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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. [ABSTRACT FROM AUTHOR]