Entropy based evolutionary algorithm with adaptive reference points for many-objective optimization problems

Many-objective optimization problems (MaOPs) have attracted more and more attention due to its challenges for multi-objective evolutionary algorithms. Reference points or weight vectors based evolutionary algorithms have been developed successfully for solving MaOPs. However, these algorithms do not solve efficiently the MaOPs with irregular Pareto fronts, such as disconnected, degenerate, and inverted. Although some algorithms with adaptive weight vectors or reference points are designed to handle the problems with irregular shapes of Pareto fronts, they still exist some drawbacks. These adaptive algorithms do not obtain good performance in solving regular problem. For solving regular and irregular Pareto fronts of the problems, a novel entropy based evolutionary algorithm with adaptive reference points, named EARPEA, is proposed to solve regular and irregular many-objective optimization problems. Entropy computed based on reference points and a learning period are employed to control adaptation of the reference points. In addition, in order to maintain diversity of the reference points, a reference point adaptation method based on cosine similarity is designed in the adjusting reference point phase. The proposed algorithm is empirically compared with eight state-of-the-art many-objective evolutionary algorithms on 72 instances of 18 benchmark problems. The comparative results demonstrate that the overall performance of the proposed algorithm is superior to the counterparts on MaOPs with regular and irregular Pareto fronts.