Finding knees in multi-objective optimization

Many real-world optimization problems have several, usually conflicting objectives. Evolutionary multi-objective optimization usually solves this predicament by searching for the whole Pareto-optimal front of solutions, and relies on a decision maker to finally select a single solution. However, in particular if the number of objectives is large, the number of Pareto-optimal solutions may be huge, and it may be very difficult to pick one "best" solution out of this large set of alternatives. As we argue in this paper, the most interesting solutions of the Pareto-optimal front are solutions where a small improvement in one objective would lead to a large deterioration in at least one other objective. These solutions are sometimes also called "knees". We then introduce a new modified multi-objective evolutionary algorithm which is able to focus search on these knee regions, resulting in a smaller set of solutions which are likely to be more relevant to the decision maker.