摘  要：為了解決單目標(biāo)優(yōu)化無法滿足實(shí)際工程應(yīng)用需求的問題，通過對一個(gè)約束性多目標(biāo)優(yōu)化問題的分析，以最大振幅和最小輸入電壓做為優(yōu)化目標(biāo)，設(shè)計(jì)參數(shù)包括連續(xù)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(jìn)行建模，進(jìn)而導(dǎo)出優(yōu)化問題的數(shù)學(xué)描述式，最后應(yīng)用多目標(biāo)進(jìn)化算法NSGA-II，估算一系列的pareto優(yōu)化設(shè)計(jì)值，分析優(yōu)化結(jié)構(gòu)，并確定最優(yōu)設(shè)計(jì)參數(shù)。   關(guān)鍵詞：壓電換能器；傳遞矩陣；多目標(biāo)進(jìn)化算法； 約束性問題；優(yōu)化設(shè)計(jì)   中圖分類號：O224；TB552        文獻(xiàn)標(biāo)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