Cooperative differential evolution framework with utility-based adaptive grouping for large-scale optimization

Decomposing the large-scale problem into small-scale subproblems and optimizing them cooperatively are critical steps for solving large-scale optimization problem. This article proposes a cooperative differential evolution with utility-based adaptive grouping. The problem decomposition is adaptively executed by the two mechanisms of circular sliding controller and relation matrix, which consider the variable interactions on the basis of the short-term and long-term utilities, respectively. The circular sliding controller provides baselines for the subproblem optimizer. The size of the sliding window and the sliding speed in the controller are adjusted adaptively so that the variables with higher activeness can be optimized extensively. The relation matrix-based grouping strategy enables interacted variables to be grouped into the same subproblem with higher probabilities. The novelty is that decomposition is conducted as the optimization process without extra computational burden. For subproblem optimization, we use a self-adaptive differential evolution operator that adaptively adjusts the parameters to guide the search to the optimum solutions of the subproblems. Experiments on the benchmarks of CEC2008 and CEC2010, and practical problems show the effectiveness of the proposed algorithm.