【文章內(nèi)容簡介】 g 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。 GAs: Geic Algorithms。 EA: Evolutionary Algorithms。 MO: Multiobjective。 MOGA: Multiobjective Geic Algorithm。 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 fing, for that reason it was necessary to introduce an additional objective function to improve the curvature of the counterweights profile. A further integration with the CAE software, as described in the second part, was performed. It was possible to improve some shapes of the crankshaft but with not so good imbalance results. The development of a new graph with the additional first eigenfrequency objective was plotted, from which important conclusions were extracted: It is necessary to prevent the sharp edges of the counterweight’s shape by adding extra restrictions as curvature of shapes. Simulation of the fing process is required in order to define a relationship between good shapescurvature and manufacturability. This bees significantly important when a proposed design outside the initial shape restrictions needs to be justified in order not to affect fe ability. This paper defined the basis and the beginning of a strategy for developing crankshafts that will include the manufacturability and functionality to pile a whole Multiobjective System Optimization. ACKNOWLEDGMENTS The authors acknowledge the support received from Teol243。gico de Monterrey through Grant No. CAT043 to carry out the research reported in this paper. REFERENCES [1] . Mourelatos, “A crankshaft system model for structural dynamic analysis of internal bustion engines,” Computers amp。 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 Syste