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The Fan-Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

Piotr Formanowicz, Krzysztof Tanaś (2012)

International Journal of Applied Mathematics and Computer Science

It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan-Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan-Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another...

Theoretical analysis of steady state genetic algorithms

Alexandru Agapie, Alden H. Wright (2014)

Applications of Mathematics

Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are...

Towards a theory of practice in metaheuristics design: A machine learning perspective

Mauro Birattari, Mark Zlochin, Marco Dorigo (2006)

RAIRO - Theoretical Informatics and Applications

A number of methodological papers published during the last years testify that a need for a thorough revision of the research methodology is felt by the operations research community – see, for example, [Barr et al., J. Heuristics1 (1995) 9–32; Eiben and Jelasity, Proceedings of the 2002 Congress on Evolutionary Computation (CEC'2002) 582–587; Hooker, J. Heuristics1 (1995) 33–42; Rardin and Uzsoy, J. Heuristics7 (2001) 261–304]. In particular, the performance evaluation of nondeterministic methods,...

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