Systematic Boolean Satisfiability Programming in Radial Basis Function Neural Network

Abstract

Radial Basis Function Neural Network (RBFNN) is a class of Artificial Neural Network (ANN) that contains hidden layer processing units (neurons) with nonlinear, radially symmetric activation functions. Consequently, RBFNN has extensively suffered from significant computational error and difficulties in approximating the optimal hidden neuron, especially when dealing with Boolean Satisfiability logical rule. In this paper, we present a comprehensive investigation of the potential effect of systematic Satisfiability programming as a logical rule, namely 2 Satisfiability (2SAT) to optimize the output weights and parameters in RBFNN. The 2SAT logical rule has extensively applied in various disciplines, ranging from industrial automation to the complex management system. The core impetus of this study is to investigate the effectiveness of 2SAT logical rule in reducing the computational burden for RBFNN by obtaining the parameters in RBFNN. The comparison is made between RBFNN and the existing method, based on the Hopfield Neural Network (HNN) in searching for the optimal neuron state by utilizing different numbers of neurons. The comparison was made with the HNN as a benchmark to validate the final output of our proposed RBFNN with 2SAT logical rule. Note that the final output in HNN is represented in terms of the quality of the final states produced at the end of the simulation. The simulation dynamic was carried out by using the simulated data, randomly generated by the program. In terms of 2SAT logical rule, simulation revealed that RBFNN has two advantages over HNN model: RBFNN can obtain the correct final neuron state with the lowest error and does not require any approximation for the number of hidden layers. Furthermore, this study provides a new paradigm in the field feed-forward neural network by implementing a more systematic propositional logic rule.

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

“…RMSE [10] is a standard error estimator, which has been commonly used in predictions and classifications. During the learning phase, RMSE measured the deviation of the error between the current value f (w i ) and y i vis-à-vis mean − f .…”

“…MAPE [10] measured the size of the error in the form of percentage terms. During the learning phase, MAPE measured the percentage difference between the current value f (w i ) and y i .…”

“…where m is the number of neuron per clause as shown in the logic programming P 2SAT in Equation (1) [10,13], x i is a binary input value for N input neurons, and Euclidean norm space as follows:…”

“…The SNN system restriction can be observed in the aspect of high computation time in search of the best number of hidden neurons in the computational process. Inspired by various works in [10][11][12], 2-satisfiability (2SAT) representation logic has been used with RBFNN for identifying the relevant parameters as the center. Moreover, 2SAT has been chosen because it can comply with the RBFNN representations and structure.…”

Energy Based Logic Mining Analysis with Hopfield Neural Network for Recruitment Evaluation

“…Villca et al [ 16 ] utilized a radial basis function neural network (RBFNN) in predicting the optimum chemical composition during mining processes especially in copper tailings flocculation processes. Mansor et al [ 17 ] incorporates Boolean 2 satisfiability logical representation into RBFNN by obtaining the special parameters such as width and centre. The effective wind speed horizon has been forecasted with higher level of correctness as shown in the work of Madhiarasan [ 18 ].…”