A new quantifying crossover with ternary representation

Liang Ming, Yuping Wang, Yiu Ming CHEUNG

Research output: Contribution to journalJournal articlepeer-review


As a fundamental operator in genetic algorithms (GAs), crossover may not only make an existing schema survive, but also construct a new one from other existing schemata. Unfortunately, the existing schema theorems do not exactly quantify the positive effects of schema construction by a crossover. Consequently, they cannot well characterize the evolution of a schema. In this paper, a new ternary representation is proposed through which the survival and construction of a schema for any crossover operator can be distinguished easily. Subsequently, the probabilities that a schema will survive and be constructed from other schemata can be estimated for an arbitrary crossover. As a result, we present four new schema theorems, through which the survival and construction abilities of different crossover operations are easier to be compared. Moreover, these results generalize the existing schema theorems.

Original languageEnglish
Pages (from-to)343-360
Number of pages18
JournalIntelligent Automation and Soft Computing
Issue number3
Publication statusPublished - Jan 2009

Scopus Subject Areas

  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Artificial Intelligence

User-Defined Keywords

  • Genetic Algorithrn
  • Schema Construction
  • Schema Survival
  • Schema Theorem


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