Hierarchical differential evolution algorithm combined with multi-cross operation

In expert systems, complex optimization problems are always characterized by nonlinearity, nonconvexity, multi-modality, discontinuity, and high dimensionality. Although classical optimization algorithms are mature, they readily fall into a local optimum. The differential evolution (DE) algorithm has been successfully applied to solve numerous problems with expert systems. However, balancing the global and local search capabilities of the DE algorithm remains an open issue and has attracted significant research attention. Thus, a hierarchical heterogeneous DE algorithm that incorporates multi-cross operation (MCO) is proposed in this article. In the proposed algorithm, success-history-based adaptive DE (SHADE) is implemented in the bottom layer, while MCO is implemented in the top layer. The MCO search is based on the SHADE results, but its search results do not affect the bottom layer. First-order stability analyses conducted for the presented MCO showed that the individual positions are expected to converge at a fixed point in the search space. The accuracy and convergence speed of the proposed algorithm were also experimentally compared with those of eight other advanced particle swarm optimization techniques and DE variants using benchmark functions from CEC2017. The proposed algorithm yielded better solution accuracy for 30- and 50-dimensional problems than the other variants, and although it did not provide the fastest convergence for all of the functions, it ranked among the top three for the unimodal and simple multimodal functions and achieved fast convergence for the other functions. (C) 2019 Elsevier Ltd. All rights reserved.