Synergizing intelligence and knowledge discovery: Hybrid black hole algorithm for optimizing discrete Hopfield neural network with negative based systematic satisfiability

The current systematic logical rules in the Discrete Hopfield Neural Network encounter significant challenges, including repetitive final neuron states that lead to the issue of overfitting. Furthermore, the systematic logical rules neglect the impact on the appearance of negative literals within the logical structure, and most recent efforts have primarily focused on improving the learning capabilities of the network, which could potentially limit its overall efficiency. To tackle the limitation, we introduced a Negative Based Higher Order Systematic Logic to the network, imposing restriction on the appearance of negative literals within the clauses. Additionally, a Hybrid Black Hole Algorithm was proposed in the retrieval phase to optimize the final neuron states. This ensured that the optimized states achieved maximum diversity and reach global minima solutions with the lowest similarity index, thereby enhancing the overall performance of the network. The results illustrated that the proposed model can achieve up to 10,000 diversified and global solutions with an average similarity index of 0.09. The findings indicated that the optimized final neuron states are in optimal configurations. Based on the findings, the development of the new systematic SAT and the implementation of the Hybrid Black Hole algorithm to optimize the retrieval capabilities of DHNN to achieve multi-objective functions result in updated final neuron states with high diversity, high attainment of global minima solutions, and produces states with a low similarity index. Consequently, this proposed model could be extended for logic mining applications to tackle classification tasks. The optimized final neuron states will enhance the retrieval of high-quality induced logic, which is effective for classification and knowledge extraction.