A ranking method based on the R2 indicator for many-objective optimization

In recent years, the development of selection mechanisms based on performance indicators has become an important trend in algorithmic design. Hereof, the hypervolume has been the most popular choice. Multi-objective evolutionary algorithms (MOEAs) based on this indicator seem to be a good choice for dealing with many-objective optimization problems. However, their main drawback is that such algorithms are typically computationally expensive. This has motivated some recent research in which the use of other performance indicators has been explored. Here, we propose an efficient mechanism to integrate the R2 indicator to a modified version of Goldberg's nondominated sorting method, in order to rank the individuals of a MOEA. Our proposed ranking scheme is coupled to two different search engines, resulting in two new MOEAs. These MOEAs are validated using several test problems and performance measures commonly adopted in the specialized literature. Results indicate that the proposed ranking approach gives rise to effective MOEAs, which produce results that are competitive with respect to those obtained by three well-known MOEAs. Additionally, we validate our resulting MOEAs in many-objective optimization problems, in which our proposed ranking scheme shows its main advantage, since it is able to outperform a hypervolume-based MOEA, requiring a much lower computational time.