Set Representation Using Schemata and its Constructing Method from Population in GA
Naohiko Hanajima, Mitsuhisa Yamashita and Hiromitsu Hikita
Dept. of Mechanical Systems Engineering, Muroran Institute of Technology, 27-1, Mizumoto-cho, Muroran, Hokkaido 050-8585, Japan
When we invoke genetic algorithms (GAs), we retrieve enormous numbers of individuals. If we can construct, simply, a set having some sense from individuals, it would make engineering applications easier. Schemata in GAs is a simple forms representing such a set. We define modified schemata where instances of a schema represent a continuous region assuming that the GA phenotype is real vector space. We induce expected and maximum numbers of schemata required to represent any continuous region. We show ways to construct a schema set from individuals in GA, constructing a Pareto optimum set on multiobjective optimization theory.
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