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Hybrid Multiobjective Framework for Boolean Satisfiability Optimization With Application to Financial Risk Prediction.

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Title: Hybrid Multiobjective Framework for Boolean Satisfiability Optimization With Application to Financial Risk Prediction.
Authors: Abubakar, Hamza1,2 (AUTHOR) zeeham4u2c@yahoo.com, Sayed, Amani Idris A.3 (AUTHOR), Karaye, Abubakar Balarabe4 (AUTHOR), Sánchez, Allan G. S. (AUTHOR) allan.soriano@itcelaya.edu.mx
Source: Journal of Applied Mathematics. 5/25/2026, Vol. 2026, p1-28. 28p.
Subjects: Hopfield networks, Swarm intelligence, Metaheuristic algorithms, Evolutionary computation, Financial risk management, Proposition (Logic)
Abstract: Financial distress prediction demands models that balance complex pattern recognition with interpretable decision logic. This study reframes the prediction task as a Boolean satisfiability (SAT) problem and introduces a hybrid neurosymbolic framework, Hopfield neural network (HNN)–RANkSATRA, that integrates HNNs with metaheuristic optimization to overcome the local minima limitations of conventional HNNs. Two hybrid architectures are developed: hybrid dragonfly–Hopfield algorithm (HNN–RANkSAT–HAD) and hybrid evolution strategy–Hopfield algorithm (HNN–RANkSAT–HES), both employing the RANkSATRA method for reverse logic mining from financial data. In computational simulations on synthetic RANkSAT benchmarks, HNN–RANkSAT–HDA consistently outperformed both the baseline HNN–RANkSAT and the HES variant, achieving superior global minima ratio (Zm = 0.90), convergence speed (10.8 iterations), energy minimization (0.10), and model calibration (log‐loss = 0.34). The baseline model demonstrated a scalability constraint, plateauing in performance beyond 70 neurons. Applied to three real‐world financial distress datasets, the German Credit dataset (GCSD), the Polish Companies dataset (PCDS), and the Taiwanese Bankruptcy dataset (TDS), the framework demonstrated robust predictive utility. HNN–RANkSAT–HDA achieved the highest median testing accuracy (0.941), F1‐score (0.938), and AUC (0.934), while also showing the best probabilistic calibration, evidenced by the lowest average log‐loss (0.315). Nonparametric statistical tests (Friedman and Wilcoxon signed‐rank) confirmed a significant performance hierarchy: HNN–RANkSAT–HDA > HNN–RANkSAT–HES > HNN–RANkSAT (p < 0.001 for all metrics). The study demonstrates that the integration of swarm intelligence, specifically the dragonfly algorithm, into a neurosymbolic SAT framework yields a powerful, interpretable, and statistically robust tool for financial risk analytics. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Financial distress prediction demands models that balance complex pattern recognition with interpretable decision logic. This study reframes the prediction task as a Boolean satisfiability (SAT) problem and introduces a hybrid neurosymbolic framework, Hopfield neural network (HNN)–RANkSATRA, that integrates HNNs with metaheuristic optimization to overcome the local minima limitations of conventional HNNs. Two hybrid architectures are developed: hybrid dragonfly–Hopfield algorithm (HNN–RANkSAT–HAD) and hybrid evolution strategy–Hopfield algorithm (HNN–RANkSAT–HES), both employing the RANkSATRA method for reverse logic mining from financial data. In computational simulations on synthetic RANkSAT benchmarks, HNN–RANkSAT–HDA consistently outperformed both the baseline HNN–RANkSAT and the HES variant, achieving superior global minima ratio (Zm = 0.90), convergence speed (10.8 iterations), energy minimization (0.10), and model calibration (log‐loss = 0.34). The baseline model demonstrated a scalability constraint, plateauing in performance beyond 70 neurons. Applied to three real‐world financial distress datasets, the German Credit dataset (GCSD), the Polish Companies dataset (PCDS), and the Taiwanese Bankruptcy dataset (TDS), the framework demonstrated robust predictive utility. HNN–RANkSAT–HDA achieved the highest median testing accuracy (0.941), F1‐score (0.938), and AUC (0.934), while also showing the best probabilistic calibration, evidenced by the lowest average log‐loss (0.315). Nonparametric statistical tests (Friedman and Wilcoxon signed‐rank) confirmed a significant performance hierarchy: HNN–RANkSAT–HDA &gt; HNN–RANkSAT–HES &gt; HNN–RANkSAT (p &lt; 0.001 for all metrics). The study demonstrates that the integration of swarm intelligence, specifically the dragonfly algorithm, into a neurosymbolic SAT framework yields a powerful, interpretable, and statistically robust tool for financial risk analytics. [ABSTRACT FROM AUTHOR]
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  Data: &lt;i&gt;Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1155/jama/9145091
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 28
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    Subjects:
      – SubjectFull: Hopfield networks
        Type: general
      – SubjectFull: Swarm intelligence
        Type: general
      – SubjectFull: Metaheuristic algorithms
        Type: general
      – SubjectFull: Evolutionary computation
        Type: general
      – SubjectFull: Financial risk management
        Type: general
      – SubjectFull: Proposition (Logic)
        Type: general
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      – TitleFull: Hybrid Multiobjective Framework for Boolean Satisfiability Optimization With Application to Financial Risk Prediction.
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            NameFull: Abubakar, Hamza
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            NameFull: Sayed, Amani Idris A.
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            NameFull: Karaye, Abubakar Balarabe
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            – D: 25
              M: 05
              Text: 5/25/2026
              Type: published
              Y: 2026
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