【正文】 ukahara, 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 forthe 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. IMECE2021學報 2021年 ASME國際機械工程國會和博覽會 2021年 10月 3111月 6日，波斯頓，馬賽諸塞州，美國 IMECE202167447 適用于多目標系統(tǒng)優(yōu)化發(fā)動機曲軸 （ 阿爾伯特因此競爭必須從優(yōu)化引擎組件這個剛面著手。一些例子是計算機設計和凸輪形狀的用于柴油發(fā)動機的優(yōu)化 [7]。 是不平衡的目標函數(shù)也高度非線性的。因此引進了完成平衡設計的程序。 圖 優(yōu)化策略 這一戰(zhàn)略的一般過程描述如下。在這種情況下 ,它是取決于幾何學的四個不同的概要文件。 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, “ The Design of Radio Telescope Array Configurations usingMultiobjective Optimization: Imaging Performance versus Cable Length,” astroph/0405183, 2021, pp. 142。在這種情況下 ,鋒利邊緣出 現(xiàn)在配置文件不是一個方便的條件從曲軸的鍛造的觀點。標準 ,然后 ,是最小化之間的差異的絕對值之和的目標值和實際值在兩個外部失衡通過修改砝碼曲軸幾何學。莫：多目標 。曲軸的設計本質(zhì)上是一個多目標優(yōu)化（ MO）的問題。氣的基礎(chǔ)可以在 1990年之前發(fā)表的一些文章中找到 [ 4 ] 。自然頻率被認為是另一個影響參數(shù)的方面。 CW: Counterweight。 FEM: Finite Element Method. OPTIMIZATION OF BALANCE WITH GEOMETRICAL Fig. 1: Imbalance graph from the original crankshaft Design Crankshaft shape parameterization In order to make geometry modifications it is decided to substitute the current shape design of the crankshaft under analysis, from the original “arcshaped” design representation of the counterweight’s profile, to a profile using spline curves The figure 2 shows a counterweight profile of the crankshaft. Fig. 2: Profile of a counterweight represented by a spline Optimization Strategies The general procedure of the strategy is described below. During the optimization loop the CAD software is automatically controlled by an optimization algorithm, . by a Geic Algorithms (GA). The y coordinates of the control points that define the splined profile of the crankshaft can be parametrically manipulated thanks to an interface programmed in JAVA. The splined profiles allow shapes to be changed by geic algorithms because the codified control points of the splines play the role of genes. The Java interface allows the CAD software to run continually with the crankshaft model loaded in the puter memory, so that every time an individual is generated the geometry automatically adapts to the new set of parameters. Fig. 3: Profile Shapes of CW1, CW2, CW8 and CW9 from an individual in the Pareto Frontier A corresponding constraint to the optimization strategy is formulated next. An additional objective function was added: the measure of the curvature of all the splines from the profiles of counterweights. As it is known, the curvature is the inverse of the radius of an inscribed circle of the curve. In this case it was decided to integrate into the geometry the required inscribed circles and analysis features to extract the maximum curvature along the profiles of the four varying Fig. 4: Curvature in CW9 profile showing an improved Curvature In the second part of this paper an additional evaluation is going to be introduced: the dynamic response of the crankshaft in order to control the first eigen frequency, with the aim of not affecting the weight. As in this first approach, the GA is going to be used to produce automatically alternative crankshaft shapes for the FEM simulator program, to run the simulator, and finally to evaluate the counterweight’s shapes on the basis of the FEM output data. SUMMARY AND CONCLUSIONS The use of the Java interface allowed the integration of the geic algorithm to the CAD software, in the first part of the paper, an optimization of the imbalance of a crankshaft was performed. It was possible the development of a Pareto frontier to find the closesttotarget individual. But the shapes of the counterweights were not so suitable for f