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- Genetic programming and bacterial algorithm for neural networks and fuzzy systems designPublication . Cabrita, Cristiano Lourenço; Botzheim, J.; Ruano, Antonio; Kóczy, László T.In the field of control systems it is common to use techniques based on model adaptation to carry out control for plants for which mathematical analysis may be intricate. Increasing interest in biologically inspired learning algorithms for control techniques such as Artificial Neural Networks and Fuzzy Systems is in progress. In this line, this paper gives a perspective on the quality of results given by two different biologically connected learning algorithms for the design of B-spline neural networks (BNN) and fuzzy systems (FS). One approach used is the Genetic Programming (GP) for BNN design and the other is the Bacterial Evolutionary Algorithm (BEA) applied for fuzzy rule extraction. Also, the facility to incorporate a multi-objective approach to the GP algorithm is outlined, enabling the designer to obtain models more adequate for their intended use.
- Genetic programming and bacterial algorithm for neural networks and fuzzy systems designPublication . Cabrita, Cristiano Lourenço; Botzheim, J.; Ruano, Antonio; Kóczy, László T.In the field of control systems it is common to use techniques based on model adaptation to carry out control for plants for which mathematical analysis may be intricate. Increasing interest in biologically inspired learning algorithms for control techniques such as Artificial Neural Networks and Fuzzy Systems is in progress. In this line, this paper gives a perspective on the quality of results given by two different biologically connected learning algorithms for the design of B-spline neural networks (BNN) and fuzzy systems (FS). One approach used is the Genetic Programming (GP) for BNN design and the other is the Bacterial Evolutionary Algorithm (BEA) applied for fuzzy rule extraction. Also, the facility to incorporate a multi-objective approach to the GP algorithm is outlined, enabling the designer to obtain models more adequate for their intended use.
- Supervised training algorithms for B-spline neural networks and fuzzy systemsPublication . Ruano, Antonio; Cabrita, Cristiano Lourenço; Oliveira, J. V.; Tikk, D.; Kóczy, László T.Complete supervised training algorithms for B-spline neural networks and fuzzy rule-based systems are discussed. By introducing the relationships between B-spline neural networks and Mamdani (satisfying certain assumptions) fuzzy model, training algorithms developed initially for neural networks can be adapted to fuzzy systems. The standard training criterion is reformulated, by separating the linear and nonlinear parameters. By employing this reformulated criterion with the Levenberg-Marquardt algorithm, a new training method, offering a fast rate of convergence is obtained. It is also shown that the standard Error-Back Propagation algorithm, the most common training method for this class of systems, exhibits a very poor performance.
- Genetic and bacterial programming for B-spline neural networks designPublication . Ruano, Antonio; Botzheim, J.; Cabrita, Cristiano Lourenço; Kóczy, László T.The design phase of B-spline neural networks is a highly computationally complex task. Existent heuristics have been found to be highly dependent on the initial conditions employed. Increasing interest in biologically inspired learning algorithms for control techniques such as Artificial Neural Networks and Fuzzy Systems is in progress. In this paper, the Bacterial Programming approach is presented, which is based on the replication of the microbial evolution phenomenon. This technique produces an efficient topology search, obtaining additionally more consistent solutions.
- A new domain decomposition for B-spline Neural NetworksPublication . Cabrita, Cristiano Lourenço; Ruano, Antonio; Kóczy, László T.B-spline Neural Networks (BSNNs) belong to the class of networks termed grid or lattice-based associative memories networks (AMN). The grid is a key feature since it allows these networks to exhibit relevant properties which make them efficient in solving problems namely, functional approximation, non-linear system identification, and on-line control. The main problem associated with BSNNs is that the model complexity grows exponentially with the number of input variables. To tackle this drawback, different authors developed heuristics for functional decomposition, such as the ASMOD algorithm or evolutionary approaches [2]. In this paper, we present a complementary approach, by allowing the properties of B-spline models to be achieved by non-full grids. This approach can be applied either to a single model or to an ASMOD decomposition. Simulation results show that comparable results, in terms of approximations can be obtained with less complex models.
