Cooperative learning for radial basis function networks using particle swarm optimization

Multi-Kernel Fusion for RBF Neural Networks

A simple yet effective architectural design of radial basis function neural networks (RBFNN) makes them amongst the most popular conventional neural networks. The current generation of radial basis function neural network is equipped with multiple kernels which provide significant performance benefits compared to the previous generation using only a single kernel. In existing multi-kernel RBF algorithms, multi-kernel is formed by the convex combination of the base/primary kernels. In this paper, we propose a novel multi-kernel RBFNN in which every base kernel has its own (local) weight. This novel flexibility in the network provides better performance such as faster convergence rate, better local minima and resilience against stucking in poor local minima. These performance gains are achieved at a competitive computational complexity compared to the contemporary multi-kernel RBF algorithms. The proposed algorithm is thoroughly analysed for performance gain using mathematical and graphical illustrations and also evaluated on three different types of problems namely: (i) pattern classification, (ii) system identification and (iii) function approximation. Empirical results clearly show the superiority of the proposed algorithm compared to the existing state-of-the-art multi-kernel approaches.

Gradient-based training and pruning of radial basis function networks with an application in materials physics

Many applications, especially in physics and other sciences, call for easily interpretable and robust machine learning techniques. We propose a fully gradient-based technique for training radial basis function networks with an efficient and scalable open-source implementation. We derive novel closed-form optimization criteria for pruning the models for continuous as well as binary data which arise in a challenging real-world material physics problem. The pruned models are optimized to provide compact and interpretable versions of larger models based on informed assumptions about the data distribution. Visualizations of the pruned models provide insight into the atomic configurations that determine atom-level migration processes in solid matter; these results may inform future research on designing more suitable descriptors for use with machine learning algorithms.

Artificial Immune System in Doing 2-Satisfiability Based Reverse Analysis Method via a Radial Basis Function Neural Network

A radial basis function neural network-based 2-satisfiability reverse analysis (RBFNN-2SATRA) primarily depends on adequately obtaining the linear optimal output weights, alongside the lowest iteration error. This study aims to investigate the effectiveness, as well as the capability of the artificial immune system (AIS) algorithm in RBFNN-2SATRA. Moreover, it aims to improve the output linearity to obtain the optimal output weights. In this paper, the artificial immune system (AIS) algorithm will be introduced and implemented to enhance the effectiveness of the connection weights throughout the RBFNN-2SATRA training. To prove that the introduced method functions efficiently, five well-established datasets were solved. Moreover, the use of AIS for the RBFNN-2SATRA training is compared with the genetic algorithm (GA), differential evolution (DE), particle swarm optimization (PSO), and artificial bee colony (ABC) algorithms. In terms of measurements and accuracy, the simulation results showed that the proposed method outperformed in the terms of Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Schwarz Bayesian Criterion (SBC), and Central Process Unit time (CPU time). The introduced method outperformed the existing four algorithms in the aspect of robustness, accuracy, and sensitivity throughout the simulation process. Therefore, it has been proven that the proposed AIS algorithm effectively conformed to the RBFNN-2SATRA in relation to (or in terms of) the average value of training of RMSE rose up to 97.5%, SBC rose up to 99.9%, and CPU time by 99.8%. Moreover, the average value of testing in MAE was rose up to 78.5%, MAPE was rose up to 71.4%, and was capable of classifying a higher percentage (81.6%) of the test samples compared with the results for the GA, DE, PSO, and ABC algorithms.

Coverage and k-Coverage Optimization in Wireless Sensor Networks Using Computational Intelligence Methods: A Comparative Study

The domain of wireless sensor networks is considered to be among the most significant scientific regions thanks to the numerous benefits that their usage provides. The optimization of the performance of wireless sensor networks in terms of area coverage is a critical issue for the successful operation of every wireless sensor network. This article pursues the maximization of area coverage and area k-coverage by using computational intelligence algorithms, i.e., a genetic algorithm and a particle swarm optimization algorithm. Their performance was evaluated via comparative simulation tests, made not only against each other but also against two other well-known algorithms. This appraisal was made using statistical testing. The test results, that proved the efficacy of the algorithms proposed, were analyzed and concluding remarks were drawn.

Using Cuckoo Search Algorithm with Q-Learning and Genetic Operation to Solve the Problem of Logistics Distribution Center Location

Cuckoo search (CS) algorithm is a novel swarm intelligence optimization algorithm, which is successfully applied to solve some optimization problems. However, it has some disadvantages, as it is easily trapped in local optimal solutions. Therefore, in this work, a new CS extension with Q-Learning step size and genetic operator, namely dynamic step size cuckoo search algorithm (DMQL-CS), is proposed. Step size control strategy is considered as action in DMQL-CS algorithm, which is used to examine the individual multi-step evolution effect and learn the individual optimal step size by calculating the Q function value. Furthermore, genetic operators are added to DMQL-CS algorithm. Crossover and mutation operations expand search area of the population and improve the diversity of the population. Comparing with various CS algorithms and variants of differential evolution (DE), the results demonstrate that the DMQL-CS algorithm is a competitive swarm algorithm. In addition, the DMQL-CS algorithm was applied to solve the problem of logistics distribution center location. The effectiveness of the proposed method was verified by comparing with cuckoo search (CS), improved cuckoo search algorithm (ICS), modified chaos-enhanced cuckoo search algorithm (CCS), and immune genetic algorithm (IGA) for both 6 and 10 distribution centers.

Training radial basis function networks for wind speed prediction using PSO enhanced differential search optimizer

This paper presents an integrated hybrid optimization algorithm for training the radial basis function neural network (RBF NN). Training of neural networks is still a challenging exercise in machine learning domain. Traditional training algorithms in general suffer and trap in local optima and lead to premature convergence, which makes them ineffective when applied for datasets with diverse features. Training algorithms based on evolutionary computations are becoming popular due to their robust nature in overcoming the drawbacks of the traditional algorithms. Accordingly, this paper proposes a hybrid training procedure with differential search (DS) algorithm functionally integrated with the particle swarm optimization (PSO). To surmount the local trapping of the search procedure, a new population initialization scheme is proposed using Logistic chaotic sequence, which enhances the population diversity and aid the search capability. To demonstrate the effectiveness of the proposed RBF hybrid training algorithm, experimental analysis on publicly available 7 benchmark datasets are performed. Subsequently, experiments were conducted on a practical application case for wind speed prediction to expound the superiority of the proposed RBF training algorithm in terms of prediction accuracy.

An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models

This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM) algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS) stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC) motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses.