The Research Of NWSA For Multi-objective Optimization Problems And The Application In Engineering

For technological advances and the development of all industry, optimization is one consistent theme. It turns out that most of the optimization problems that need to be solved are the multi-objective optimization problems, which exist in many valuable jobs such as industrial design, economic decisions, traffic plans and business management. The research on the multi-objective optimization and its application is necessary and has practical significance.The article supported by Science and Technology Development Plan of Jilin Province and its assorted project, FAW Group Combined Action Plan,carries out research deeply on the multi-objective optimization method and its application in extent optimization of car body. The main work includes as follows.(1) A summary of the multi-objective optimization and its applicationThe details of the research status of the multi-objective optimization are presented. The classification of the multi-objective optimization which is based on the solution mode is described. The multi-objective optimization algorithms are divided into the numerical one and the intelligent one. The principles of these two typical multi-objective optimization algorithms and their development processes are described, respectively. The application status in practice of the multi-objective optimization is studied and the reasons why the multi-objective optimization is popular in practice and the defects on computational efficiency that should not be neglected are described. Finally, the design goals of the multi-objective optimization and some typical multi-objective optimization algorithms which are necessary in designing the numerical multi-objective optimization are explained briefly. This section can be the basis of the research.(2) Proposing the Newton Weighted Sum AlgorithmFirstly, the standard mathematical model of the unconstrained multi-objective optimization problem and the concepts of Pareto optimal solution and Pareto optimal front points are introduced. An algorithm is based on the Newton method and the linear weighted sum method which can solve the unconstrained multi-objective optimization problem, which is called the Newton Weighted Sum Algorithm(NWSA), are proposed. In respect of solving efficiency, when the objective function is the twice continuously differentiable and convex, the Newton Weighted Sum Algorithm is super linearly convergent; when the objective function is quadratic differential convex and satisfies the Lipschitz continuity, the Newton Weighted Sum Algorithm is super quadratic convergent.(3) Discussing the solving properties of the Newton Weighted Sum AlgorithmThe set methods of weighting factors when solving the optimization problems having two and three objects using the Newton Weighted Sum Algorithm are introduced, respectively. Then this mode is extended to the situation in which there’s more objects. Three selection processes are designed for the initial values of the Newton Weighted Sum Algorithm: random initial values, same initial values and optimal initial values. It is confirmed that the precision of the results is almost the same and computational efficiency is different significantly calculated by different initials values using examples. The computing time and average iteration speed under the optimal initial values way are far smaller than other ways. The optimal initial values are selected as the initial values of the Newton Weighted Sum Algorithm, which can further improving the computational efficiency. The multi-objective optimization examples are selected from published papers as testing problems, and, the Multi-objective Genetic Algorithms and the Newton Weighted Sum Algorithm are utilized to make calculations, respectively. Test results are compared from the view of the result accuracy, Pareto front distributed quality and calculation efficiency, drawing conclusions that the Newton Weighted Sum Algorithm has higher calculation efficiency and accuracy in the unconstrained multi-objective optimization, while the Pareto front distributed quality is general.(4) Proposing Newton Weighted Sum Frisch AlgorithmThere are many multi-objective optimization problems with inequality constrains. As a result, Newton Weighted Sum Frisch Algorithm is proposed by adding a method to handle constraints to the Newton Weighted Sum Algorithm. Two standard examples are chose, and the Multi-objective Genetic Algorithms from the genetic algorithm toolbox in MATLAB and the Newton Weighted Sum Algorithm are utilized to make calculations. The results are compared, validating the feasibility and high-efficiency of using the Newton Weighted Sum Frisch Algorithm to solve inequality constrained multi-objective optimization. Finally, based on the Newton Weighted Sum Frisch Algorithm, a concept of first solving then selecting to solve engineering multi-objective optimization is proposed and it is displayed by an engineering example.(5) The multi-objective optimization in the sectional of the front railThe vehicle front impact is described, showing that in the view of mechanics, the automobile impact problem is essentially the research on the contact problems. The fundamentals and computing methods of nonlinear finite element method of contact impact are summarized. The common impact simulation software as also as the basic operating process of the software is introduced. Based on the experiment design method and results of finite element simulation analysis, an agent model of the sectional structure of the impact properties is built. Then Newton Weighted Sum Frisch Algorithm is utilized to compute the multi-objective optimization problem, resulting in the optimal Pareto front of the front rail impact. Then the properties of the original structure are compared with the Pareto front. Seeking for the referenced scheme of optimized design, the multi-objective optimization of the front rail structure is achieved. Finally, by the simulation of the improved structure impact results, the improvement of the front rail impact properties is verified.