基于代理模型的多目标优化方法及其在车身设计中的应用
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摘要
实际工程优化问题通常涉及多个目标,这些目标往往不能显式表达而要通过仿真计算来获取,这便在一定程度上加大了多目标优化求解的难度。多目标智能优化方法可以在不考虑问题具体特征的前提下进行优化解的搜寻,适用于处理实际工程问题,但受到进化规模和收敛速度的影响而需要较多次数的目标值计算,限制了在目标求解耗时的问题中的应用。常见的基于代理模型的多目标优化方法因能较好地处理效率问题而成为研究热点,但目前该类方法面临着求解精度较低的问题。鉴于此,本文针对基于代理模型的多目标优化方法展开了深入的研究,力求在快速、有效的算法本身及其在车身设计中的应用方面,开展一些尝试和探索。本文研究内容主要包括以下几个方面：
1)提出基于自适应径向基函数的多目标优化算法。该算法通过遗传拉丁超立方实验设计、径向基函数和隔代映射遗传算法等技术,系统地评价代理模型。通过合并样本点和测试点来逐步地提升模型的精度。采用改进的贪婪算法挑选最后迭代步中的测试点到最终样本空间,构建整个设计域上的自适应径向基函数模型,并基于此模型结合具有代表性的NSGA-Ⅱ算法进行多目标优化。测试函数中验证了自适应径向基函数具备有效评价和逐步提升模型精度的能力。该算法应用于车身薄壁构件耐撞性多目标优化设计中,快速地找到了多组设计方案,较好地平衡了薄壁构碰撞过程中的吸能量和碰撞力。
2)提出基于智能布点技术的微型多目标遗传算法。该算法首先采用加强径向基函数构建全局代理模型,再采用高效的微型多目标遗传算法进行近似优化。根据优化结果信息进行智能布点,反馈到设计空间进而不断更新代理模型,使实验设计过程和近似优化过程形成闭环过程。由于充分利用了近似优化的信息,使仅关注代理模型在关键区域而非全局的精度,从而提高了优化效率。在测试函数中验证了该方法的求解精度和效率。最后将其应用于某重型商用车驾驶室动态特性优化中,获得多组支配优化前的设计方案,使驾驶室动态特性更好并且质量更轻。
3)针对求解耗时的复杂工程多目标优化问题,提出基于信赖域模型管理的优化算法。该算法将整个设计空间上的复杂优化问题,转化为一系列信赖域上的近似多目标优化问题。通过每个信赖域上的近似优化结果,确定信赖度和下代域的中心、半径,进而不断地缩放、平移信赖域,来保证获得与真实模型一致的非支配解。数值算例表明该方法降低了对代理模型精度的依赖,对处理复杂多目标优化问题具有一定的优势和潜力。该算法应用于某车门结构的优化中,通过匹配关键部件的厚度,很好地平衡了车门的各项动静态特性指标。
4)结合信赖域和智能布点技术,发展出一种高效的非线性多目标优化求解算法。通过样本遗传策略,遗传落在下代信赖域空间上的样本,减少实验设计样本个数从而提高效率。通过遗传智能布点策略,从非支配解外部解集中挑选部分到信赖域空间,提高关键区域代理模型的精度从而加快收敛。从而较好地处理了信赖域模型管理需要多次重采样导致效率低下的问题。该算法成功解决了不同类型的测试问题,并在与常见优化方法的比较中验证了其求解精度和效率。最后该算法应用于基于耐撞性和模态特性的轿车车身轻量化设计中,解决了实际工程多目标优化问题。
Most engineering optimization problems involve multiple objectives, which can not be expressed explicitly but acquired by complex computational model, and thus it increases the difficulty of solving multi-objective optimization problems. Intelligent optimization method is able to search for multiple optimal solutions in one single simulation run, and it is suitable for dealing with engineering problems, but the low efficiency limits its application to complex problems. Common multi-objective optimization methods based on metamodel can well deal with the low efficiency and become a research focus, but the solution accuracy is usually low. Therefore, this paper studies the multi-objective optimization methods based on metamodel, aims to improve the efficiency and accuracy, and makes the method well-employed in the design of vehicle body. The main contents are given as follows:
A new multi-objective optimization algorithm is proposed based on adaptive radial basis function. This method effectively assesses metamodel by using inherit Latin hypercube design, radial basis function and intergeneration projection genetic algorithm. Then through the combination of sampling points and testing points, the method gradually improves the metamodel accuracy. An extented greed algorithm is adopted to filter testing points from the last iterative into the final sample space to acquire adaptive radial basis function in the entire design region, and then adaptive radial basis function combines NSGA-Ⅱ to perform multi-objective optimization. The test functions have verified that adaptive radial basis function possesses the abilities of effectively assessing and gradually improving the accuracy. At last, the proposed method is applied to the thin-walled sections for structural crashworthiness. With the application of the method, it is beneficial to quickly find multi-group design schemes, which can well balance energy absorption and collision force.
