AutoDesign (TM) is meta model based optimization software. It is offered within mutibody dynamics simulation software RecurDyn.

The ultimate advantages of ‘Auto Design’ is that you can achieve optimization with a significantly smaller number of evaluation than any other optimization tools. Let me like to explain how it can be realized with this article.

First, we need to understand what meta-model is, because meta-model is used in Auto Design. It is used with other optimization tools as well. Meta-model is a (mathematical) approximation model which represents real system. In a very simple case, you can consider curve fitting, or interpolation as a meta-model. Recently, it becomes popular with machine learning, and AI, because it uses same concept. cf.) Meta model is also called as surrogate model. According to the information in Wiki pedia. It is explained as like below.

https://en.wikipedia.org/wiki/Metamodeling

There are different types of meta-model techniques. For example; 1) Kriging method 2) Radial basis function 3) Response surface method Please note that these meta-models are developed as an approximation model with its own purpose. For example, Kriging is developed to estimate the height of ground(mountain) on the map. In other words, it is not developed for optimization originally. How meta-model relates to optimization with CAE? It is an important issue that the design optimization strategy should reduce the number of evaluations. To do this, modern design optimization software has used meta-models widely. Real(physical) model is represented as (approximated mathematical) meta-model. Next, the typical numerical optimization solvers used to solve the design optimization problems which are composed of meta-models. Meta-model requires initial sampling points to construct it in the beginning. Optimization solver returns new design. Its convergency is evaluated. If it is not converged, meta model is updated. Optimization solver returns new design again. Convergency is checked. It is iterated. So, it is called as iterative method. To create the best meta model for the entire design area, the number of sample points must be large. There is significant difference in number of sample points(evaluations) between conventional optimization tools, and Auto Design. As it is written above, a meta model has developed to fit its own purpose. To fit its purpose, and improve efficiency, it has a kind of regulation for selecting sample points. In other words, sample points should be selected according to its rule. The figure below shows it.

At the initial DOE sampling, there is about 25 sampling point, and location. This is a rule that similar number of points, and position is required to use a meta model. As you see, at the new design-K, there must be similar sampling points, and location. Therefore, the number of sampling points increased a lot as its number of iterations increased. At the same time, previous sampling points are ignored, after making new sampling points. By the way, Auto Design is different. It does not need the similar number of sampling points when new design is updated. New design is added to the previous sampling points. In other words, the sampling points are updated, NOT ignored. Auto Design calls it as Progressive meta model. As a result of this we can get the optimization result even though the sampling points are much less than conventional method. The figure below shows less number of sampling points.

How it can be realized? These are ultimate advantages of Auto Design. Why don't other optimization tools use the same method as Auto Design? It is because that there is two major difficulties which are not solved by them, yet. These two things are 1) Solve numerical singularity in meta model 2) Optimization between fitting, and interpolation in a meta model The reason why each meta model has a regulation for selecting number of sampling points, and location is to avoid numerical singularity in solving. If it meets singularity, it cannot be solved. Dr. Kim develops a method to control singularity efficiently even though new design point is added randomly. It is implemented in Auto Design. A meta model has parts for fitting, and interpolation in formulation. Dr. Kim develops algorithms which controls fitting, and interpolation to choose the method that is advantageous for optimization. It is implemented in Auto Design. If you see Auto Design manual, there is title in red as shown below.

The things in red are things which are available in Auto Design only. In addition, the detailed techniques used for multi-objective optimization, robust optimization, and six-sigma optimization are much more practical and mathematically complete than existing software. Please refer to the contents of part I of the manual for the contents mentioned in (1) to (3). If you like to study progressive meta model, you can read the part in the order 1, 2, and 3 of part 1. If you like to research progressive meta model with purpose in short time, you can read the part in the order 3, 2, and 1 of part 1. If you are urgent to achieve optimization problem, you can refer to part 4.