Generalization and completeness of stochastic local search algorithms

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Loscos Barroso, Daniel and Martí Oliet, Narciso and Rodríguez Laguna, Ismael (2021) Generalization and completeness of stochastic local search algorithms. Swarm and Evolutionary Computation, 68 . p. 100982. ISSN 2210-6502

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Official URL: https://doi.org/10.1016/j.swevo.2021.100982



Abstract

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.


Item Type:Article
Additional Information:

CRUE-CSIC (Acuerdos Transformativos 2021)

Uncontrolled Keywords:Stochastic local search; Evolutionary computation, Swarm intelligence, Formal languages, Operational semantics, Generalization, Computability, Turing-completeness
Subjects:Sciences > Computer science
Sciences > Computer science > Computer programming
ID Code:70334
Deposited On:10 Feb 2022 13:11
Last Modified:18 Feb 2022 09:49

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