Expensive Discrete Black Box Optimization for Vehicle Structures

Abstract

In the world of vehicle structure optimization the goal is to find car components that are, for example, as light or cheap as possible while still being able to fulfill all legal bindings of crash safety. Therefore, bounded constrained optimization problems with one objective and several constraints must be solved. Like with most engineering optimization problems one big limiting aspect arises: The runtime of function-evaluations is tremendous. Hence it is necessary to find a way of optimizing without knowing the exact behaviour of objective and constraints but only by several evaluations. This thesis will present a way of solving such expensive non-linear constrained black box problems. When constructing vehicles not only continuous variables occur, but also categorical ones defining different building materials. That is why the problem is in fact a so-called expensive mixed integer non-linear constrained black box problem. This thesis will focus on ways discrete variables can be optimized. For that purpose a general optimization routine solving expensive mixed integer non-linear constrained black box problems is presented. In this routine the black box functions are approximated by Gaussian regression models. In order to define their input Latin Hypercube Sampling is used. In the pure optimization step it becomes obvious that the global optimizer SCIP outperforms other implemented optimizers. Chapter 6 will discuss different options of dealing with categorical variables. Here it appears that depending on the use case different approaches are appropriate. Mostly One-Hot encoding should be used. For greater problems also Logarithmic encoding can be suitable. In chapter 7, more light is shed on the algorithm's implementation in Python. All mathematically derived results will be verified in chapter 8. Since it turns out that the basic algorithm leaves some room for improvements, a heuristic adaptation is explained in chapter 9.