Optimization of the Number of Evaluations in Optimization

Abstract

Any automobile existing today constitutes of thousands of parts. Each part when under analysis can be characterized by different parameters. The numbers of parameters associated to each part depend on the complexity of that particular part e.g. body or the engine of the vehicle which needs millions of parameters to be clearly defined to be reproducibly manufactured. The engine can be build up by a system, which we can say is a black-box, which for instance can describe the gasoline consumption of the engine of a car. In practice it is impossible to work with an unknown system while investigating the optimization methods, therefore we assume that we have a quadratic function instead. In the optimization we fit the quadratic function with linear models of four different kinds. These are the gradient method, the design of experiments, the spherical method and the lean optimization method. Supersaturated design approach (which we did use in the spherical and the lean optimization method) is a way to make the number of experiments less than the number parameters of a system. The spherical method was the best one in the optimization of the functions. It gives the smallest standard deviation among these four methods. From the optimization of functions it was possible to see that the spherical method gives very good optimum values (close to zero). The methods are possible to be used for optimization but not for prediction. In the prediction we are removing some values and using some model-values instead of these values. The standard deviation of the original function value was better than the standard deviation of the difference of the four different optimization functions and the original function.