An Interval Optimization Method And Application For Solving Problems Under Large Uncertainty

Uncertainty widely exists in practical engineering problems, and studying the algorithms of uncertain optimization is of importance for uncertain optimization design of products. Probabilistic optimization and fuzzy optimization are two types of uncertain optimization methodologies, in which a great amout of uncertain information is required to construct the precise probability distributions or fuzzy membership functions. Unfortunately, it often seems very difficult or sometimes expensive to obtain sufficient uncertainty information, and hence these two types of methods will encounter some limitations in applicability. The interval number optimization is a newly developed uncertain optimization method, in which interval is used to model the uncertainty of a variable. Thus the variation bounds of the uncertain variables are only required, which can be obtained through only a small amount of uncertainty information. On the aspect of uncertain model construction, the interval optimization method has an advantage of convenience and economy.Interval optimization problems in which uncertain parameters exist in not only the objective function but also the constraints are studied in this paper. An efficient algorithm is developed for solving problems under high uncertainty, and then it is employed to deal with the uncertain optimization of the frame of a commercial truck. An uncertain optimization software based on interval optimization method is developed finally. As a result, the following studies are carried out in this dissertation:First of all, this paper presents an efficient algorithm for solving nonlinear interval number optimization problems with high uncertainty. Nonlinear optimization problems are converted to linear optimization problems at each iteration step. Based on subinterval analysis methods, response intervals of the objective function and constraints are obtained. It is transformed into a deterministic optimization problem. And then, the optimization results in the current design domain are obtained. By use of changing of the design vector and design step, the updating of the design domain is achieved until that the algorithm is converged.Secondly, the commercial vehicle frame's parametirc FEM model is constructed. The structural stiffness and strength of the commercial vehicle is solved. Considering the material uncertainty introduced during the manufacturing process, interval structural analysis is performed based on the interval structural analysis method. The suggested optimization method in this paper is employed to implement the optimization design of the commercial vehicle, and the stiffness is improved obviously.Finally, the software named interval uncertain optimization design version 1.0 is developed. The optimization algorithm is achieved by use of Fortran language, and the software interface is implemented through VC++ language. There are two main characteristics of this software:friendly interface and convenient implementation. When using the software, the engineers don't have to spend much time on the optimization algorithm, and just need construct the optimization task card following the manual.