Towards a Complexity Theory of Randomized Search Heuristics: Ranking-Based Black-Box Complexity

Abstract

Randomized search heuristics are a broadly used class of general-purpose algorithms. Analyzing them via classical methods of theoretical computer science is a growing field. A big step forward would be a useful complexity theory for such algorithms. We enrich the two existing black-box complexity notions due to Wegener and other authors by the restrictions that not actual objective values, but only the relative quality of the previously evaluated solutions may be taken into account by the algorithm. Many randomized search heuristics belong to this class of algorithms. We show that the new ranking-based model gives more realistic complexity estimates for some problems, while for others the low complexities of the previous models still hold.