HPDE: A dynamic Hierarchical Population based Differential Evolution with novel diversity metric

Abstract

Differential Evolution (DE) is one of the most effective methods for single-objective numerical optimization, however, the former state-of-the-art DE variants ignore the huge differences among the individuals in the population. To take full advantage of different individuals in the population, in this paper, a dynamic Hierarchical Population based Differential Evolution (HPDE) with novel diversity metric is proposed, and the HPDE algorithm has the following innovations: Firstly, the individuals in the hierarchical population are dynamically divided into two layers, the layer of elites, and the layer of ordinary individuals. Moreover, the ordinary layer individuals are further divided into secondary elites and inferior individuals. The individuals in the two layers employed different mutation strategies and the corresponding parameter control schemes. Secondly, a novel hierarchical population based mutation strategy is firstly proposed in our HPDE algorithm and the individuals in the elite layer employ the novel mutation strategy aiming at scouting the landscape of the objective while the ordinary individuals employ an improved “DE/target-pbest/1/bin” strategy aiming at getting a better balance between exploration and exploitation of the solution space. Thirdly, a Novel Parameter Control technique, namely NPC technique, is employed in the adaptation of control parameters during the evolution. Fourthly, a new metric of population diversity is proposed and premature convergence can be avoided by maintaining better population diversity. To evaluate the performance of our HPDE algorithm, intensive experiments are conducted on 88 benchmark functions from the CEC2013, CEC2014 and CEC2017 test suites, and the results show the competitiveness of our HPDE with six recent state-of-the-art DE variants, e.g. it obtained 28 similar or better performance improvements out of the total 30 benchmarks on 30D optimization in comparison with the winner algorithm, the LSHADE algorithm, of the CEC2014 competition and it also obtained 19 similar or better performance improvements out of the total 30 benchmarks on 30D optimization in comparison with the winner DE variant, the jSO algorithm, of the CEC2017 competition. Furthermore, the novel HPDE algorithm is utilized to estimate the parameters of the photovoltaic model, and the experiment results support its superiority as well.