Fundamental differences between optimization code test problems in engineering applications

Abstract

The purpose here is to suggest that there is at least one fundamental difference between the problems used for testing optimization codes and the problems that engineers often need to solve; in particular, the level of precision that can be practically achieved in the numerical evaluation of the objective function, derivatives, and constraints. This difference affects the performance of optimization codes, as illustrated by two examples. Two classes of optimization problem were defined. Class One functions and constraints can be evaluated to a high precision that depends primarily on the word length of the computer. Class Two functions and/or constraints can only be evaluated to a moderate or a low level of precision for economic or modeling reasons, regardless of the computer word length. Optimization codes have not been adequately tested on Class Two problems. There are very few Class Two test problems in the literature, while there are literally hundreds of Class One test problems. The relative performance of two codes may be markedly different for Class One and Class Two problems. Less sophisticated direct search type codes may be less likely to be confused or to waste many function evaluations on Class Two problems. The analysis accuracy and minimization performance are related in a complex way that probably varies from code to code. On a problem where the analysis precision was varied over a range, the simple Hooke and Jeeves code was more efficient at low precision while the Powell code was more efficient at high precision.