# Biblio

Swarm Intelligence (SI) algorithms, such as Fish School Search (FSS), are well known as useful tools that can be used to achieve a good solution in a reasonable amount of time for complex optimization problems. And when problems increase in size and complexity, some increase in population size or number of iterations might be needed in order to achieve a good solution. In extreme cases, the execution time can be huge and other approaches, such as parallel implementations, might help to reduce it. This paper investigates the relation and trade off involving these three aspects in SI algorithms, namely population size, number of iterations, and problem complexity. The results with a parallel implementations of FSS show that increasing the population size is beneficial for finding good solutions. However, we observed an asymptotic behavior of the results, i.e. increasing the population over a certain threshold only leads to slight improvements.

This paper proposes a cooperative continuous ant colony optimization (CCACO) algorithm and applies it to address the accuracy-oriented fuzzy systems (FSs) design problems. All of the free parameters in a zero- or first-order Takagi-Sugeno-Kang (TSK) FS are optimized through CCACO. The CCACO algorithm performs optimization through multiple ant colonies, where each ant colony is only responsible for optimizing the free parameters in a single fuzzy rule. The ant colonies cooperate to design a complete FS, with a complete parameter solution vector (encoding a complete FS) that is formed by selecting a subsolution component (encoding a single fuzzy rule) from each colony. Subsolutions in each ant colony are evolved independently using a new continuous ant colony optimization algorithm. In the CCACO, solutions are updated via the techniques of pheromone-based tournament ant path selection, ant wandering operation, and best-ant-attraction refinement. The performance of the CCACO is verified through applications to fuzzy controller and predictor design problems. Comparisons with other population-based optimization algorithms verify the superiority of the CCACO.