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Axioms
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Advances and Applications in Mathematical Modeling and Optimization
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Advances and Applications in Mathematical Modeling and Optimization

A Special Issue of Axioms (ISSN 2075-1680) belonging to the section "Mathematical Analysis".

Deadline for manuscript submissions: 30 April 2027 | Viewed by 2098

Editor

Prof. Dr. Glenn Ledder

E-Mail Website
Guest Editor
Department of Mathematics, University of Nebraska–Lincoln, Lincoln, NE 68588, USA
Interests: mathematical modeling; epidemiology; dynamical systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue focuses very broadly on mathematical optimization. Papers may primarily be focused on developments in mathematical methods, developments in numerical methods, applications of optimization in mathematical models, or any combination of these areas. Papers on mathematical or numerical methods should be careful to explain how the new method fits into the overall context of optimization methods and should show how the new method improves on the body of optimization methods. Papers on applications of optimization should be careful to describe the context for the optimization model and justify all modeling and mathematical assumptions. 

All areas of optimization will be considered: continuous, discrete, and mixed optimization of control vectors and the calculus of variations and optimal control.

Prof. Dr. Glenn Ledder
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical optimization
  • numerical optimization
  • continuous optimization
  • discrete optimization
  • mixed optimization
  • nonlinear optimization
  • calculus of variations
  • optimal control

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Published Papers (4 papers)

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Research

26 pages, 2645 KB  
Article
Differential Evolution Flexible Integrated Assembly Production Distribution Scheduling (DE-FIAPDS)
by Anak Agung Ayu Putri Ardyanti, Zhiqiang Xie and Henokh Lugo Hariyanto
Axioms 2026, 15(8), 566; https://doi.org/10.3390/axioms15080566 - 30 Jul 2026
Viewed by 218
Abstract
This study addresses the gap in research on distributed integrated scheduling for complex products by presenting a tree-structured framework enhanced with Differential Evolutionary Flexible Integrated Assembly Production Distribution Scheduling (DE-FIAPDS). The algorithm’s effectiveness is demonstrated by validating standard benchmark problems and custom-generated test [...] Read more.
This study addresses the gap in research on distributed integrated scheduling for complex products by presenting a tree-structured framework enhanced with Differential Evolutionary Flexible Integrated Assembly Production Distribution Scheduling (DE-FIAPDS). The algorithm’s effectiveness is demonstrated by validating standard benchmark problems and custom-generated test cases. Using Taguchi’s method and comparative analysis, we developed GA and DE heuristic evolutionary algorithms for the scheduling problem. Over the course of 30 independent replications, applied to 100 randomly generated instances, the DE-FIAPDS algorithm was observed to produce an average final-generation makespan. We calculate the time complexity of the basic DE by combining these additional steps with the basic DE time complexity, such as forward conversion, backward conversion and local search, which can be expressed as O(Gmax·Npop·(d+noplognop)), where Gmax is the maximum number of generations, Npop is the number of individuals in the given population, d is the dimension of the problem, and nop is the the number of operations in FIAPDS. The proposed DE-FIAPDS gives the same results as GA-FIAPDS, although in some instances they differ by a huge difference in makespan. On the other hand, its computing time was 100 times quicker. Full article
(This article belongs to the Special Issue Advances and Applications in Mathematical Modeling and Optimization)
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19 pages, 312 KB  
Article
Generalized Convexity via Clarke Subdifferential of Interval Mappings and Its Optimization Applications
by Shexiang Hai and Yanmei Zhang
Axioms 2026, 15(7), 509; https://doi.org/10.3390/axioms15070509 - 6 Jul 2026
Viewed by 366
Abstract
Clarke subdifferential and directional derivative theories are well developed for real functions. However, the nonsmooth analysis framework for interval mappings is still incomplete. Few works reveal the inherent relationship between Clarke directional derivatives of interval mappings and their endpoint functions. This paper addresses [...] Read more.
Clarke subdifferential and directional derivative theories are well developed for real functions. However, the nonsmooth analysis framework for interval mappings is still incomplete. Few works reveal the inherent relationship between Clarke directional derivatives of interval mappings and their endpoint functions. This paper addresses these gaps. We first explore the relationships between Clarke directional derivatives of interval mappings and their endpoint functions. The Clarke subdifferential of interval mappings is defined by means of directional derivatives and interval order relations, with its fundamental properties established. A new generalized convexity concept for interval mappings is further introduced based on the proposed Clarke subdifferential. Finally, sufficient conditions for efficient solutions to interval nonsmooth optimization are derived under the new generalized convexity framework. Full article
(This article belongs to the Special Issue Advances and Applications in Mathematical Modeling and Optimization)
25 pages, 848 KB  
Article
A Fuzzy Stochastic DEA Model Considering an Input–Output Structure
by Lei Deng and Chong Li
Axioms 2026, 15(5), 376; https://doi.org/10.3390/axioms15050376 - 17 May 2026
Viewed by 592
Abstract
Traditional DEA models can neither effectively handle fuzzy random variables nor achieve a complete ranking of decision-making units (DMUs). Based on the conventional fuzzy stochastic DEA model, this study introduces an exponential distribution extension. By incorporating fuzzy random variables, it significantly simplifies the [...] Read more.
Traditional DEA models can neither effectively handle fuzzy random variables nor achieve a complete ranking of decision-making units (DMUs). Based on the conventional fuzzy stochastic DEA model, this study introduces an exponential distribution extension. By incorporating fuzzy random variables, it significantly simplifies the deterministic transformation of chance-constrained models. Moreover, most existing DEA ranking methods only consider the relative efficiencies among DMUs while ignoring their internal structural characteristics. To address this issue, we develop a deterministic model for the exponentially extended fuzzy stochastic DEA and design a weight formula that reflects the internal input–output structure of each DMU. This approach makes the complete ranking of DMUs more reasonable and better aligned with practical situations. Finally, the rationality and effectiveness of the proposed model are verified through a comparative analysis of rankings obtained from different DEA models. The results indicate that the input–output structure within a decision-making unit plays a significant role in its efficiency ranking. Full article
(This article belongs to the Special Issue Advances and Applications in Mathematical Modeling and Optimization)
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17 pages, 473 KB  
Article
A Subspace Derivative-Free Conjugate Gradient Method for Solving Nonlinear Monotone Equations with Convex Constraints
by Zongxu Li, Zhuo Fang, Mingyuan Cao, Yueting Yang, Ruobing Mei and Siqi Liu
Axioms 2026, 15(5), 351; https://doi.org/10.3390/axioms15050351 - 9 May 2026
Viewed by 384
Abstract
We propose a novel subspace derivative-free conjugate gradient method for solving large-scale nonlinear monotone equations with convex constraints. At each iteration, the search direction is constructed by minimizing a quadratic model within a subspace spanned by the current negative function value vector and [...] Read more.
We propose a novel subspace derivative-free conjugate gradient method for solving large-scale nonlinear monotone equations with convex constraints. At each iteration, the search direction is constructed by minimizing a quadratic model within a subspace spanned by the current negative function value vector and the two most recent search directions. The algorithm incorporates a hyperplane projection technique to generate feasible iterative points. Under reasonable assumptions, we establish the global convergence and R-linear convergence rate of the proposed method. Extensive numerical experiments on benchmark problems demonstrate that the new algorithm significantly outperforms state-of-the-art derivative-free methods in terms of number of iterations, function evaluations, and CPU time. The results confirm the efficiency and robustness of the proposed approach for solving large-scale monotone systems. Full article
(This article belongs to the Special Issue Advances and Applications in Mathematical Modeling and Optimization)
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