Year: 2005
Type: conference-paper
Abstract: Due to experimental evidence it is incontestable that crossover is essential for some fitness functions. However, theoretical results without assumptions are difficult. So-called real royal road functions are known where crossover is proved to be essential, i.e., mutation-based algorithms have an exponential expected runtime while the expected runtime of a genetic algorithm is polynomially bounded. However, these functions are artificial and have been designed in such a way that crossover is essential only at the very end (or at other well-specified points) of the optimization process.Here, a more natural fitness function based on a generalized Ising model is presented where crossover is essential throughout the whole optimization process. Mutation-based algorithms such as (μ+λ) EAs with constant population size are proved to have an exponential expected runtime while the expected runtime of a simple genetic algorithm with population size 2 and fitness sharing is polynomially bounded.
Author: Dirk Sudholt
Institution: TU Dortmund University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W2160241726