Hybrid Machine Learning and Deep Learning Techniques for Optimization and Numerical Modeling

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 28 February 2026 | Viewed by 165

Special Issue Editor


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Guest Editor
School of Computer Engineering, Universidad de Valparaíso, Valparaíso 2362905, Chile
Interests: bio-inspired algorithms; optimization algorithms; machine/deep learning
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Special Issue Information

Dear Colleagues,

Hybrid machine learning and deep learning techniques combine data-driven models with metaheuristics such as PSO, ACO, and GA to solve complex optimization and numerical modeling problems. These hybrid approaches enable solvers to adapt their behavior in real time, refining parameter settings, search strategies, and pattern recognition. Recent work shows that embedding learning mechanisms improves flexibility and performance, especially in high-dimensional and combinatorial problems.

Although many studies have reported successful results, challenges remain. Most existing methods are tied to specific problem domains and struggle to transfer learned behaviors to new tasks. Additionally, the internal processes of hybrid solvers often lack transparency, limiting their adoption in fields where explainability and traceability are essential.

This Special Issue invites contributions on hybrid ML and DL methods applied to optimization and numerical modeling. Topics may include, but are not limited to, combinatorial optimization, reinforcement learning in metaheuristics, deep learning-enhanced simulations, explainable AI within optimization frameworks, transfer learning for optimization, meta-feature extraction for adaptive solvers, reactive and autonomous optimization components, search space reduction techniques, methods for tracing and interpreting solver behavior over time, cross-domain generalization, multi-level hybrid architectures, and the development of explainability metrics, visualization tools, and interpretability standards for hybrid solvers. Both methodological developments and applied studies are welcome. Review articles that provide an overview of recent advances in the field are also encouraged.

Dr. Rodrigo Olivares
Guest Editor

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Keywords

  • hybrid optimization algorithms
  • machine learning in optimization
  • deep learning for numerical modeling
  • data-driven metaheuristics
  • transfer learning in optimization
  • explainable AI (XAI)
  • reactive and adaptive solvers

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Published Papers (1 paper)

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Research

26 pages, 1562 KB  
Article
Hybrid Statistical–Metaheuristic Inventory Modeling: Integrating SARIMAX with Skew-Normal and Zero-Inflated Errors in Clinical Laboratory Demand Forecasting
by Fernando Rojas, Jorge Yáñez and Magdalena Cortés
Mathematics 2025, 13(18), 3001; https://doi.org/10.3390/math13183001 - 17 Sep 2025
Abstract
Clinical laboratories require accurate forecasting and efficient inventory management to balance service quality and cost under uncertain demand. In this study, we propose a hybrid forecasting–optimization framework tailored to hospital clinical determinations with highly irregular, zero-inflated, and asymmetric consumption patterns. Demand series for [...] Read more.
Clinical laboratories require accurate forecasting and efficient inventory management to balance service quality and cost under uncertain demand. In this study, we propose a hybrid forecasting–optimization framework tailored to hospital clinical determinations with highly irregular, zero-inflated, and asymmetric consumption patterns. Demand series for 34 items were modeled using Seasonal AutoRegressive Integrated Moving Average with eXogenous regressors (SARIMAX) structures combined with skew-normal (SN) and zero-inflated skew-normal (ZISN) residuals, with residual centering, truncation, and lambda regularization applied to ensure stable estimation. Model performance was benchmarked against Gaussian SARIMA and non-linear MLP forecasts. The SN/ZISN models achieved improved forecasting accuracy while preserving interpretability and explainability of residual behavior. Forecast outputs were integrated into a Particle Swarm Optimization (PSO) layer to determine cost-minimizing order quantities subject to packaging and budget constraints. The proposed end-to-end framework demonstrated a potential 89% reduction in inventory costs relative to the hospital’s historical policy while maintaining service levels above 85% for high-volume determinations. This hybrid approach provides a transparent, domain-adapted decision support system for supply chain governance in healthcare settings. Beyond the specific case of Chilean hospitals, the framework is adaptable to broader healthcare supply chains, supporting generalizable applications in diverse institutional contexts. Full article
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