摘  要：为了解决单目标优化无法满足实际工程应用需求的问题，通过对一个约束性多目标优化问题的分析，以最大振幅和最小输入电压做为优化目标，设计参数包括连续变量（换能器的尺寸）和离散变量（材料类型），利用基于分析模型的传递矩阵法对压电换能器进行建模，进而导出优化问题的数学描述式，最后应用多目标进化算法NSGA-II，估算一系列的pareto优化设计值，分析优化结构，并确定最优设计参数。   关键词：压电换能器；传递矩阵；多目标进化算法； 约束性问题；优化设计   中图分类号：O224；TB552        文献标识码：A          文章编号：1672-4984（2008）03-0124-03   Piezoelectric transducer optimized design based on Multi-objective evolutionary algorithms   MU Fei， FU Bo， HUANG Zhen-wei   （College of Manufacturing Science and Engineering，Sichuan University，Chengdu 610065，China）   Abstract： Since the single-objective optimization could not solve the complicated situation in applications,  the design of a Langevin transducer had been described as a constrained multi-objective optimization problem. The maximum vibration amplitude and minimum electrical input power were considered as optimization objectives. Design variables involved continuous and discrete variables. The transfer matrix method based on analytical models was used to simulate the behavior of transducers. A multi-objective evolutionary algorithms（NSGA-II） was used, and the set of pareto-optimal solutions was calculated. At last, the optimized results were analyzed, and the preferred design was determined.   Key words： Piezoelectric transducers； Transfer matrices； Multi-objective evolutionary algorithms； Restrict problems； Optimal design   Editor：liyan