The goal of neural network engineering (NNE) is to study the advantages and disadvantages of neural networks and also providing methods to increase their performance. One of the problems in NNE is determination of optimal topology of neural networks for solving a given problem. There is no method to determine the optimal topology of multi-layer neural networks for a given problem. Usually, the designer selects a topology for neural networks and then trains it. The selected topology remains fixed during the training period. The performance of neural network depends on its size (number of hidden layers and hidden units). Determination of the optimal topology of neural network is an intractable problem. Therefore, most of algorithms for determination of the topology of neural network are approximate algorithms. These algorithms could be classified into five main groups: pruning algorithms, constructive algorithms, hybrid algorithms, evolutionary algorithms, and learning automata based algorithms. The only learning automata (LA) based algorithms, called survival algorithm, has been proposed by Beigy and Meybodi. This algorithm uses an object migrating learning automata and error back propagation (BP) algorithm and determines the number of hidden units of three layers neural networks, as training proceeds. In this paper, we propose three algorithms which are based on LA and BP. These algorithms determine a near optimal topology with low time complexity and high generalization capability for a given training set. These algorithms have two parts: determination of number of hidden units and determination of the number of hidden weights. One of the proposed algorithms uses the survival algorithm to determine the number of hidden units. A new algorithm based on LA is proposed to determine the number of hidden weights.  This algorithm deletes weights with small effect, which leads to lower time complexity and higher generalization rate. Two other algorithms do not omit the hidden units explicitly; a hidden unit is omitted when all its input weights are deleted. Most of the reported algorithms in the literature for determination of topology of neural networks use hill-climbing method and may stuck at local minima. The proposed algorithms use global search method which results in increasing the probability of escaping from local minima. The proposed algorithms have been tested on several problems such as: recognition of Farsi and English digits. Simulation results show that the produced networks have good performance. The proposed algorithms are compared with Karnin pruning algorithm.

One of the unsolved problems in multi-layer neural networks is the problem of determination of optimal topology a topology with minimum number of hid den units. There is no method to determine the optimal topology for multi-layer neural networks for a given problem. Usually the designer selects a topology for the network and then trains it. The selected topology remains fixed during the training period. Since the problem of determination of optimal topology for neural networks belongs to class of NP-Hard problems, most of the existing algorithms for determination of the topology are approximate algorithms. These algorithms could be classified into four main groups pruning algorithms, constructive algorithms, hybrid algorithms, and evolutionary algorithms. These algorithms can produce near optimal solutions. Most of these algorithms use hill-climbing method and may stick at local minima. In this paper a learning automata based algorithm called survival algorithm, for determination of the number of hidden units of three layers neural networks is proposed. The proposed algorithm uses learning automaton as a global search method in order to increase the probability of escaping from local minima and hence to increase the probability of obtaining the optimal topology. In survival algorithm, the training begins with a large network, and then by adding and deleting hidden units the optimal topology is obtained.        

BP algorithm has been used for wide range of applications. One of the most important limitations of this algorithm, is the low rate of convergence. The important reason behind this, is the saturation property of its activation functions. Once the output of a unit lies in the saturation area, the corresponding decent gradient would take a very small value. This will result in very little progress in the weight adjustment, if one takes affixed small learning rate parameter. To avoid this undesired phenomenon, one may consider a relative large learning rate. Unfortunately this would be dangerous, because it may take the algorithm diverges especially when the weight adjustment happens to fall into the surface regions with a large steepness. So, we require algorithms capable of tuning dynamically learning rate according to changes of gradient values. In this paper, different methos of dynamic changing of learning rate has been considered. Variable Learning Rate (VLR) algorithm and learning automata based learning rate adaptation algorithms are considered and compared with each other. Because the VLR parameters have important influence in its performance, so we use learning automata for adjusting them. In the proposed algorithm called Adaptive Variable Learning Rate (AVLR) algorithm, VLR parameters are adapted dynamically by learning automata according to error changes. Simulation results on various problems highlight better the merit of the proposed AVLR.

In this paper, we introduce open cellular learning automata and then study its convergence behavior. It is shown that for a class of rules called commutative rules, the open cellular learning automata in stationary external environments converges to a stable and compatible configuration. The numerical results also confirm the theory.  

Agents are software entities that act continuously and autonomously in a special environment. It is very essential for the agents to have the ability to learn how to act in the special environment for which they are designed to act in, to show reflexes to their environment actions, to choose their way and pursue it autonomously, and to be able to adapt and learn. In multi-agent systems, many intelligent agents that can interact with each other cooperate to achieve a set of goals. Because of the inherent complexity that exists in dynamic and changeable multi-agent environments, there is always a need to machine learning in such environments. As a model for learning, learning automata act in a stochastic environment and are able to update their action probabilities considering the inputs from their environment, so optimizing their functionality as a result. Learning automata are abstract models that can perform some numbers of actions. Each selected action is evaluated by a stochastic environment and a response is given back to the automata. Learning automata use this response to choose its next action. In this paper, the goal is to investigate and evaluate the application of learning automata to cooperation in multi-agent systems, using soccer server simulation as a test-bed. Because of the large state space of a complex Multi-agent domains, it is vital to have a method for environmental states’ generalization. An appropriate selection of such a method can have a great role in determining agent states and actions. In this paper we have also introduced and designed a new technique called “The best corner in State Square” for generalizing the vast number of states in the environment to a few number of states by building a virtual grid in agent’s domain environment. The efficiency of this technique in a cooperative multi-agent domain is investigated.