A formal approach to deriving factored evolutionary algorithm architectures

Factored Evolutionary Algorithms (FEA) are a class of evolutionary search-based optimization algorithms that have been applied successfully to various problems, such as training neural networks and performing abductive inference in graphical models. An FEA is unique in that it factors the objective function by creating overlapping subpopulations that optimize over a subset of variables of the function. One consideration in using an FEA is determining the appropriate factor architecture, which determines the set of variables each factor will optimize. In this paper, we provide a formal method for deriving factor architectures and give theoretical justification for its use. Specifically, we utilize factor graphs of variables in probabilistic graphical models as a way to define factor architectures. We also prove how a class of problems, like maximizing NK landscapes, are equivalent to abductive inference in probabilistic graphical models. This allows us to take a factor graph architecture and apply it to NK landscapes and a set of commonly used benchmark functions. Finally, we show empirically that using the factor graph representation to derive factors for FEA provides the best performance in the majority of cases studied.