A novel tournament selection based on multilayer cultural characteristics in gene-culture coevolutionary multitasking

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.