The supreme discipline of engineers

The aim of optimization is to interpret or vote a system in such a way, that it meets one or more requirements in the best possible way.



This abstract description is to be concretized using the example of a motor whose efficiency is determined by the rotation speed and the torque as parameters. Rotation speed and torque are called parameters or design variables, efficiency degree is the target function. The task of the optimization is now, to define the parameters in such a way, that the efficiency degree will get maximum.



Various techniques are used to determine extreme values, which can be distinguished into derivation-free methods and methods that require the target function in addition to their derivations. The Downhill-Simplex method and the Conjugated-Gradient method are examples. It should be noted that the target function can have multiple extreme points, so that a distinction is made between local and global optimization.



In the above case, it is about a parameterized optimization. In contrast, there are also non-parametric optimizations. A classic example is the topology optimization of a solid body. With topology optimization, filigree structures can be generated from primitive bodies, which efficiently transfer applications of load via normal stresses. Design variables are here for example, the volume of the solid body, which is to be reduced to a fixed value with optimization, and the distortion energy, which is calculated with the distortion field and the stress field. It is essential, that the above-named design variables do not represent direct parameters such as the elasticity modulus and the radical stain coefficient of the material, as they are indirectly determined with the integration over the entire solid body.



In addition to the objective function, an optimization can also formulate auxiliary conditions which are additionally to be observed on the edge of the structure. Regarding to topology optimization, storage conditions and load application areas in particular are to be mentioned here.


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