A Study On The Improvement Of Expensive Multi-Objective Evolutionary Algorithm Based On The Non-decomposition Principle

Expensive multi-objective problem is a hotspot as well as a difficulty of real projects in recent years. It usually need to trade-offs among multiple conflicting goals at the same time when optimize the expensive multi-objective problem. And the objectives are in coupled competitive relationship with different meaning and dimension. So it is difficult to evaluate their advantages and disadvantages and hard to achieve the optimal value simultaneously. The expensive multi-objective problems usually have complex mechanism model with no clear expression of the objective function, and every calculation has to spend high costs of time and economic for modeling and performance evaluation with simulation software.With the gradual development of the hardware and computational Intelligence, the evolutionary algorithm has been widely used to solve the multi-objective optimization problems for its superior robustness and global character. Although the evolutionary theory in multi-objective optimization is becoming more mature, and the evolutionary algorithm has meet the accuracy requirements of general applications. It still has a lot of limitations applied in real projects. Evolutionary algorithm has to do plenty of evaluation with fitness function, and it needs thousands of evaluations to get better results. So most of the time will be waste in the evaluation process, but little in the search part while solving the expensive multi-objective problem by evolution algorithms, which has a adverse impact on the performance and efficiency of the algorithm.It is a feasible method that structuring a surrogate model instead of the expansive evaluation process by samples gained in the search process to reduce the number of calling s imulation software while solving expensive multi-objective optimization problem under the guaranteeing accurancy. The surrogate model has a small amount of calculation and a similar result to the numerical analysis and physical experiment. Calculating the points in the searching space by the surrogate model to guide the evolutionary trend of evolutionary algorithm, and update the surrogate model by calibration poins evaluated by real modle timely until it meet the convergence requirements. The surrogate model can reduce the number of real evaluation from million to hundred, and save time greatly. EGO algorithm is an efficient global optimization algorithm of single objective based on the DACE surrogate model. Its advantage is high accuracy for predict, good approximation and significantly reduce the amount of computation. It is an effective way to solve the expensive multi-objective problem by combining the EGO algorithm and evolutionary computation. This article implemented the NSGAII-EGO algorithm by using the EGO algorithm as surrogate model and NSGAII algorithm as the main framework.The NSGAII-EGO algorithm chooses the individuals with maximum El value in every objctive as calibration points to increase the difference of the calibration points, but it is proved to have a bad performance. The key to restrict the optimization efficiency is the selection strategy of calibration points. The optimal solution might end not the same with the global pareto set when the surrogate model has large errors with the actual evaluation model. And the selection strategy of calibration points has a direct impact on the quality and efficiency of the update of the surrogate model. So the process of select calibration points is not only improving the model accuracy but also reducing the false information. An inordinate number of calibration points will increase the computational complexity of rebuilding model and inadequate number may hard to improve the accurancy of the surrogate model. In addition, unpropriate calibration points may guide the algorithm to the wrong direction. So it is important to select the appropriate number of high-quality calibration points. The article took example by the correction point selection strategy of the MOEA/D-EGO algorithm. It introduced the K-means clustering to NSGA-II EGO algorithm to distinguish the differences between individuals, and it designed a random selection strategy, a maximum average EI value selection strategy and an El perato selection strategy to improve the NSGA-Ⅱ EGO algorithm. It implemented the KMN-EGO algorithm with a good efficiency which can improve the diversity of calibration points while guarantee the best selection.The article investigated the KMN-EGO algorithm by the classic ZDT and DTZL test function set to verify its correctness and effectiveness. The result showed that sometimes there were modeling pitfalls, but all the three selection strategy of calibration points had good efficiency of model modification and better performance than the NSGA Ⅱ-EGO algorithm. Optimization test functions with the KMN-EGO algorithm, the NSGA II-EGO algorithm and the MOEA/D-EGO algorithm. The IGD indicators showed that the KMN-EGO algorithm had better convergence, and its results were more uniform distribution. Finally, the KMN-EGO algorithm was successfully applied to the parameter design of the MEMS microwave relays, and received results much batter than the targets in a limited number of evaluations. It means that the KMN-EGO algorithm has excellent performance and high efficiency, and can reduce the cost of evaluations for expensive evaluation in a large degree. The KMN-EGO algorithm overcomes the limitations of classic evolutionary algorithm for multi-objective problems in actual project. It can optimize the results that approximate the pareto front in200-300times, and effectively shorten design cycle, improve product performance and reduce the economic costs. The KMN-EGO algorithm greatly expands the scope of application of multi-objective evolutionary algorithm, and has a broad development space and application prospects.