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

翻译：我们将随机局部搜索启发式算法统一归纳为一个形式化模型。该模型包含两个关键组成部分：一个被设计为尽可能通用的公共结构，以及一个被设计为尽可能精简的参数化结构。每种启发式算法均可通过对参数化部分进行不同实例化而获得。本文具体展示了遗传算法、蚁群优化算法和粒子群优化算法的实例。随后，我们运用该模型证明了随机局部搜索算法整体具有图灵完备性。证明过程通过构建能够模拟任意图灵机的遗传算法来实现。这种图灵完备性意味着：对于遗传算法乃至广义的随机局部搜索方法集合（尽管不一定适用于每个具体方法），判定其输入与计算输出之间关系的任何非平凡性质都是不可判定的。本文还对粒子群优化算法和蚁群优化算法给出了类似的非形式化证明。