Based on mating and environmental selections employed, multi-objective evolutionary algorithms (MOEAs) are classified as Pareto-based, decomposition-based and indicator-based approaches that are associated with their own advantages and disadvantages. To benefit from the advantages of different MOEAs, we propose an ensemble framework (ENMOEA) in which mating and environmental selections of diverse MOEAs are combined. ENMOEA is a single-population competitive ensemble, where resource allocation to individual mating operators is done adaptively. In addition, ENMOEA employs a two-level environmental selection where constituent environmental selection operators are first applied to label solutions as “selected” and “non-selected”. Solutions “selected” by most operators are preferred for future evolution. An external archive is employed to facilitate effective usage of function evaluations and achieve a better comprise between convergence and diversity. To demonstrate generality of ENMOEA, we developed two variants: 1) specific case (ENMOEA_S - combines different Pareto-based MOEAs) and 2) general case (ENMOEA_G - combines Pareto-based, indicator-based and decomposition-based MOEAs). From simulation results on various test suites (DTLZ, WFG and 16 real-world problems), it is evident that ENMOEA is robust to the parameters of the constituent algorithms. In addition, it evident that the effectiveness of ensemble improves with the diversity of the constituent algorithms.

基于交配和使用的环境选择，多目标进化算法（MOEA）被分类为基于帕累托，分解和指标的方法，这些方法都具有各自的优点和缺点。为了从不同的MOEA的优势中受益，我们提出了一个集合框架（ENMOEA），其中将多种MOEA的交配和环境选择结合在一起。ENMOEA是一个单一人口的竞争性合奏，其中自适应地分配给各个交配运营商的资源。此外，ENMOEA采用两级环境选择，其中首先将组成环境选择操作员应用于标签解决方案，包括“选定”和“未选定”。大多数运营商“选择”的解决方案是未来发展的首选。外部档案库被用来促进功能评估的有效使用，并在融合和多样性之间实现更好的融合。为了证明ENMOEA的通用性，我们开发了两种变体：1）特定案例（ENMOEA_S-结合不同的基于Pareto的MOEA）和2）一般情况（ENMOEA _G-结合基于Pareto，基于指标和基于分解的MOEA）。从各种测试套件（DTLZ，WFG和16个实际问题）的仿真结果来看，很明显ENMOEA对组成算法的参数具有鲁棒性。另外，很明显，集成算法的有效性随着组成算法的多样性而提高。