Recursive Hierarchical Particle Swarm Optimization for Global Optima

The solution space is segmented into multiple regions through hierarchical decomposition. The optimization process is divided into multiple levels where each level explores a different scale of the solution space. This segmentation allows the algorithm to escape local optima by exploring multiple regions systematically rather than being trapped in a single region.

The algorithm implements nested optimization loops where inner PSO runs are contained within outer PSO runs. The inner loops explore local regions with fine granularity while outer loops explore broader regions. This nesting structure enables the algorithm to maintain both local exploitation capability and global exploration capability simultaneously.

The algorithm performs preliminary exploration at coarser levels before conducting detailed searches at finer levels. By identifying promising regions in advance through outer-loop exploration, the algorithm can focus computational resources on those specific regions in inner loops, avoiding wasted computation in unpromising areas while still maintaining comprehensive coverage.

The algorithm dynamically adjusts the search scope and particle swarm parameters at different hierarchical levels. Outer loops use larger search spaces with fewer particles for broad exploration, while inner loops use smaller search spaces with more particles for detailed exploitation. This dynamic adaptation optimizes the balance between exploration and exploitation at each stage.