Page - 109 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

E Simplex Method by Nelder-Mead This description of the method is based on the lecture of Oberle, [Obe12]. The objec- tive in the given example is to minimize f (P) with respect to the parameters P =[ P1 P2 · ·· PnP ]T . The idea behind this method is to calculate the function value f (P) fornP+1 parameter sets, which are called simplex. The maximum function value is replaced by a new function value. This process is repeated until an exit condition is fulfilled. Figure E.1 shows the different steps. The method was limited to two parameters (nP = 2) in order to provide good visualization in two-dimensional plots. It could be easily extended for more parameters due to the compact notation in vector form. The first step is to calculate the function values for a set ofnP+1. The function values are sorted according to the rule f (Pb)<f (Pib)<f (Pw), (E.1) where the index bmeans best, ibmeans in between, andwmeans worst. In the next step, the mean value of the parameters, excluding the worst one, are calculated, which reads P¯= 1 nP ∑ i 6=w Pi. (E.2) A new parameter set is generated by the reflection of Pw at P¯ by using Pn1 = P¯+α ( P¯−Pw ) . (E.3)