基于Pareto解的交互式模糊优化及其应用

设计参数内关外联的属性和设计约束的模糊性、相关性和传播性往往导致多目标优化设计中冲突发生和目标间协调性差等现象。针对这些问题,应用模糊数学原理,构造尺度函数,增加附加约束,并基于Pareto解处的冲突矩阵、协同灵敏度分析以及目标重要度阈值的交互选择,建立了基于Pareto解的模糊交互式多目标优化模型。结果表明:提出的模型在兼顾主、客观要求的前提下,可降低目标之间的冲突程度,得到最大的满意度。以实例验证了模型的有效可行性。

Interactive fuzzy optimization and its application based on Pareto solutions

The coupling of design parameters and the fuzziness of the design process result in optimization problems, such as poor collaboration among design objectives and poor resolution of design conflicts. A fuzzy interactive multi-objective optimization model was developed based on Pareto solutions which includes a metric function and additional constraints to ensure collaboration among design objectives. A trade-off matrix was developed for the Pareto solutions with a method for selecting the objective weighting coefficients. The result generates a Pareto optimal set, a maximum satisfaction degree and a minimum distance from the ideal solution. The global optimal solution is selected from the Pareto optimal set by analyzing the trade-off matrix and the collaborative sensitivity. The results show that the proposed method effectively reduces the conflicts among design objectives, gives the maximal satisfaction degree and reduces information loss.