Evolutionary optimization of neuron-state distributions for logic-driven associative memory systems

Reliable optimization of neuron states in Discrete Hopfield Neural Networks (DHNNs) is essential for logic-driven associative memory because conventional learning algorithms often suffer from limited neuron-state diversity together which often leads to suboptimal neuron states. To address these limitations, this paper proposes a Multi-Objective Hybrid Differential Evolutionary Algorithm (MHDEA) to optimize the learning capability of DHNN governed by the Y-type Random 2-Satisfiability (YRAN2SAT) formulation. The proposed framework introduces a multi-objective optimization strategy that simultaneously maximizes clause satisfaction while promoting neuron-state diversity through six coordinated operators operating within a unified optimization framework. Extensive experiments conducted under diverse YRAN2SAT logical environments with varying clause compositions demonstrate that MHDEA consistently achieves accurate synaptic-weight learning, generates highly diversified neuron states, and successfully retrieves globally optimal logical solutions. Comparative analyses against classical optimization algorithms together with recent state-of-the-art multi-objective evolutionary methods further validate the robustness, effectiveness, and competitiveness of the proposed framework across diverse logical environments. Furthermore, theoretical analyses on convergence behavior, entropy–fitness synchrony, and computational complexity provide theoretical justification for the optimization dynamics of MHDEA.