A New Framework for the Valuation of Algorithms for Black-Box Optimization

Black-box optimization algorithms optimize a fitness function f without knowledge of the specific parameters of the problem instance. Their run time is measured as the number of f -evaluations. This implies that the usual algorithmic complexity of a problem cannot be applied in the black-box scenario. Therefore, a new framework for the valuation of algorithms for black-box optimization is presented allowing the notion of the black-box complexity of a problem. For several problems upper and lower bounds on their black-box complexity are presented. Moreover, it can be concluded that randomized search heuristics whose (worst-case) expected optimization time for some problem is close to the black-box complexity of the problem are provably efficient (in the black-box scenario). The new approach is applied to several problems based on typical example functions and further interesting problems. Run times of general EAs for these problems are compared with the black-box complexity of the problem.