A multi-layered gravitational search algorithm for function optimization and real-world problems

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.