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: 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.

A full process algebraic representation of Ant Colony Optimization

We present a process algebra capable of specifying parallelized Ant Colony Optimization algorithms in full detail: PA$^2$CO. After explaining the basis of three different ACO algorithms (Ant System, MAX-MIN Ant System, and Ant Colony System), we formally define PA$^2$CO and use it for representing several types of implementations with different parallel schemes. In particular fine-grained and coarse-grained specifications, each one taking advantage of parallel executions at different levels of system granularity, are formalized.

Measuring the benefits of lying in MARA under egalitarian social welfare

When some resources are to be distributed among a set of agents following egalitarian social welfare, the goal is to maximize the utility of the agent whose utility turns out to be minimal. In this context, agents can have an incentive to lie about their actual preferences, so that more valuable resources are assigned to them. In this paper we analyze this situation, and we present a practical study where genetic algorithms are used to assess the benefits of lying under different situations.