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

Yunjie Chang; Mohd Shareduwan Mohd Kasihmuddin; Yuan Gao; Yueling Guo; Nur Ezlin Zamri; Xiaofeng Jiang; Yunjie Chang; Mohd Shareduwan Mohd Kasihmuddin; Yuan Gao; Yueling Guo; Nur Ezlin Zamri; Xiaofeng Jiang

doi:10.3934/math.2026910

AIMS Mathematics

2026, Volume 11, Issue 7: 22495-22542. doi: 10.3934/math.2026910

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Research article

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

Yunjie Chang ^1,2,
Mohd Shareduwan Mohd Kasihmuddin ^{1
,
,},
Yuan Gao ³,
Yueling Guo ⁴,
Nur Ezlin Zamri ⁵,
Xiaofeng Jiang ¹

1.
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
2.
School of Computer Science and Engineering, Hunan Institute of Technology, Hengyang 421002, Hunan, China
3.
School of Intelligent Medicine, Chengdu University of Traditional Chinese Medicine, Chengdu 611137, Sichuan, China
4.
School of Science, Hunan Institute of Technology, Hengyang 421002, Hunan, China
5.
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received: 20 March 2026 Revised: 07 May 2026 Accepted: 12 May 2026 Published: 27 July 2026
MSC : 68T05, 90C27, 90C59

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.
Citation: Yunjie Chang, Mohd Shareduwan Mohd Kasihmuddin, Yuan Gao, Yueling Guo, Nur Ezlin Zamri, Xiaofeng Jiang. Two-stage asymmetric hybrid binary particle swarm optimization with adaptive-parameter learning in discrete Hopfield neural networks[J]. AIMS Mathematics, 2026, 11(7): 22495-22542. doi: 10.3934/math.2026910

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Abstract

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.

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