On some difficulties in local evolutionary search

We consider the very simple problem of optimizing a stationary unimodal function over Rⁿ without using analytical gradient information. There exist numerous algorithms from mathematical programming to evolutionary algorithms for this problem. We have a closer look at advanced evolution strategies (GSA, CMA), the evolutionary gradient search algorithm (EGS), local search enhancement by random memorizing (LSERM), and the simple (1+1)-evolution strategy. These approaches show different problem-solving capabilities for different test functions. We introduce different measures which reflect certain aspects of what might be seen as the problem difficulty. Based on these measures it is possible to characterize the weak and strong points of the approaches which may lead to even more advanced algorithms