Modeling and convergence analysis of distributed co-evolutionary algorithms

A theoretical foundation is presented for modeling and convergence analysis of distributed co-evolutionary algorithms applied to optimization problems in which the variables are partitioned among p nodes. An evolutionary algorithm at each of the p nodes performs a local evolutionary search based on its own set of primary variables, and the secondary variable set at each node is clamped during this phase. An infrequent intercommunication between the nodes updates the secondary variables at each node. The local search and intercommunication phases alternate, resulting in a cooperative search by the p nodes. First, we specify a theoretical basis for centralized evolutionary algorithms in terms of construction and evolution of sampling distributions over the feasible space. Next, this foundation is extended to develop a general model of distributed co-evolutionary algorithms. Convergence and convergence rate analyses are pursued for certain basic classes of objective functions. Also considered are relative computational delays of the centralized and distributed algorithms when they are implemented in a network environment.