- Fuzzy rule extraction by bacterial memetic algorithmsPublication . Botzheim, J.; Cabrita, Cristiano Lourenço; Kóczy, László T.; Ruano, AntonioIn our previous papers, fuzzy model identification methods were discussed. The bacterial evolutionary algorithm for extracting fuzzy rule base from a training set was presented. The Levenberg–Marquardt method was also proposed for determining membership functions in fuzzy systems. The combination of the evolutionary and the gradient-based learning techniques is usually called memetic algorithm. In this paper, a new kind of memetic algorithm, the bacterial memetic algorithm, is introduced for fuzzy rule extraction. The paper presents how the bacterial evolutionary algorithm can be improved with the Levenberg–Marquardt technique.
- Estimating fuzzy membership functions parameters by the levenberg-marquardt algorithmPublication . Botzheim, J.; Cabrita, Cristiano Lourenço; Kóczy, László T.; Ruano, AntonioIn previous papers from the authors fuzzy model identification methods were discussed. The bacterial algorithm for extracting fuzzy rule base from a training set was presented. The Levenberg-Marquardt algorithm was also proposed for determining membership functions in fuzzy systems. In this paper the Levenberg-Marquardt technique is improved to optimise the membership functions in the fuzzy rules without Ruspini-partition. The class of membership functions investigated is the trapezoidal one as it is general enough and widely used. The method can be easily extended to arbitrary piecewise linear functions as well.
- Extending the functional training approach for B-splinesPublication . Cabrita, Cristiano Lourenço; Ruano, Antonio; Ferreira, P. M.; Kóczy, László T.When used for function approximation purposes, neural networks belong to a class of models whose parameters can be separated into linear and nonlinear, according to their influence in the model output. This concept of parameter separability can also be applied when the training problem is formulated as the minimization of the integral of the (functional) squared error, over the input domain. Using this approach, the computation of the gradient involves terms that are dependent only on the model and the input domain, and terms which are the projection of the target function on the basis functions and on their derivatives with respect to the nonlinear parameters, over the input domain. This paper extends the application of this formulation to B-splines, describing how the Levenberg- Marquardt method can be applied using this methodology. Simulation examples show that the use of the functional approach obtains important savings in computational complexity and a better approximation over the whole input domain.
- Exploiting the functional training approach in B-SplinesPublication . Ruano, Antonio; Cabrita, Cristiano Lourenço; Ferreira, P. M.; Kóczy, László T.When used for function approximation purposes, neural networks belong to a class of models whose parameters can be separated into linear and nonlinear, according to their influence in the model output. This concept of parameter separability can also be applied when the training problem is formulated as the minimization of the integral of the (functional) squared error, over the input domain. Using this approach, the computation of the gradient involves terms that are dependent only on the model and the input domain, and terms which are the projection of the target function on the basis functions and on their derivatives with respect to the nonlinear parameters, over the input domain. These later terms can be numerically computed with the data. The use of the functional approach is introduced here for B-splines. An example shows that, besides great computational complexity savings, this approach obtains better results than the standard, discrete technique, as the performance surface employed is more similar to the one obtained with the function underlying the data. In some cases, as shown in the example, a complete analytical solution can be found.
- An hybrid training method for B-spline neural networksPublication . Cabrita, Cristiano Lourenço; Botzheim, J.; Ruano, Antonio; Kóczy, László T.Current and past research has brought up new views related to the optimization of neural networks. For a fixed structure, second order methods are seen as the most promising. From previous works we have shown how second order methods are of easy applicability to a neural network. Namely, we have proved how the Levenberg-Marquard possesses not only better convergence but how it can assure the convergence to a local minima. However, as any gradient-based method, the results obtained depend on the startup point. In this work, a reformulated Evolutionary algorithm - the Bacterial Programming for Levenberg-Marquardt is proposed, as an heuristic which can be used to determine the most suitable starting points, therefore achieving, in most cases, the global optimum.