Hierarchical information tree

Global optimization of multi-variable functions has been challenging because early algorithms often lead to search inefficiencies or trapped situations at local minima. To solve these problems, inspired by complex hierarchical structures in human societies, we propose a set of principles as a blueprint of a hierarchical information tree (HIT) algorithm with multiple layers. Specifically, we give up the concept of inertia and velocity in particle swarm optimization (PSO) and adopt a highly stochastic method to superimpose current best information at different layers of the tree to guide the next search, slow down the propagation of global best information by designing and tuning of information flow, and enhance the collision checking efficiency among agents by the fractal nature of the tree. Next, by using Lennard-Jones (LJ) potential containing 48 variables with random starting configurations as a benchmark, we find that HIT successfully identifies the global best configuration in 97.5% of the runs within 50000 steps. In contrast, PSO with the same number of agents fails in 86% of the runs. Additionally, HIT is successful for the majority of runs in the Schwefel function with 5 variables, while PSO fails over 95% of times. Also, HIT finds the most stable reconstructions of Si surface and optimizes Ackley function. Additionally, HIT only contains a few critical tuning parameters and may easily be adaptable for other problems. Based on our statistical analysis, one explanation for the superior efficiency of HIT may be attributed to by an inherent emerging phenomenon of short-term and long-term memory. • A global searching algorithm with multi-agents imitates social hierarchy systems. • It optimizes a 32-atom LJ bulk, surface, Schwefel and Ackley, challenging for PSO. • Inaction and superposition principles with stochastic sampling are foundations. • Collision-checking and information flow are implemented to enhance diversity. • Short/Long-term memory are obtained by agents at different hierarchy.