Region of interest based non-dominated sorting genetic algorithm-II

Evolutionary multi-objective optimization plays a vital role in solving many complex real-world optimization problems. Numerous approaches have been
proposed over the years, and popular methods such as NSGA and its variants incorporate non-dominated sorting selection into evolutionary genetic
algorithms to extract competing Pareto-optimal solutions from all over the objective space. However, in applications where the decision-maker is interested
in a region of interest, a global optimization wastes effort to find irrelevant solutions outside of the preferred region. In this work, we propose an approach
named ROI-NSGA-II to limit the optimization effort to a region of interest defined by the boundaries provided by the decision-maker. The ROI-NSGA-II invites
the classical NSGA-II algorithm into the desired region using a modified dominance relation and conquers solutions within this region using a modified
crowding distance based selection. The effectiveness of our approach is demonstrated on a set of benchmark problems with up to ten objectives and a
real-world application, and the results are compared to a state-of-the-art R-NSGA-II.