Optimisation for multilevel problems: a comparison of various algorithms

摘要

The optimization of imprecisely specified functions is a common problem occurring in various applications. Models of physical Systems can differ according to computational cost, accuracy and precision. In multilevel optimization, where differentmodels of a system are used, there is a great benefit in understanding how many, fast evaluations of limited accuracy may be combined with a few accurate calculations to yield an optimum solution. The combination of different models or levels ofrepresentations can lead to an objective function surface characterized by multiple values at a single point. This paper compares various optimization methods with genetic algorithms using three different strategies of multilevel optimization. A modified'bump' function is used as an example to compare the different methods and strategies. A sequential mixing strategy applied to a Genetic Algorithm with niche forming is shown to give best results. The paper highlights the need to develop a specializedoptimization algorithm for this kind of problem.