A Note on Usefulness of Geometrical Crossover for Numerical Optimization Problems

Numerical optimization problems enjoy a signi cant popularity in evolutionary computation community; all major evolutionary techniques (genetic algorithm, evolution strategies, evolutionary programming) have been applied to these problems. However, many of these techniques (as well as other, classical optimization methods) have di culties in solving some real-world problems which include non-trivial constraints. For such problems, very often the global solution lies on the boundary of the feasible region. Thus it is important to investigate some problem-speci c operators, which search this boundary in an e cient way. In this study we discuss a new experimental evidence on usefulness of so-called geometrical crossover, which might be used for a boundary search for particular problems. This operator enhances also the e ectiveness of evolutionary algorithms (based on oating point representation) in a signi cant way.