Performance Analysis on Knee Point Selection Methods for Multi-Objective Sparse Optimization Problems

Some multi-objective evolutionary algorithms have been introduced to solve sparse optimization problems in recent years. These multi-objective sparse optimization algorithms obtain a set of solutions with different sparsities. However, for a specific sparse optimization problem, a unique sparse solution should be selected from the whole Pareto Set (PS). Usually, knee point in the PF is a preferred solution if the decision maker has no special preference. An effective knee point selection method plays a pivotal role in multi-objective sparse optimization. In this paper, a study on the knee point selection methods in multiobjective sparse optimization problems has been done. Three knee point selection methods, which are angle-based method, the weighted sum of objective values method and the distance to the extreme line method, are compared and the experimental results indicate that the second method is better than the others. Finally, an analysis of parameter in the best knee point selection method is conducted and an optimal setting range of parameters is given.