An approach to multicriterion optimization problems for engineering design
An approach to multicriterion optimization problems for engineering design
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DOI：
10.1016/0045-7825(78)90046-4
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发表时间：
1978-09
影响因子：
7.2
通讯作者：
A. Osyczka
中科院分区：
文献类型：
--
作者：
A. Osyczka
机械工程设计中的优化问题通常被建模为非线性规划问题。本文提出了一种求解该问题的多准则优化方法。给出了问题的形式，并讨论了该问题的极小极大原理。在此基础上，给出了一种基于最小-最大最优原理的最优解比较算法，该最优解可以称为同时考虑所有准则的最优折衷。这一原理在数学上是完全形式化的，并用于自动获得最优解。比较解的算法从任何解集合中给出最小-最大意义上的最优解。寻找最小-最大意义上的最优解可以用许多不同的方法来实现。提出了一些基于蒙特卡罗方法和权衡研究的方法，并将该方法应用于机床变速箱的设计。将该问题转化为求基本结构参数(模数、齿数等)的问题。指同时使四个目标函数最小化的变速箱：元件体积、齿轮之间的周向速度、变速箱的宽度和输入轴和输出轴之间的距离。文中还给出了车床变速箱优化问题的具体算例。算例表明，对于某些机械工程优化问题，利用该方法可以自动得到设计者可以接受的最优解。
Optimization problems in mechanical engineering design are often modelled as nonlinear programming problems. A multicriterion optimization approach to this problem is developed in this work. The problem formulation is given, and the min-max principle for this problem is discussed. Next, an algorithm is provided for comparing solutions using this principle.The solution which is defined by the min-max principle of optimality may be called the best compromise considering all the criteria simultaneously and on equal terms of importance. This principle is fully formalized mathematically and used to obtain the optimal solution automatically. The algorithm for comparing solutions gives us, from any set of solutions, the one which is optimal in the min-max sense.Seeking the optimal solution in the min-max sense can be carried out in many different ways. Some methods based upon the Monte Carlo method and trade-off studies are proposed.The approach as discussed here is applied to the design of machine tool gearboxes. The problem is formulated as finding the basic constructional parameters (modules, numbers of teeth etc.) of a gearbox which minimizes simultaneously four objective functions: volume of elements, peripheral velocity between gears, width of gearbox and distance between axes of input and output shafts. A detailed example considering a lathe gearbox optimization problem is also presented. This example indicates that for some mechanical engineering optimization problems, using this approach, we can automatically obtain a solution which is optimal and acceptable to the designer.