**6. Acknowledgments**

The authors would like to thank Dr. Alberto Moraglio for his encouragement and valuable comments in improving this study. This work was supported by the Research and Development of Advanced Weather Technology of National Institute of Meteorological Research (NIMR) of Korea in 2011.

#### **7. References**


14 Will-be-set-by-IN-TECH

In this chapter, we tried to analyze distinct roles of crossover and mutation when using real encoding in genetic algorithms. We investigated the bias of crossover and mutation. From this investigation, we could know that extended crossover and mutation can reduce the inherent

We also studied the functions of crossover and mutation operators through experiments for various combinations of both operators. From these experiments, we could know that extended-box crossover is good in the case of using only crossover without mutation. However, it is possible to surpass the performance of extended-box crossover using well-designed combination of crossover and mutation. In the case of other crossover operators, not only the function of perturbation but also that of fine tuning by mutation is

There are many other test functions defined on real domains. We conducted experiments with limited test functions. We may obtain more reliable conclusions through experiments with more other functions. So, more extended experiments on more various test functions are needed for future work. We may also find other useful properties from those empirical study.

The authors would like to thank Dr. Alberto Moraglio for his encouragement and valuable comments in improving this study. This work was supported by the Research and Development of Advanced Weather Technology of National Institute of Meteorological

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**1. Introduction**

of GEAs.

Most of the real-world problems could be encoded by different representations, but genetic and evolutionary algorithms (GEAs) may not be able to successfully solve the problems based on their phenotypic representations, unless we use some problem-specific genetic operators. Therefore, a proper genetic representation is necessary when using GEAs on the real-world

**A Splicing/Decomposable Binary Encoding** 

**and Its Novel Operators for Genetic and** 

**Evolutionary Algorithms** 

*Macau University of Science and Technology* 

**5**

Yong Liang

*China* 

A large number of theoretical and empirical investigations on genetic representations were made over the last decades. Earlier work (Goldberg, 1989c; Liepins & Vose, 1990) has shown that the behavior and performance of GEAs is strongly influenced by the representation used. As a result many genotypic representations were made for proper GEAs searching. Among of them, the binary, integer, real-valued, messy and tree structure representations are the most

To investigate the performance of the genetic representations, originally, the schema theorem proposed by Holland (1975) to model the performance of GEAs to process similarities between binary bitstrings. Using the definition of the building blocks (BBs) as being highly fit solutions to sub-problems, which are decomposed by the overall problem, the building block hypothesis (Goldberg, 1989c) states that GEAs mainly work due to their ability to propagate short, low order and highly fit BBs. During the last decade, (Thierens, 1995; Miller, 1996; Harik, 1997; Sendhoff, 1997; Rothlauf, 2002) developed three important elements towards a general theory of genetic representations. They identified that redundancy, the scaling of Building Blocks (BBs) and the distance distortion are major factors that influence the

A genetic representation is denoted to be redundant if the number of genotypes is higher than the number of phenotypes. Investigating redundant representation reveals that give more copies to high quality solutions in the initial population result in a higher performance of GEAs, whereas encodings where high quality solutions are underrepresented make a problem more difficult to solve. Uniform redundancy, however, has no influence on the performance

The order of scaling of a representation describes the different contribution of the BBs to the individual's fitness. It is well known that if the BBs are uniformly scaled, GEAs solve all BBs

problems (Goldberg, 1989; Liepins, 1990; Whitley, 2000; Liang, 2011).

performance of GEAs with different genetic representations.

important and widely used by many GEAs.

