A rigorous runtime analysis of different nature inspired meta-heuristics will be analysed in this projectin order to gain a deeper understanding of when and why a given meta-heuristic is expected to perform well or poorly. Various nature inspired meta-heuristics have been applied successfully to combinatorial optimisation in many scientific fields.However, their computational complexity is far from being understood in depth. It is still unclear how powerfulthey are for solving combinatorial optimisation problems, and where their real power is in comparison with the more traditional deterministic algorithms.Evolutionary Algorithms (EAs), Ant Colony Optimisation (ACO) and Artificial Immune System (AIS) algorithms will be studied in this project.Since the knowledge level of their computational complexity is at very different stages, two different types of results will be produced.One is the computational complexity results of realistic EAs, not (1+1)-EAs, on selected well-known combinatorial optimisation problems. A setup of complexity classes will be built revealing what classes of problems are hard (or easy) for which kind of EAs.The other is a setup of the first basis for a systematic computational complexity analysis of ACO and AIS other popular nature inspired meta-heuristics for which very few runtime results are available.The expected outcomes of this project will not only provide a solid foundation, but also insights and guidance in understandingwhich meta-heuristic should be preferred for a given problem and in the design of more efficient variants.