A micro multi-objective genetic algorithm based on intelligent sampling technology is put forward. The algorithm adopts the extented radial basis function to build a global metamodel, and then employs the efficient micro multi-objective genetic algorithm for approximate optimization. In the following, intelligent sampling is achieved accroding to the optimization result with its feedback to the design space, and then continuously updates the metamodel, forming a closed loop process of experiment design and approximate optimization. In that case, the approximate optimization information has been fully utilized, and due to the method focusing only on the accuracy of metamodel in the concerned region rather than the global region, the optimization efficiency has been improved. Test functions have verified the accuracy and efficiency. Finally, the method has been used in the dynamic characteristic optimization of a heavy commercial vehicle cab and obtains many optimal design schemes.
Optimization algorithm based on trust region model management is proposed to solve the multi-objective optimization problem in complex engineering. The method transforms the complex optimization problems in the entire design space into a series of approximation problems in trust region, in which the optimazation result determines the reliability of center and radius of the next region. With constantly zooming, translating the trust region, the method ensures the non-dominated solutions in consistent with the true problem. Numerical examples show that this method reduces the dependance on metamodel accuracy and prove the method has certain advantages and potential in dealing with complex multi-objective optimization problems. Finally, the method has been applied in a door structure optimization, and well balances the static and dynamic performance by matching the thickness of key components.
Based on trust region and intelligent sampling technology, an efficient multi-objective method is developed. With the help of sample inheriting strategy, the method can inherit samples falling in the next trust region to reduce the number of experimental design samples, and thus the efficiency is increased. Based on intelligent sampling strategy, the method can select part of the solutions from external solutions into the next trust region, so improves the accuracy of the metamodel in concerned space to accelerate convergence. The method has successfully solved different types of testing problems, and compared with the common method, it not only obtains better optimial solutions, but also improves the optimization efficiency. Finally, the method has been successfully used in the lightweight design of car body based on crashworthiness and modal characteristics, and demonstrates its ability to solve multi-objective optimization problems in practical engineering.
1)提出基于自适应径向基函数的多目标优化算法。该算法通过遗传拉丁超立方实验设计、径向基函数和隔代映射遗传算法等技术,系统地评价代理模型。通过合并样本点和测试点来逐步地提升模型的精度。采用改进的贪婪算法挑选最后迭代步中的测试点到最终样本空间,构建整个设计域上的自适应径向基函数模型,并基于此模型结合具有代表性的NSGA-Ⅱ算法进行多目标优化。测试函数中验证了自适应径向基函数具备有效评价和逐步提升模型精度的能力。该算法应用于车身薄壁构件耐撞性多目标优化设计中,快速地找到了多组设计方案,较好地平衡了薄壁构碰撞过程中的吸能量和碰撞力。
2)提出基于智能布点技术的微型多目标遗传算法。该算法首先采用加强径向基函数构建全局代理模型,再采用高效的微型多目标遗传算法进行近似优化。根据优化结果信息进行智能布点,反馈到设计空间进而不断更新代理模型,使实验设计过程和近似优化过程形成闭环过程。由于充分利用了近似优化的信息,使仅关注代理模型在关键区域而非全局的精度,从而提高了优化效率。在测试函数中验证了该方法的求解精度和效率。最后将其应用于某重型商用车驾驶室动态特性优化中,获得多组支配优化前的设计方案,使驾驶室动态特性更好并且质量更轻。
3)针对求解耗时的复杂工程多目标优化问题,提出基于信赖域模型管理的优化算法。该算法将整个设计空间上的复杂优化问题,转化为一系列信赖域上的近似多目标优化问题。通过每个信赖域上的近似优化结果,确定信赖度和下代域的中心、半径,进而不断地缩放、平移信赖域,来保证获得与真实模型一致的非支配解。数值算例表明该方法降低了对代理模型精度的依赖,对处理复杂多目标优化问题具有一定的优势和潜力。该算法应用于某车门结构的优化中,通过匹配关键部件的厚度,很好地平衡了车门的各项动静态特性指标。
4)结合信赖域和智能布点技术,发展出一种高效的非线性多目标优化求解算法。通过样本遗传策略,遗传落在下代信赖域空间上的样本,减少实验设计样本个数从而提高效率。通过遗传智能布点策略,从非支配解外部解集中挑选部分到信赖域空间,提高关键区域代理模型的精度从而加快收敛。从而较好地处理了信赖域模型管理需要多次重采样导致效率低下的问题。该算法成功解决了不同类型的测试问题,并在与常见优化方法的比较中验证了其求解精度和效率。最后该算法应用于基于耐撞性和模态特性的轿车车身轻量化设计中,解决了实际工程多目标优化问题。
Most engineering optimization problems involve multiple objectives, which can not be expressed explicitly but acquired by complex computational model, and thus it increases the difficulty of solving multi-objective optimization problems. Intelligent optimization method is able to search for multiple optimal solutions in one single simulation run, and it is suitable for dealing with engineering problems, but the low efficiency limits its application to complex problems. Common multi-objective optimization methods based on metamodel can well deal with the low efficiency and become a research focus, but the solution accuracy is usually low. Therefore, this paper studies the multi-objective optimization methods based on metamodel, aims to improve the efficiency and accuracy, and makes the method well-employed in the design of vehicle body. The main contents are given as follows:
