Modeling and convergence analysis of distributed coevolutionary algorithms

A theoretical foundation is presented for modeling and convergence analysis of a class of distributed coevolutionary 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 a class of centralized evolutionary algorithms in terms of construction and evolution of sampling distributions over the feasible space. Next, this foundation is extended to develop a model for a class of distributed coevolutionary algorithms. Convergence and convergence rate analyses are pursued for basic classes of objective functions. Our theoretical investigation reveals that for certain unimodal and multimodal objectives, we can expect these algorithms to converge at a geometrical rate. The distributed coevolutionary algorithms are of most interest from the perspective of their performance advantage compared to centralized algorithms, when they execute in a network environment with significant local access and internode communication delays. The relative performance of these algorithms is therefore evaluated in a distributed environment with realistic parameters of network behavior.

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