A Note on the Griewank Test Function

In this paper we analyze a widely employed test function for global optimization, the Griewank function. While this function has an exponentially increasing number of local minima as its dimension increases, it turns out that a simple Multistart algorithm is able to detect its global minimum more and more easily as the dimension increases. A justification of this counterintuitive behavior is given. Some modifications of the Griewank function are also proposed in order to make it challenging also for large dimensions.