Spatially Structured Evolutionary Algorithms: Graph Degree, Population Size and Convergence Speed

摘要

An evolutionary algorithm (EA) is said to be spatially structured when its individuals are arranged in an incomplete graph and interact only with their neighbors. Previous studies argue that spatially structured EAs are less likely to converge prematurely to local optima. Furthermore, they have been initially designed for distributed computing and it is often claimed that their parallelization is simpler than the equivalent non-structured algorithm. However, most of the empirical studies on spatially structured EAs use a predefined and fixed population size, whereas the full potential of this or any other any kind of EA can only be explored if the population size is properly set. This paper investigates optimal population sizes of spatially structured EAs (cellular EAs, in particular) and the relationship between that size, convergence speed and the degree of the structuring network. EAs structured by regular graphs with different degrees have been tested on different types of fitness landscapes. We conclude that in most cases graphs with low degree require smaller populations to converge consistently to global optima. However, if the population size is properly set, EAs structured by graphs with higher degrees not only converge to global optima with high probability, but also converge faster.