Based on Fuzzy Non-dominant and Sparse Individuals to Improve Many-Objective Differential Evolutionary

In the classical multi-objective algorithm, after sorting all the solutions of population, the non-dominant sorting method selects the better half of the solutions to enter the next generation. In solving the many objective optimization problem, due to the small environmental selection pressure, there will be a lot of redundancy when the selection solution enters the next generation. In order to solve this problem, a fuzzy non-dominant sorting method is proposed to sort the individual population. This method can determine the dominant relationship between the two individuals by comparing to three objectives just, which makes the calculation cost of many-objective approximate to three objectives. Meanwhile, the proposed method increases the selection pressure and improves the computational efficiency. In addition, due to the number of objectives is large, the traditional methods cannot accurately calculate the congestion distance. We design a method based on inflection point and hyperplane to calculate the congestion distance; thus, the selected individuals are evenly distributed by means of sparse individuals. A many-objective evolution algorithm is obtained by using the differential evolution search framework and combining the proposed methods of fuzzy non-dominant sorting and sparse individuals. Finally, the proposed algorithm is used to solve the standard test function DTLZ1-DTLZ6. The simulation results show that the performance of our algorithm on the IGD is similar with the famous comparison algorithms, and that is better than the famous comparison algorithm in running time.