A novel bitwise arithmetic optimization algorithm for the rule base optimization of deep neuro-fuzzy system

Abstract

The novel Deep Neuro-Fuzzy System (DNFS) has attracted significant attention from researchers due to the model's adaptability and rule-based structure. The model has been successfully implemented in various real-world applications. However, despite its success, the DNFS experience difficulties applying high-dimensional data. The rule base in the DNFS expands exponentially with the number of features affecting the transparency of the model. Additionally, the typical gradient-descent (GD) technique used in the DNFS rule-base optimization frequently encounters the issue of being trapped in local minima. This study aims to introduce a modern optimization approach to address these drawbacks. Therefore, the novel Bitwise Arithmetic Optimization Algorithm (BAOA) has been proposed in this work. The BAOA method has been implemented as a feature selection approach to solve the large rule base problem due to applying high dimensional data. Moreover, the DNFS’ rule base optimization was carried out using the proposed BAOA algorithm to escape the local minima issue owing to the GD algorithm. The simulation results obtained on twelve benchmark datasets illustrated that the BAOA has been able to select the least number of features from high-dimensional data with an average accuracy of 95.53%. In terms of rule base optimization, the novel BAOA achieved better performance with average training and testing accuracies of 96.87% and 96.25%, respectively, on benchmark datasets compared to the Arithmetic Optimization Algorithm (AOA) (average training and testing accuracies of 95.66% and 94.54%) and GD-based optimization (average training and testing accuracies of 94.07% and 93.19%). Additionally, the Wilcoxon test revealed a significant difference between the performances of the proposed BAOA algorithm and comparative methods. The findings indicate that the proposed BAOA approach is highly effective for high-dimensional real-world problems.

Keywords

• Machine learning
• Deep learning
• Bitwise arithmetic optimization algorithm
• Metaheuristics
• Gradient-descent