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Not all algorithms converging in value are also converging in model. For example, this is the case for the algorithm that explores the configuration space in a uniform and independent way, known as Random Search (RS). In fact, we have pv (t) = 1 A | X ∗ | At → 0, while it holds pm ( x ∗ , t) = . 1− |X| |X| In the following, we will only cope with the case where the ACO algorithm does not use the visibility matrix ηij . In this case, the configuration of each ant of the colony is built by a path over the construction graph [Gutjahr (2000)]: p( j | s p ) = τijα ∑ j∈ N ( s p) τijα ∀ j ∈ N (s p ) , (1) where (i, j) is the arc by which we continue the partial path s p , τij is its current pheromone value, and α is a positive parameter.

Branke, J. (2001). Evolutionary Approaches to Dynamic Environments - updated survey, GECCO Workshop on Evolutionary Algorithms for Dynamic Optimization Problems. pdf Branke, J. (2003). Evolutionary Approaches to Dynamic Optimization Problems: Introduction and Recent Trends, in J. ), GECCO Workshop on Evolutionary Algorithms for Dynamic Optimization Problems. document=2003 Cedeno, W. & Vemuri, V. R. (1997). On the Use of Niching for Dynamic Landscapes, International Conference on Evolutionary Computation, IEEE.

S is the total of OR neuron. Layer 5 (defuzzification layer): There is only one node in this layer, but includes forward compute and backward training. Center-of-gravity method is adopted for former compute as follows. z = O5 = ∑O h ∑O 4 l l ,1 4 l (11) where l = 1, 2," , s , H is the membership function of consequents. The latter is only imported to train data for optimization next. There is no conflict because the double directions are time-sharing. (8) − ( z d − m j )2 O = μ Bl ( zd ) = e 5 σ2 (12) 3.

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