On Takeover Times in Spatially Structured Populations: Array and Ring

The takeover time is the expected number of iterations of some selection method until a population consists entirely of copies of the best individual under the assumption that only one best individual is contained in the initial population. This quantity may be used to assess and compare the ‘selection pressures’ of selection methods used in evolutionary algorithms. Here, the notion is generalized from spatially unstructured to structured populations. Lower bounds are derived for arbitrary connected neighborhood structures, lower and upper bounds for array-like structures, and an exact closed form expression if the neighborhood structure is a ring.