The Uncertainty Multi-objective Optimization Based On Non-probabilistic Convex Model And It’s Application

With the high development of science and technology, the practice engineeringproblems which we considered are become more and more complex, many engineeringproblems often need to be considered more than one designing objective, and theseobjectives are always competitive and conflicting, so these multi-objectives can’t besolved by using the single objective optimization method. In the meantime, theuncertainties always exists in the practical engineering problems, so the conventionaloptimization methods can’t be used to solve these problems. Because it is hard toconstruct the precise probability distributions or fuzzy membership functions for thestochastic and fuzzy optimizations, but it is easy to construct the non-probabilityconvex model, it only need few samples information to construct the bounds of theuncertain variables. Therefore, this paper study on the uncertainty multi-objectiveoptimization problems which use the non-probability convex model to simulate theuncertain parameters, and these methods are applied to the practical engineeringproblems. The works are summarized as following:Firstly, the uncertainty multi-objective based on interval is constructed. Thismethod use the interval structure analysis method to calculate the upper and lowerbounds of every objective and constraint functions for each vector, by using the centervalue of the interval objective function, to calculate the non-dominated solution of themulti-objective optimization problems，with the interval possibility degrees, we changethe nonlinear interval multi-objective problems into the deterministic multi-objectiveproblems. We use the μMOGA to calculate the converted deterministic multi-objectiveproblems.Secondly, another multi-objective optimization method is suggested based on theconvex model. This method uses the convex model to simulate the uncertainparameters, and let the uncertain parameters represent as a hyper-ellipsoid model. Weuse the nominal value of the uncertain parameters to solve the objective function, asthe uncertain constraint, we use the reliable analysis method, let the uncertaintyquestion transform to the deterministic question.The research productions are applied to the commercial automobile frameoptimization and the vehicle crashworthiness optimization; the results of theseexamples demonstrate these methods have the good engineering practicability.