A gravitational search algorithm ( GSA ) uses gravitational force among individuals to evolve population. Though GSA is an effective population-based algorithm, it exhibits low search performance and premature convergence. To ameliorate these issues, this work proposes a multi-layered GSA called MLGSA. Inspired by the two-layered structure of GSA, four layers consisting of population, iteration-best, personal-best and global-best layers are constructed. Hierarchical interactions among four layers are dynamically implemented in different search stages to greatly improve both exploration and exploitation abilities of population. Performance comparison between MLGSA and nine existing GSA variants on twenty-nine CEC2017 test functions with low, medium and high dimensions demonstrates that MLGSA is the most competitive one. It is also compared with four particle swarm optimization variants to verify its excellent performance. Moreover, the analysis of hierarchical interactions is discussed to illustrate the influence of a complete hierarchy on its performance. The relationship between its population diversity and fitness diversity is analyzed to clarify its search performance. Its computational complexity is given to show its efficiency. Finally, it is applied to twenty-two CEC2011 real-world optimization problems to show its practicality.

中文翻译：

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用于函数优化和实际问题的多层重力搜索算法

引力搜索算法（GSA）利用个体之间的引力来演化种群。尽管GSA是一种有效的基于人口的算法，但它具有较低的搜索性能和过早的收敛性。为了改善这些问题，这项工作提出了一个称为MLGSA的多层GSA。受GSA两层结构的启发，构建了四层，分别是人口层，迭代最佳层，个人最佳层和全局最佳层。在不同的搜索阶段动态地实现了四层之间的分层交互，从而大大提高了人口的勘探和开发能力。MLGSA和九种现有GSA变体在29个CEC2017测试功能（低，中和高尺寸）之间的性能比较表明，MLGSA是最具竞争力的一种。还将它与四个粒子群优化变体进行比较，以验证其出色的性能。此外，讨论了层次结构交互作用的分析，以说明完整层次结构对其性能的影响。分析了其种群多样性与适应性多样性之间的关系，以阐明其搜索性能。给出其计算复杂度以显示其效率。最后，将其应用于22个CEC2011实际优化问题中以证明其实用性。给出其计算复杂度以显示其效率。最后，将其应用于22个CEC2011实际优化问题中以证明其实用性。给出其计算复杂度以显示其效率。最后，将其应用于22个CEC2011实际优化问题中以证明其实用性。