  This work proposes a novel approach to evaluate and analyze the behavior of
multi-population parallel genetic algorithms (PGAs) when running on a cluster
of multi-core processors. In particular, we deeply study their numerical and
computational behavior by proposing a mathematical model representing the
observed performance curves. In them, we discuss the emerging mathematical
descriptions of PGA performance instead of, e.g., individual isolated results
subject to visual inspection, for a better understanding of the effects of the
number of cores used (scalability), their migration policy (the migration gap,
in this paper), and the features of the solved problem (type of encoding and
problem size). The conclusions based on the real figures and the numerical
models fitting them represent a fresh way of understanding their speed-up,
running time, and numerical effort, allowing a comparison based on a few
meaningful numeric parameters. This represents a set of conclusions beyond the
usual textual lessons found in past works on PGAs. It can be used as an
estimation tool for the future performance of the algorithms and a way of
finding out their limitations.
