Finding Outstanding Solutions for Multi-objective Optimization Problems

A finite set of best trade-off solutions, or Pareto frontier, is the searching result of a multi-objective optimization algorithm against a multi-objective optimization problem. However, not all the solutions of the set are equally important to decision makers. They typically utilize only a few outstanding solutions, and the solutions located at the maximum convex bulge on the Pareto frontier are usually embraced when no preference is available; they are called knee solutions. There are several knee searching algorithms in the last decades, but most of them failed to isolate the knee solutions from the near knee solutions. In this paper, we propose a posteriori knee searching algorithm that can identify and isolate the knee solutions, based on the farthest distance to a hyperplane among the neighborhood solutions. The proposed algorithm is tested against well-known benchmark problems: ZDT3, DEB2DK and DEB3DK. The results show that the proposed algorithm can identify outstanding solutions which are knee solutions accurately.