The influence of different coding schemes on the computational complexity of genetic algorithms in function optimization

Abstract

Function optimization is a typical application domain for genetic algorithms (GAs). Traditionally, GAs work on bit strings of fixed total length l. Significant research has been done on designing and analyzing different coding schemes, of which Gray coding is one of the most used forms. Surprisingly little attention has been devoted to directly encoding the parameters by floating-point values provided by the programming language. This form of coding has been in favor in evolution strategy. This paper discusses several coding schemes and derives the resulting complexity when optimizing functions with n independent continuous parameters. It turns out that the direct use of real-valued parameters has certain advantages. First of all, it speeds up convergence by a factor of up to l ^q −1, where q denotes the number of bits per parameter. Furthermore, the use of real-valued parameters allows for more flexibility in designing the mutation operator and eases many implementation issues. The theoretical analysis presented here strongly suggests that real-valued parameters (implemented by floating point values provided by the programming language) should be the best choice when applying a GA in the field of function optimization.