Finding a preferred diverse set of Pareto-optimal solutions for a limited number of function calls

Evolutionary Multi-objective Optimization aims at finding a diverse set of Pareto-optimal solutions whereof the decision maker can choose the solution that fits best to her or his preferences. In case of limited time (of function evaluations) for optimization this preference information may be used to speed up the search by making the algorithm focus directly on interesting areas of the objective space. The R-NSGA-II algorithm [1] uses reference points to which the search is guided specified according to the preferences of the user. In this paper, we propose an extension to R-NSGA-II that limits the Pareto-fitness to speed up the search for a limited number of function calls. It avoids to automatically select all solutions of the first front of the candidate set into the next population. In this way non-preferred Pareto-optimal solutions are not considered thereby accelerating the search process. With focusing comes the necessity to maintain diversity. In R-NSGA-II this is achieved with the help of a clustering algorithm which keeps the found solutions above a minimum distance ε. In this paper, we propose a self-adaptive ε approach that autonomously provides the decision maker with a more diverse solution set if the found Pareto-set is situated further away from a reference point. Similarly, the approach also varies the diversity inside of the Pareto-set. This helps the decision maker to get a better overview of the available solutions and supports decisions about how to adapt the reference points.