【正文】 function consisting of both imbalances [9]. Unlike the singleobjective optimization, the solution to this problem is not a single point, but a family of points known as the Paretooptimal set. Each point in this set is optimal in the sense that no improvement can be achieved in one objective ponent that does not lead to degradation in at least one of the remaining ponents [10]. The objective functions of imbalance are also highly nonlinear. Auxiliary information, like the derivatives of the objective function, is not available. The fitnessfunction is available only in the form of a puter model of the crankshaft, not in analytical form. Since in general our approach requires taking the objective function as a black box, and only the availability of the objective function value can be guaranteed, no further assumptions were considered. The Paretobased optimization method, known as the Multiple Objective Geic Algorithm (MOGA) [11], is used in the present MO problem, to finding the Pareto front among these two fitness functions. In GA’s, the natural parameter set of the optimization problem is coded as a finitelength string. Traditionally, GA’s use binary numbers to represent such strings: a string has a finite length and each bit of a string can be either 0 or 1. By maintaining a population of solutions, GA’s can search for many Paretooptimal solutions in parallel. This characteristic makes GA’s very attractive for solving MO problems. The following two features are desired to solve MO problems successfully: 1) the solutions obtained are Paretooptimal and 2) they are uniformly sampled from the Paretooptimal set. NOMENCLATURE CAD: Computer Aided Design。 Structures, vol. 79, 2021, . [2] P. Bentley, Evolutionary Design by Computers, USA:Man Kaufmann, 1999. [3] . Goldberg, Geic Algorithms in Search ,Optimization and Machine Learning, USA: AddisonWesley Longman Publishing Co., 1989. [4] . Coello Coello, “A Comprehensive Survey of EvolutionaryBased Multiobjective Optimization Techniques,” Knowledge and Information Systems, , 1999, pp. 129156. [5] . Cohanim, . Hewitt, and O. de Weck, “TheDesign of Radio Telescope Array Configurations using Multiobjective Optimization: Imaging Performance versus Cable Length,” astroph/0405183, 2021, pp. 142。 CAE 適用于動(dòng)態(tài)限制 (學(xué) )。燃油經(jīng)濟(jì)性、耐用性和內(nèi)燃機(jī)的可靠性 ,呼吁減少大小、重量、振動(dòng)和噪音，成本等力量推動(dòng)著市場(chǎng)快速發(fā)展。目前研究的目標(biāo)是 :建立一個(gè)戰(zhàn)略發(fā)展的發(fā)動(dòng)機(jī)曲軸的集成工藝 :CAD 和 CAE(計(jì)算機(jī)輔助設(shè)計(jì)與工程 )軟件模按照型遺傳算法評(píng)價(jià)功能參數(shù)、使用樣條曲線的形狀結(jié)構(gòu)和 Java 語(yǔ)言編程的集成系統(tǒng)優(yōu)化方法。有對(duì)形狀判定應(yīng)用程序中的機(jī)器部件的設(shè)計(jì)和對(duì)這些部件的功能性能的優(yōu)化，例如天線 [5] ，渦輪葉片 [ 6 ]等在機(jī)械工程 IELD ，基于進(jìn)化算法的結(jié)構(gòu)拓?fù)鋬?yōu)化方法用于獲取被普遍只有通過(guò)昂貴和耗時(shí)的迭代過(guò)程逼近最優(yōu)幾何解決方案。本文提出了一種方法，該任務(wù)的還有一些方法，可以 用來(lái)建立在曲軸設(shè)計(jì)和發(fā)展?fàn)顩r的戰(zhàn)略。在這個(gè)集合中的每個(gè)點(diǎn)是最佳的，任何改進(jìn)可以在一個(gè)目標(biāo)組件，它不會(huì)導(dǎo)致降解中的其余組分中的至少 1 [10]來(lái)實(shí)現(xiàn)的感覺(jué)。這一特點(diǎn)使得遺傳算法的解決問(wèn)題的 MO非常有吸引力的。有限元法：有限元方法 幾何限制下的平衡優(yōu)化 作者 [12]之前的工作中 ,探測(cè) CAD 曲軸模型不平衡的設(shè)計(jì)，取決于 CAD 軟件。這是一個(gè)適應(yīng)度函數(shù)選擇的反應(yīng)同樣的加權(quán)函數(shù)之間的差異指定目標(biāo)上的失衡和當(dāng)前的不穩(wěn)定校正飛機(jī)位于兩個(gè)外 部的曲軸 (CW1 和 CW9)[13]。 to 原始的不平衡設(shè)計(jì) 圖 曲軸形狀參數(shù)化 為了使幾何修改決定替代當(dāng)前形狀下的曲軸設(shè)計(jì)分析 ,從原始的“弧形”設(shè)計(jì) 表示抗衡的形象 ,一個(gè)概要文件使用樣條曲線，如圖 2 顯示了一個(gè)制衡的曲軸。 盡管結(jié)果獲得改善 ,融合還沒(méi)有令人滿(mǎn)意，因?yàn)槟繕?biāo)不能達(dá)到平衡內(nèi)部的設(shè)計(jì)約束了幾何圖形的運(yùn)用的要求 ,從而進(jìn)行了一些試驗(yàn)允許花鍵贖愆幾何約束，最后一代一個(gè)人被發(fā)現(xiàn)非常接近平衡的目標(biāo)。眾所周知 ,曲率是內(nèi)切圓半徑的曲線決定的。這樣可以提高曲軸的一些形狀 ,但不太好控制失衡的效果。 [6] M. Olhofer, Yaochu Jin, and B. Sendhoff, “ Adaptive encoding for aerodynamic shape optimization using evolution strategies,” Evolutionary Computation,Seoul: 2021, pp. 576583. [7] J. Lampinen, “ Cam shape optimisation by geic algorithm,” ComputerAided Design, vol. 35, 2021, . [8] M. Eldred et al., DAKOTA, A Multilevel Parallel ObjectOriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis. Reference Manual, USA: Sandia Laboratories, 2021. [9] Y. Kang et al., “ An accuracy improvement for balancing crankshafts,” Mechanism and Machine Theory, vol. 38, 2021, pp. 14491467. [10] S. Obayashi, T. Tsukahara, and T. Nakamura, “ Multiobjective geic algorithm applied to aerodynamic design of cascade airfoils,” Industrial Electronics, IEEE Transactions on, vol. 47, 2021, . [11] . Fonseca and . Fleming, “ An Overview of Evolutionary Algorithms in Multiobjective Optimization,” Evolutionary Computation, vol. 3, 1995, pp. 116. [12] ., “ Comparison of Strategies for the Optimization/Innovation of Crankshaft Balance,” Trends in Computer Aided Innovation, USA: Springer, 2021, pp. 201210. [13] S. Rao, Mechanical vibrations, USA: AddisonWesley,1990. [14] . Coello Coello, An empirical study of evolutionary techniques for multiobjective optimization in engineering design, USA: Tulane University, 1996. [15] N. LeonRovira et al., “ Automatic Shape Variations in 3d CAD Environments,” 1st IFIPTC5 Working Conference on Computer Aided Innovation, Germany: 2021, pp. 200210. [16] . Smith, . Dike, and . Stegmann, “ Fitness inheritance in geic algorithms,” ACM symposium on Applied puting, USA: ACM, 1995, pp. 345350. 。但抗衡的形狀不太適合鍛造 ,因此有必要引入一個(gè)額外的目標(biāo)函數(shù)來(lái)提高砝碼的曲率。