The Interval Non-probabilistic Multi-objective Optimization Mehod And Its Applications In Design Of Vehicle Body

The rapid development with modern industry and economy has made the optimization technique be greatly used in many kinds of fields.Many engineering problems often involve multi-objective optimization problem. Multiple objectives are always competitive and conflicting, which often result in inexistence of optimal solution. Therefore, multi-objective optimization problem (MOOP) can't be efficiently solved by using the single objective optimization method.Moreover, the uncertainties also cause many difficulties to directly use the conventional optimization approaches and optimization theories,and bring challenges for MOOP. Stochastic and fuzzy multi-objective optimizations are two types of traditional uncertain multi-objective optimization methodologies. Unfortunately, and it is difficult to construct the precise probability distributions or fuzzy membership functions. The interval number optimization is a relatively newly-developed uncertain optimization method, in which interval is used to model the uncertainty of variables. Thus the variation bounds of the uncertain variables are only required, which can be obtained through only a small amount of uncertainty information. The interval number optimization method mostly focuses on the single objective optimization in dealing with uncertainties, while uncertain multi-objective optimization more often involves in engineering problems. It is still at preliminary stage for the nonlinear interval number optimization research. So far, a nonlinear interval number algorithm with fine efficiency and precision has still not been developed to deal with this class of problems. So it is necessary to study the nonlinear interval uncertain multi-objective optimization (NIUMO).This dissertation mainly focuses the NIUMO problem. Firstly, a transformation model is proposed to deal with the NIUMO problem, through which the uncertain optimization can be transformed into a deterministic optimization problem. Secondly, an adaptive approximation method is presented to solve the low efficiency problem, which is caused by the nesting optimization. Thirdly, the transformation model is extended to uncertain multidisciplinary design optimization problem. Thus, an algorithm is constructed to solve the interval multidisciplinary multi-objective problem. Finally, the algorithm is applied to the design problem of vehicle body. The main contents are given as follows:(1) A new uncertain multi-objective optimization method is developed based on a nonlinear interval number programming. Based on the order relation of interval number and possibility degree of interval number, the uncertain multi-objective optimization is transformed into a deterministic non-constraint multi-objective optimization in terms of a penalty function. The multi-objective genetic algorithm and sequential quadratic programming algorithm are used to solve two layers nesting optimization problems, which are based on the deterministic multi-objective model of transformation. Thus, a new hybrid algorithm is proposed to solve the nonlinear interval number optimization problem. The optimization algorithm is successfully applied in complicated engineering problems, including the crashworthiness and sheet metal forming optimization. The application of the engineering problem demonstrates the effectiveness of the present method.(2) An adaptive approximation method is suggested to deal with an nonlinear interval uncertain multi-objective optimization (NIUMO) problem. The whole optimization process consists of a sequence of approximate optimization problems. The approximation models of uncertain objective functions and constrains are constructed by the Kriging models with the Latin Hypercube Design (LHD) samples in design space and uncertain field. In each iteration step, the approximate optimization can be created, and it can be solved by NIUMO. Then a Pareto set predicted by the approximations is identified through the NIUMO method, and an uncertainty set is generated by the Pareto set. Then design points set can be obtained, which consists of the Pareto set and uncertainty set. According to a space-filling design criterion, the approximation models are updated using a few design points belonging to design points set of the current iteration until convergence. This algorithm can improve the precision of approximation models by updating the design space and uncertain space. Furthermore, the algorithm can reduce the sample points at a certain extent and improve the optimization efficiency.(3) Based on the definition of non-probability reliability index, a mathematical model for nonlinear interval multi-objective optimization design considering reliability constraints is formulated as a nested optimization problem, in which the inner layer is a min-max problem associated with evaluation of the reliability index. An approach is proposed to transform the optimization problem into its equivalent form. Based on the order relation of interval number, the objective function robustness can be ensured.(4) A method is suggested to solve uncertain multidisciplinary multi-objective optimization problem based on the multidisciplinary feasible method (MDF) and interval. It is three-loop optimization procedure. The state variables are solved by the iteration of the multidisciplinary system analysis in the inner loop. The interval of objective functions and constraints are obtained in the middle loop. Based on the order relation of interval number and possibility degree of interval number, the uncertain multidisciplinary optimization can be transformed into the deterministic multidisciplinary optimization. The multi-objective optimization algorithm is used to solve the deterministic multidisciplinary multi-objective optimization problem in the outer loop. Numerical examples are presented to demonstrate the effectiveness and practicability of the present method.