Main

• AgE project home page
• Evolutionary multi-agent systems
• Computing environment (PL)

• Introduction
• EMAS
• iEMAS
• NN optimization
• Papers

Neural network architecture optimization is difficult but important task. Because of problems with understanding the neural models, it is almost impossible to propose optimal architecture of the neural network for certain task (usually, there are only general remarks about applying certain NN e.g. for classification or clustering). The process of optimization of this architecture is usually performed by an expert, involves many steps of complete training of different networks and is a very time-consuming job. However, there exist several classical techniques aimed at automatic optimization of neural network architecture based on mathematical features of neural networks. There are two approaches to solving this problem:

• destructive - algorithm starts from relatively complex network and removes unwanted neurons,
• constructive - algorithm starts from relatively simple network, and adds neurons when needed. The examples of popular destructive techniques are OBD (Optimal Brain Damage) and OBS (Optimal Brain Surgeon).

Evolutionary algorithms being an universal optimization algorithms are of course used also in the mentioned problem of neural network architecture optimiation. General structure of such an algorithm is as follows:

1. Create the population of the genotypes (random network structures)
2. Compute the fitness (this step involves the training and testing of all neural networks in the population)
3. Apply the selection, crossover and mutation to the population of genotypes, based on fitness values, creating subsequent population.
4. Go to 1. However, in order to perform this algorithm, a way must be proposed to encode an architecture of the neural network into a genotype. Generally this step may be performed in one of the folowing ways:
5. direct (strong) encoding, based on looseless transforming of the network structure, usually with use of adjacency matrix (but one of the most interesting is grammatical approach by Hiroaki Kitano), it is not effective because the genotypes are complex,
6. indirect (weak) encoding, based on approximate transforming of the network structure, in the simplest one may encode the number of the neurons in layers as natural numbers, assuming that there exists full connection among the neurons in subsequent layers, this approach is more effective. Both approaches suffer from noisy fitness evaluation (one genotype may yield different values of the fitness depending on the way of training of the neural network).

EMAS being universal optimization technique easily adapts to the problem of neural network optimization. The networks are entrusted to agents, and every agent performs the process of training of its network. During this process, the outcome of the network may be evaluated and based on this values, energy of the agent is exchanged amongh its neighbors.

In order to correctly evaluate the outcome (in the means of e.g. classification or prediction accuracy) of an evolutionary system, several techniques for managing such "collective intelligence" were presented. Neural-Agent system may be perceived as collective intelligent, because it consists the agents, every agent contains the network and every agent becomes a kind of expert - it may present the answer to the given problem. In order to compute the answer to the problem for the whole system (containing many experts) following techniques may be used:

1. Winner Takes All - based on the current value of the fitness (or energy in EMAS), the answer of the whole system is the answer of currently the best agent,
2. Winner Takes Most - the answer is based on appropriately defined weighted sum of particular agents' answers (an interesting approach was presented by Petridis and Kehagias - PREMONN).

Neural-based predicting EMAS merges the collective intelligence managing approach with EMAS idea. One more thing is the handling of the analyzed data, the subsequent values of the predicted time series is presented on the input of every agent in the system as soon as it becomes available. After computing the prediction by every agent, the answer of the whole system is computed based on PREMONN or simple WTA approach, and it is returned to the user. The error of prediction becomes main component of the fitness computation. More detailed description of this idea may be found in ByrDorNaw:IAI2002, ByrDor:ICCS2007.