A three-dimensional objective space (3DOS) optimization strategy using an enhanced multi-objective artificial bee colony (ABC) algorithm for the design optimization of layered radar absorbing material (LRAM) is presented in this study. The multi-objective exploitation ability of ABC is improved with regard to the convergence and diversity by integrating a pioneer Pareto (PP) solution to the onlooker bee phase, which is selected from the Pareto optimal set. Initially, the performance of PP-ABC is successfully verified by a comparison with ABC and the well-known multi-objective counterparts like particle swarm optimization (PSO) and differential evolution (DE) algorithms. The comparison is carried out through five multi-objective benchmark functions with respect to three favorable and reliable multi-objective indicators such as hypervolume (HV), HV ratio and Pareto sets proximity (PSP). The employed three objective functions to be the dimensions of 3DOS are weighted bandwidth-based total reflection coefficient involving sub-reflection waves of a wide oblique incident angular range 0$°$–75$°$, the total thickness and the number of layers. By using PP-ABC, a 3D designed LRAM operating at a large frequency band of 2–18 GHz is then designed for synchronously minimizing the three objective vectors by finding out the design variables: thickness and material types. Meanwhile, the material types of the proposed LRAM are optimally picked up from a composite material database with 51 specimens from 9 previously reported studies (51/9#database). In order to point out the effectiveness of the proposed 3DOS optimization strategy, three LRAMs are also compared with respective reported designs whose material type is selected from a database with 6 specimens (6/1#database). The results show that the proposed LRAMs are hence the global optimal designs in terms of all objective functions thanks to the proposed 3DOS optimization strategy based on PP-ABC.

本研究提出了一种使用增强型多目标人工蜂群（ABC）算法的三维目标空间（3DOS）优化策略，用于分层雷达吸收材料（LRAM）的设计优化。通过将先驱者帕累托（PP）解决方案集成到从帕累托最优集合中选出的旁观者蜜蜂阶段，可以提高ABC在融合和多样性方面的多目标开发能力。最初，PP-ABC的性能是通过与ABC和著名的多目标对等对象（如粒子群优化（PSO）和差分进化（DE）算法）进行比较而成功验证的。比较是通过五个多目标基准函数，针对三个有利且可靠的多目标指标（例如超量（HV），HV比和帕累托设定接近度（PSP）。用作3DOS维度的三个目标函数是基于加权带宽的总反射系数，其中包括宽斜入射角范围的子反射波0$°$–75$°$，总厚度和层数。通过使用PP-ABC，然后设计了一种3D设计的LRAM，该LRAM在2-18 GHz的较大频带上工作，通过找出设计变量：厚度和材料类型，来同步最小化三个目标矢量。同时，从9个先前报告的研究（51/9＃数据库）中的51个标本的复合材料数据库中，最佳地选择了建议的LRAM的材料类型。为了指出所提出的3DOS优化策略的有效性，还将三个LRAM与各自报告的设计进行了比较，这些设计的材料类型是从具有6个样本的数据库（6/1＃数据库）中选择的。