Social behaviour is mainly based on swarm colonies, in which each individual shares its knowledge about the environment with other individuáis to get optimal solutions. Such co-operative model differs from competitive models in the way that individuáis die and are born by combining information of alive ones. This paper presents the particle swarm optimization with differential evolution algorithm in order to train a neural network instead the classic back propagation algorithm. The performance of a neural network for particular problems is critically dependant on the choice of the processing elements, the net architecture and the learning algorithm. This work is focused in the development of methods for the evolutionary design of artificial neural networks. This paper focuses in optimizing the topology and structure of connectivity for these networks.

Particle swarm optimization is a heuristic and stochastic technique inspiredby the flock of birds when looking for food. It is currently being used to solve continuous and discrete optimization problems. This paper proposes a hybrid, genetic inspired algorithm that uses random mutation/crossover operations and adds penalty functions to solve a particular case: the multidimensional knapsack problem. The algorithm implementation uses particle swarm for binary variables with a genetic operator. The particles update is performed in the following way: flrst using the iterative process (standard algorithm) described in the PSO algorithm and then using the best particle position (local) and the best global position to perform a random crossover/mutation with the original particle. The mutation and crossover operations speciflcally apply to personal and global best individuáis. The obtained results are promising compared to those obtained by using the probability binary particle swarm optimization algorithm.

Transition P System are a parallel and distributed computational model based on the notion of the cellular membrane structure. Each membrane determines a region that encloses a multiset of objects and evolution rules. Transition P Systems evolve through transitions between two consecutive configurations. Moreover, transitions between two consecutive configurations are provided by an exhaustive non-deterministic and parallel application of evolution rules inside each membrane of the P system. Hence, rules application is critical for the whole evolution process efficiency, because it is performed in parallel inside each membrane in each one of the evolution steps. It is known that P systems have a high degree of nondeterminism and parallelism. A transition in such a system consists in applying in parallel a set of atomic actions (e.g.,evolution rules) and this set of atomic actions is randomly chosen from a domain of possible next transitions. This paper tries to characterize this domain as the hyperspace defined by a set of diophantine equations and then to develop an algorithm which randomly chooses solutions from this hyperspace. Those solutions are uniquely related to the number of times that certain evolution rules are applied. The work presented here includes an algorithm based on resolving linear systems equations and explain into detail the process that the algorithm must follow.

Membrane systems are parallel and bioinspired systems which simúlate membranes behavior when processing information. As a part of unconventional computing, P-systems are proven to be effective in solving complex problems.A software technique is presented here that obtain good results when dealing with such problems. The rules application phase is studied and updated accordingly to obtain the desired results. Certain rules are candidate to be eliminated which can make the model improving in terms of time.

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