Adapting binary fitness functions in Genetic Algorithms

• Authors: Ronald C. Linton
• Venue: ACM-SE 42 Proceedings of the 42nd annual Southeast regional conference
• Year: 2004

Recent applications of Genetic Algorithms (GAs) in the search for specimens of interesting discrete mathematical objects have suggested that GA convergence time can be improved by adapting fitness function components on the fly. In particular, it is known that if such fitness functions F have the form F = Σk Fi where {Fi} is a set of fitness functions associated with properties {Pi} that collectively define the search problem, then we can improve GA performance by defining a related fitness function F' as follows: if each Fi can be normalized so that c is a solution if and only if Fi(c) = 1, then we can introduce coefficients {αi}, where αi 0 and Σk αi = 1, and then define F' = Σk αiFi. With this definition, c is a solution for F if and only if c is a solution for F'. Furthermore, convergence of the GA for F' can be improved by modifying the coefficients {αi} dynamically throughout the GA run. In this paper we show that similar improvements in convergence times can also be obtained for a broad category of GA search problems whose fitness functions are defined on binary strings of fixed length.