Generalization and completeness of stochastic local search algorithms

2021-09-01

Swarm and Evolutionary Computation

AI Summary

Existing research lacks a unified formal model for stochastic local search (SLS) algorithms, hindering a systematic characterization of their computational power and theoretical limits. This work proposes the first general formal framework that decomposes SLS algorithms into a common structural skeleton and parameterizable components, encompassing representative methods such as genetic algorithms, ant colony optimization, and particle swarm optimization through concrete instantiations. Leveraging this model, we construct an SLS instance capable of simulating any Turing machine, thereby rigorously establishing—for the first time—the Turing completeness of the entire class of SLS algorithms. Consequently, we derive the undecidability of nontrivial properties of these algorithms, revealing fundamental theoretical limitations inherent in their input–output behavior.

Technology Category

• Search and Optimization: Local Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Problem

• Stochastic Local Search
• Turing-completeness
• undecidability
• formal model
• heuristics

Innovation

• Stochastic Local Search
• Turing-completeness
• formal model
• Genetic Algorithms
• undecidability