Adaptive Particle Swarm Optimizer Combining Hierarchical Learning With Variable Population

Particle swarm optimizer (PSO) is an optimization technique that has been applied to solve various problems. In its variants, hierarchical learning and variable population are two commonly used learning strategies. The former is used to employ more potentially good particles to lead the swarm, which is very effective in the early search phase. However, in the later search phase, such mechanism impedes PSO's convergence. This work proposes an adaptive particle swarm optimizer combining hierarchical learning with variable population (PSO-HV), in which a heap-based hierarchy is first proposed to organize particles to hierarchically learn from the ones with better fitness in the same and upper levels. The levels of particles are determined and updated according to their current fitness in each iteration. Meanwhile, an adaptive variable population strategy is introduced and eliminates redundant particles based on the population's evolution state. In this way, the swarm is more explorative upon the hierarchical structure and improves its exploitation capability due to the variable population mechanism. Ten state-of-the-art PSO contenders, including two hierarchical ones and two variable population-based ones, are compared with the proposed method on 57 benchmark functions and the experimental results verify its effectiveness and efficiency.