In this study, a novel promotive particle swarm optimizer with double hierarchical structures is proposed. It is inspired by successful mechanisms present in social and biological systems to make particles compete fairly. In the proposed method, the swarm is first divided into multiple independent subpopulations organized in a hierarchical promotion structure, which protects subpopulation at each hierarchy to search for the optima in parallel. A unidirectional communication strategy and a promotion operator are further implemented to allow excellent particles to be promoted from low-hierarchy subpopulations to high-hierarchy subpopulations. Furthermore, for the internal competition within each subpopulation of the hierarchical promotion structure, a hierarchical multiscale optimum controlled by a tiered architecture of particles is constructed for particles, in which each particle can synthesize a set of optima of its different scales. The hierarchical promotion structure can protect particles that just fly to promising regions and have low fitness from competing with the entire swarm. Also, the double hierarchical structures increase the diversity of searching. Numerical experiments and statistical analysis of results reported on 30 benchmark problems show that the proposed method improves the accuracy and convergence speed especially in solving complex problems when compared with several variations of particle swarm optimization.

中文翻译：

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具有双层次结构的促进粒子群优化器。

在这项研究中，提出了一种具有双层结构的新型促进粒子群优化器。它受到社会和生物系统中存在的使粒子公平竞争的成功机制的启发。在所提出的方法中，群体首先被分成多个独立的子种群，这些子种群以分层提升结构组织，保护每个层次的子种群以并行搜索最优值。进一步实施单向通信策略和提升算子，以允许优秀粒子从低层级子种群提升到高层级子种群。此外，对于分层晋升结构的每个子群体内部的竞争，为粒子构造了由粒子的分层结构控制的分层多尺度最优，其中每个粒子可以合成一组其不同尺度的最优。分层提升结构可以保护刚飞到有前途区域且适应度低的粒子免于与整个群体竞争。此外，双层次结构增加了搜索的多样性。对 30 个基准问题报告的结果进行数值实验和统计分析表明，与粒子群优化的几种变体相比，所提出的方法提高了精度和收敛速度，尤其是在解决复杂问题时。分层提升结构可以保护刚飞到有前途区域且适应度低的粒子免于与整个群体竞争。此外，双层次结构增加了搜索的多样性。对 30 个基准问题报告的结果进行数值实验和统计分析表明，与粒子群优化的几种变体相比，所提出的方法提高了精度和收敛速度，尤其是在解决复杂问题时。分层提升结构可以保护刚飞到有前途区域且适应度低的粒子免于与整个群体竞争。此外，双层次结构增加了搜索的多样性。对 30 个基准问题报告的结果进行数值实验和统计分析表明，与粒子群优化的几种变体相比，所提出的方法提高了精度和收敛速度，尤其是在解决复杂问题时。