Recently, gene-culture coevolutionary multitasking, i.e., the multifactorial evolutionary algorithm (MFEA and MFEA-II), has become increasingly popular in the area of evolutionary computation. One of the most fascinating aspects of the MFEA is that it can obtain better optimization performance by exploiting underlying complementarities and/or commonalities between different tasks synchronously. In this area, tournament selection is an important ingredient in the nondominated sorting genetic algorithm II (NSGA-II) not only for a single task but also in multitasking. When it is used in the NSGA-II, it mainly concerns individual selection for a single task. However, the selection mechanism has to be reformulated in evolutionary multitasking with different cultural characteristics. Unfortunately, until now, there has been no relevant research discussing tournament selection mechanisms in gene-culture coevolutionary multitasking. Accordingly, to clarify its selection mechanism by fully considering the cultural characteristics built into multitasking, in this paper, a novel tournament selection method based on multilayer cultural characteristics in evolutionary multitasking is proposed. In the presented method, the concept of overall rank (OR) representing a comprehensive cultural indicator is given based on the rank of the Pareto front (PF) and crowding distance. Then, the each task, PF and OR of every individual are defined as the multilayer cultural characteristics that determine the selection order. Finally, the new selection mechanism is stated clearly based on the three proposed binary tournament selection methods. The efficacy of the developed mechanism is demonstrated through testing on several benchmark functions as well as aluminum electrolysis process design in evolutionary multitasking.

最近，基因-文化协同进化多任务，即多因子进化算法（MFEA 和 MFEA-II），在进化计算领域变得越来越流行。MFEA 最吸引人的方面之一是它可以通过同步利用不同任务之间的潜在互补性和/或共性来获得更好的优化性能。在这个领域，锦标赛选择是非支配排序遗传算法 II (NSGA-II) 的重要组成部分，不仅适用于单任务，而且适用于多任务。在 NSGA-II 中使用时，主要涉及单个任务的个体选择。然而，选择机制必须在具有不同文化特征的进化多任务中重新制定。不幸的是，直到现在，目前还没有相关研究讨论基因-文化协同进化多任务中的锦标赛选择机制。因此，为了充分考虑多任务中的文化特征，阐明其选择机制，本文提出了一种基于进化多任务中多层文化特征的新型锦标赛选择方法。在所提出的方法中，基于帕累托前沿 (PF) 的等级和拥挤距离给出了代表综合文化指标的整体等级 (OR) 的概念。然后，将每个人的每个任务、PF 和 OR 定义为决定选择顺序的多层文化特征。最后，基于提出的三种二元锦标赛选择方法，清楚地说明了新的选择机制。