Reasons for premature convergence of self-adapting mutation rates

To self-adapt ([Schwefel, 1981], [Fogel et al., 1991]) a search parameter, rather than fixing the parameter globally before search begins the value is encoded in each individual along with the other genes. This is done in the hope that the value will then become adapted on a per-individual basis. While this mechanism is very powerful and in some cases essential to achieving good search performance, the dynamics of the adaptation of such traits are often complex and difficult to predict. This paper presents a case study in which self-adapting mutation rates were found to quickly drop below the threshold of effectiveness, bringing productive search to a premature halt. We identify three conditions that may in practice lead to such premature convergence of self-adapting mutation rates. The third condition is of particular interest, involving an interaction between self-adaptation and a process referred to here as "implicit self-adaptation". Our investigation ultimately underlines a key aspect of population-based search: namely, how strongly search is directed toward finding solutions that are not just of high quality, but those which also produce other high quality solutions when subjected to the chosen variation process.