Hierarchical importance sampling instead of annealing

This paper proposes a novel method, hierarchical importance sampling (HIS), which can be used instead of converging the population for evolutionary algorithms based on probabilistic models (EAPM). In HIS, multiple populations are simulated simultaneously so that they have different diversities. This mechanism allows HIS to obtain promising solutions with various diversities. Experimental comparisons between HIS and the annealing (i.e., general EAPM) have revealed that HIS outperforms the annealing when applying to a problem of a 2D Ising model, which have many local optima. Advantages of HIS can be summarized as follows: (1) Since populations do not need to converge and do not change rapidly, HIS can build probability models with stability; (2) Since samples with better cost function values can be used for building probability models in HIS, HIS can obtain better probability models; (3)HIS can reuse historical results, which are normally discarded in the annealing.