A new multi-objective optimization algorithm is proposed based on adaptive radial basis function. This method effectively assesses metamodel by using inherit Latin hypercube design, radial basis function and intergeneration projection genetic algorithm. Then through the combination of sampling points and testing points, the method gradually improves the metamodel accuracy. An extented greed algorithm is adopted to filter testing points from the last iterative into the final sample space to acquire adaptive radial basis function in the entire design region, and then adaptive radial basis function combines NSGA-Ⅱ to perform multi-objective optimization. The test functions have verified that adaptive radial basis function possesses the abilities of effectively assessing and gradually improving the accuracy. At last, the proposed method is applied to the thin-walled sections for structural crashworthiness. With the application of the method, it is beneficial to quickly find multi-group design schemes, which can well balance energy absorption and collision force.
A micro multi-objective genetic algorithm based on intelligent sampling technology is put forward. The algorithm adopts the extented radial basis function to build a global metamodel, and then employs the efficient micro multi-objective genetic algorithm for approximate optimization. In the following, intelligent sampling is achieved accroding to the optimization result with its feedback to the design space, and then continuously updates the metamodel, forming a closed loop process of experiment design and approximate optimization. In that case, the approximate optimization information has been fully utilized, and due to the method focusing only on the accuracy of metamodel in the concerned region rather than the global region, the optimization efficiency has been improved. Test functions have verified the accuracy and efficiency. Finally, the method has been used in the dynamic characteristic optimization of a heavy commercial vehicle cab and obtains many optimal design schemes.
Optimization algorithm based on trust region model management is proposed to solve the multi-objective optimization problem in complex engineering. The method transforms the complex optimization problems in the entire design space into a series of approximation problems in trust region, in which the optimazation result determines the reliability of center and radius of the next region. With constantly zooming, translating the trust region, the method ensures the non-dominated solutions in consistent with the true problem. Numerical examples show that this method reduces the dependance on metamodel accuracy and prove the method has certain advantages and potential in dealing with complex multi-objective optimization problems. Finally, the method has been applied in a door structure optimization, and well balances the static and dynamic performance by matching the thickness of key components.
Based on trust region and intelligent sampling technology, an efficient multi-objective method is developed. With the help of sample inheriting strategy, the method can inherit samples falling in the next trust region to reduce the number of experimental design samples, and thus the efficiency is increased. Based on intelligent sampling strategy, the method can select part of the solutions from external solutions into the next trust region, so improves the accuracy of the metamodel in concerned space to accelerate convergence. The method has successfully solved different types of testing problems, and compared with the common method, it not only obtains better optimial solutions, but also improves the optimization efficiency. Finally, the method has been successfully used in the lightweight design of car body based on crashworthiness and modal characteristics, and demonstrates its ability to solve multi-objective optimization problems in practical engineering.
引文
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