Stochastic Global Optimization: Problem Classes and Solution Techniques

There is a lack of a representative set of test problems for comparing global optimization methods. To remedy this a classiication of essentially un-constrained global optimization problems into unimodal, easy, moderately diicult, and diicult problems is proposed. The problem features giving this classiication are the chance to miss the basin of the global minimum, the dispersion of minima, and the number of minima. The classiication of some often used test problems are given and it is recognized that most of them are easy and some even unimodal. Working global optimization solution techniques treated are global, local, and adaptive search and their use for tackling diierent classes of problems is discussed. The problem of fair comparison of methods is then adressed. Further possible components of a general global optimization tool based on the problem classes and working solution techniques is presented.