Generalization and completeness of stochastic local search algorithms

We generalize Stochastic Local Search (SLS) heuristics into a unique formal model. This model has two key components: common structure designed to be as large possible and parametric intended small possible. Each heuristic is obtained by instantiating the part in different way. Particular instances for Genetic Algorithms (GA), Ant Colony Optimization (ACO), Particle Swarm (PSO) are presented. Then, we use our prove Turing-completeness of SLS algorithms general. The proof uses framework construct GA able simulate any Turing machine. implies that determining non-trivial property concerning relationship between inputs computed outputs undecidable and, extension, general set methods (although not necessarily each particular method). Similar proofs more informally presented PSO ACO.