R. A. Caruana and J. D. Schaffer. Representation and hidden bias: Gray versus binary coding for genetic algorithms. In Proceedings of the Fifth International Conference on Machine Learning, pages 153--162, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....cardinality codes. In keeping with the opinions of the majority of GA researchers and Goldberg s results, binary coding is used exclusively in this research. Even among binary codings, there are alternatives. Some authors advocate the use of Gray code as opposed to the more traditional base 2 [3, 11]. In the Gray code, any two adjacent base 10 integers differ at only one bit location. Adjacent base 10 integers represented in base 2, on the other hand, may differ at all bit locations. For example, 3 2 = 011 and 4 2 = 100. Gray code is therefore thought to be more compatible with the mutation ....

R. A. Caruana and J. D. Schaffer. Representation and hidden bias: Gray versus binary coding for genetic algorithms. In Proceedings of the Fifth International Conference on Machine Learning, pages 153--162, 1988.

....with one neighboring solution containing 29 zeros, and another containing 29 ones. It is not surprising that no bits are lost, since the final population contains both of these neighboring solutions. This form of bitwise diversity is not very useful. Some would argue for the use of Gray codes (Caruana Schaffer, 1988). One untested possibility is to revert to genotypic comparison, but to use the more complementary Gray codes. The primary argument for maintaining bitwise diversity is that such diversity will somehow prevent premature convergence. As suggested above, and as can be demonstrated with the use of ....

Caruana, R. A., & Schaffer, J. D. (1988). Representation and hidden bias: Gray versus binary coding for genetic algorithms. Proceedings of the Fifth International Conference on Machine Learning, 153-161.

....property expounded in the Subsection 3.6.1. 3.7.1. Problems in Continuous Search Spaces Two types of binary coding were mainly considered for representing a parameter x i belonging to a continuous interval S i = a i ; b i ] the binary code (Holland, 1975; Goldberg, 1989a) and the Gray code (Caruana et al. 1988). Prior to the codification, a transformation from the interval [a i ; b i ] to the set f0; 2 L i g (L i is the number of bits in the coding) is carried out. Then, the resultant elements are coded using one of the aforesaid codings. This transformation implies a discretization of the ....

....between them is too high (three changes for accessing from 011 to 100 are required) This access is improbable when using the mutation operator (it is of O(p 3 m ) Therefore, convergence is likely to be produced towards the element 011. This problem may be solved by using the Gray code (Caruana et al. 1988), but doing so introduces higher order nonlinearities with respect to recombination, which causes the degree of implicit parallelism to be reduced (Goldberg, 1989b) 3.7.2. Redundance When the binary alphabet is assumed for coding a parameter belonging to a finite discrete set with a cardinal ....

Caruana, R.A. & Schaffer, J.D. (1988). Representation and Hidden Bias: Gray versus Binary Coding for Genetic Algorithms. Proc. of the Fifth International Conference on Machine Learning, 153-162.

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