syntax definition which translates chromosomes to functions or programs. Chromosome in a binary number is translated to that in a decimal number for every bit. The rules are selected from the BNF syntax list according to the remainder of the decimal numbers with respect to the total number of candidate rules. The traditional grammatical evolution still has one difficultly. When, in the case of a discontinuous function such as a step function, the function should be defined with the help of the conditional sentences, the original GE cannot keep explicitly the construction of the conditional sentences in the genotype during the search process. The use of the genetic operators destroys the good schemata in the population and therefore, the GE convergence property is not good for the problems. To overcome this difficulty, we adopt the two-dimensional chromosome. The conditional sentence is composed of the conditional statements and the executing statements. In the two-dimensional chromosome, the conditional statements, the executing statements and their numbers are defined in the different rows of the two-dimensional structure. The present algorithm is applied to the function identification problem of the step function in order to discuss the effectiveness of the algorithm. The remaining part of this paper is as follows. The original GE and the improved GE are explained then numerical results are given. Finally, the discussion is summarized. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £42 +P&P)
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