On stochastic global optimization of one-dimensional functions

We consider the applicability of stochastic global optimization algorithms on test-functions whose domain of definition is a simply-connected and finite interval of real numbers. We argue on the basis of theoretical reflections of statistical physics (namely random-walk) and computer simulations that there is a decisive difference between test-problems in one and multiple dimensions pointing to the necessity to only consider test-functions in higher dimensions. We argue that only test-problems in two or more dimensions provide for the possibility to discriminate the efficiency of stochastic global optimization algorithms with respect to the complexity of the underlying physical system at all. (c) 2005 Elsevier B.V. All rights reserved.