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研究目的:为改善实际工程结构在不确定性条件下的多性能指标,提供一种高效的区间多目标优化方法。创新要点:建立一个目标和约束均为区间不确定性参数函数的区间约束多目标优化模型,提出并实现基于径向基函数、区间分析和非支配排序遗传算法(NSGA-II)的区间多目标优化算法。研究方法:首先,利用区间序关系将每个区间目标转换为同时优化其中点和半径的确定性双目标,利用区间可能度法将区间约束转换为确定性约束,并在此基础上,利用加权法和罚函数法将每个区间目标的约束优化问题转换为相应的无约束优化问题;然后,利用拉丁超立方实验设计和有限元分析构建预测各待优化结构性能指标值的径向基函数;最后,将径向基函数、区间分析法与NSGA-II相结合,快速求出转换后确定性无约束多目标优化问题的所有Pareto最优解,并通过考虑材料不确定性的高速压力机滑块机构设计实例验证该方法的有效性。重要结论:目标和约束均为不确定性参数函数的区间多目标优化模型能有效反映实际工程中同时改善结构多性能指标的需求。基于径向基函数、区间分析和NSGA-II相结合的区间多目标优化算法将传统区间优化模型求解中的嵌套优化过程简化为单层遗传优化过程,大大提高了求解效率,并可获得多目标优化问题的所有Pareto最优解。
Research purposes: In order to improve the multi-performance index of the actual engineering structure under the condition of uncertainty, an efficient interval multi-objective optimization method is provided. Innovative Points: To establish a multi-objective optimization model of interval constraints with both the objective and the constraints as the parameters of interval uncertainties, an interval multi-objective (RBF) based on radial basis function, interval analysis and non-dominated ranking genetic algorithm (NSGA- optimization. Research methods: Firstly, we use the interval order relation to convert each interval target to a deterministic dual target that simultaneously optimizes its midpoint and radius, and uses the interval probability method to convert interval constraints to deterministic constraints. Based on this, Then the constrained optimization problem of each interval target is transformed into the corresponding unconstrained optimization problem by using the method of law and penalty function. Then, the radial basis function of predicting the performance index of each structure to be optimized is constructed by using Latin hypercube experimental design and finite element analysis. Finally, by combining the radial basis function and interval analysis method with NSGA-II, all the Pareto optimal solutions of the deterministic unconstrained multiobjective optimization problem after the transformation are obtained quickly and quickly by the high-speed press sliding with material uncertainty Block organization design example to verify the effectiveness of the method. Important conclusions: The interval multi-objective optimization model with both the objective and the constraints as uncertain parameter functions can effectively reflect the demand of improving the structural multi-performance indicators in the actual project at the same time. The interval multi-objective optimization algorithm based on radial basis function, interval analysis and NSGA-II simplifies the nested optimization process in the traditional interval optimization model to a single-layer genetic optimization process, which greatly improves the efficiency of the solution and obtains more All Pareto optimal solutions to the objective optimization problem.