A Theoretical Development and Analysis of Jumping Gene Genetic Algorithm

Recently, gene transpositions have gained their power and attentions in computational evolutionary algorithm designs. In 2004, the Jumping Gene Genetic Algorithm (JGGA) was first proposed and two new gene transposition operations, namely, cut-and-paste and copy-and-paste, were introduced. Although the outperformance of JGGA has been demonstrated by some detailed statistical analyses based on numerical simulations, more rigorous theoretical justification is still in vain. In this paper, a mathematical model based on schema is derived. It then provides theoretical justifications on why JGGA is superiority in searching, particularly when it is applied to solve multiobjective optimization problems. The studies are also further verified by solving some optimization problems and comparisons are made between different optimization algorithms.