Pareto Explorer for Finding the Knee for Many Objective Optimization Problems

Optimization problems where several objectives have to be considered concurrently arise in many applications. Since decision-making processes are getting more and more complex, there is a recent trend to consider more and more objectives in such problems, known as many objective optimization problems (MaOPs). For such problems, it is not possible any more to compute finite size approximations that suitably represent the entire solution set. If no users preferences are at hand, so-called knee points are promising candidates since they represent at least locally the best trade-off solutions among the considered objective values. In this paper, we extend the global/local exploration tool Pareto Explorer (PE) for the detection of such solutions. More precisely, starting from an initial solution, the goal of the modified PE is to compute a path of evenly spread solutions from this point along the Pareto front leading to a knee of the MaOP. The knee solution, as well as all other points from this path, are of potential interest for the underlying decision-making process. The benefit of the approach is demonstrated in several examples.