Reference Point Based NSGA-III for Preferred Solutions

The recent advances in evolutionary many-objective optimization (EMOs) have allowed for efficient ways of finding a number of diverse trade-off solutions in three to 15-objective problems. However, there are at least two reasons why the users are, in some occasions, interested in finding a part, instead of the entire Pareto-optimal front. First, after analyzing the obtained trade-off solutions by an EMO algorithm, the user may be interested in concentrating in a specific preferred region of the Pareto-optimal front, either to obtain additional solutions in the region of interest or to investigate the nature of solutions in the preferred region. Second, the user may already have a well-articulated preference among objectives and is straightaway interested in finding preferred solutions. In this paper, we suggest a reference point based evolutionary many-objective optimization procedure for achieving both of these purposes. Additionally, we suggest an extended version of a previously proposed reference-point based evolutionary multi-objective optimization method. Our proposed procedures are capable of handling more than one reference point simultaneously. We demonstrate the working of our proposed procedures on a number of test and real-world problems. The results are encouraging and suggest the use of the concept to other evolutionary many-objective optimization algorithms for further study.