The two steps training method is proposed to replace the iterative way of local principal component analysis algorithm in the regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA). In the phase of training model of improvement algorithm,the K-means clustering method is used to partition the points in population into primary K disjoint clusters at the first step,and then the clustering method based manifold is used to partition at the second step. Simulation results of the six benchmark instances show that the improvement algorithm can maintain the convergence and diversity performance,and decline the computation time greatly.

Multiobjective Particle Swarm Optimization ＆ Estimation of Distribution Algorithm of offspring solutions are updated by the Particle Swarm Optimization (PSO) algorithm with mutation which has the ability of global search.Another half of offspring solutions are created by the Estimation of Distribution Algorithm (EDA) which has better ability of learning and local research.EDA explicitly extracts globally statistical information from the selected solutions and builds a posterior probability distribution model of promising solutions based on the extracted information.Compared with some other performance on ZDT1～ZDT3,ZDT6,ZDT6-1 instances,and the performance metrics of convergence and diversity on ZDT4 are moderate.

The mathematical model of vacancy course path optimization of laser machining is built and changed to the travelling salesman problem (TSP). The Nearest Neighbor (NN) is modified to Adaptive Neighborhood Method (ANM). In ANM one mimics the traveller whose rule of thumb is not always to go next to the nearest as-yet-unvisited location. The next city is randomly selected from the unvisited cities in adaptive neighborhood. While solving the TSP, ANM is used to create the initial population at first, then iterations are done through selection, cross and mutation operation. In selection, the proposed algorithm only keep 90% samples from the previous generation, the remained agents are supplied by the new sample created by ANM. The results show that the algorithm shortens vacancy course in laser machining and the manufacturing efficiency is improved.