Abstract
In the preference-based multi-objective optimization, the lack of priori-knowledge makes it difficult for the decision maker to specify an informed preference. Thus, the knees are regarded as the naturally preferred solutions on the Pareto optimal front. However, most research is based on a given large number of solutions and a posteriori identifies the knee candidates among them.
Based on the alpha-dominance relationship, this paper proposes a new framework to a priori search the knee regions. Firstly, a number of reference vectors are generated in the objective space. During the environmental selection, all solutions are associated to their closest reference vectors. The solutions associated to different reference vectors are deemed to be non-alpha-dominated with each other. If they are correlated with the same reference vector, the alpha-dominance relationship is adopted to sort the solutions into different frontiers. Therefore, the knee candidates are assigned to the first layer and selected with a higher priority, so that more knee information from the previous generation will be preserved and more potential knee regions will be explored. The comparative experiments demonstrate that the proposed method is competitive in identifying convex knee regions.