Improvement of multi-objective evolutionary algorithm and optimization of mechanical bearing

In some algorithms, Euclidean distance is used to calculate the crowded distance between subproblems. When Euclidean distance is used to calculate subproblems, it is found that the distribution of congestion degree is not ideal. Sub-problems with relatively high degree of congestion are often distributed in the center of Pareto frontier, while sub-problems with relatively low degree of congestion are distributed at the edges of Pareto frontier, especially the Pareto frontier shape is convex and reference vectors are constructed from the ideal point using Das and Dennis's method for generation of points on unit simplex. To solve the above problems, an improved multi-objective evolutionary algorithm is proposed, called MOEA/D-ROE, and a weight vector adjustment strategy based on regional online evaluation is proposed by using the modified form of Tchebycheff function. In MOEA/D-ROE, subproblems with different congestion levels are divided into different areas. By setting corresponding parameters for each region and introducing Pareto advantages, the weights are adjusted regularly. Therefore, the weights of subproblems can be redistributed more evenly to obtain more uniform solutions. Finally, the regional online evaluation strategy is embedded into other algorithms to verify the effectiveness and portability of this strategy, and MOEA/D-ROE algorithm is applied to an application example. At the same time, it is proved that the improvement of the algorithm is meaningful for the optimization of practical problems.