Two-stage asymmetric hybrid binary particle swarm optimization with adaptive-parameter learning in discrete Hopfield neural networks

Propositional satisfiability in discrete Hopfield neural network (DHNN) is widely studied, but its practical use is limited by low storage capacity, slow convergence, and repetitive neuron states. To address these limitations, we proposed a two-stage asymmetric hybrid binary particle swarm optimization (HBPSO) framework for enhancing the weighted C-type random 2-satisfiability logic in DHNN. In the first stage, a multi-objective-guided strategy combining fixed-parameter and adaptive-parameter HBPSO was introduced to improve storage capacity and guide the network toward optimal synaptic weight configurations. In the second stage, the fixed-parameter HBPSO was employed to further reduce repetitive neuron states and enhance solution diversity. Experimental results showed that the method achieves 100% fitness, identifies over 8.4 distinct optimal weight configurations with a 100% uniqueness ratio, and reduces the average iterations to 25.81. It also remained robust under noise levels from 0.1 to 1.0, with only a 41.2% increase in iterations. Overall, the proposed asymmetric HBPSO framework provides an effective approach for solving complex combinatorial optimization problems in computational intelligence.