摘  要：為了解決單目標優化無法滿足實際工程應用需求的問題，通過對一個約束性多目標優化問題的分析，以最大振幅和最小輸入電壓做為優化目標，設計參數包括連續變量（換能器的尺寸）和離散變量（材料類型），利用基于分析模型的傳遞矩陣法對壓電換能器進行建模，進而導出優化問題的數學描述式，最后應用多目標進化算法NSGA-II，估算一系列的pareto優化設計值，分析優化結構，并確定最優設計參數。   關鍵詞：壓電換能器；傳遞矩陣；多目標進化算法； 約束性問題；優化設計   中圖分類號：O224；TB552        文獻標識碼：A          文章編號：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