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This problem can be studied for some classes of ACO algorithms, by using discrete time Markov chains on a countably infinite state space. We will describe now some general results which can be used to provide upper bounds for the expected time needed by a certain class of ACO algorithms to find an optimal solution [Gutjahr & Sebastiani (2008)]. To show their utility, we will also apply them to the MMAS algorithm [Gutjahr & Sebastiani (2008)]. The class of ACO algorithms involved are those such that the recursive rule for the pheromone only depends on the best-so-far-solution xb (t).

7. It is obviously that there are 5 AND neurons and 3 OR neurons left, that is, 5 pieces of fuzzy rules and 3 complex rules. The ultimate better performance result is compared with fuzzy control system. Test data set is Δψ(k) W V H γ (k) Fig. 7. The AND-OR FNN ship controller structure δ (K) Z An AND-OR Fuzzy Neural Network 37 Fig. 8. The performance index compared form the different part with training data in the same sequence introduce above. Fig. 8 shows the error comparison between test results and objective data.

W. and Rocha. : Fuzzy-set based models of neurons and knowledge-based networks. Trans. : Knowledge-based networks in classification problems. : Genectic granular classifiers in modeling software quality. : ATwo Layer Network using the OR/AND Neuron [A]. In: proc. 1566-1571. 38 Ant Colony Optimization - Methods and Applications [8] Pedrycz W. : Weighted fuzzy production rules. : Neural network structure optimization based on genetic algorithm. : Improving artificial neural networks with a pruning methodology and genetic algorithms for their application in microbial growth prediction in food.

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