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Axioms
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Mathematical Optimizations and Operations Research
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Mathematical Optimizations and Operations Research

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 May 2026 | Viewed by 9313

Special Issue Editors

Dr. Shen Peng

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
Interests: optimization method and its applications; stochasitic programming; robust optimization
Special Issues, Collections and Topics in MDPI journals
Dr. Jia Liu

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China
Interests: stochasitic programming; robust optimization; reinforcement learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The importance of optimization is increasing in addressing complex, real-world problems across various industries and disciplines. As the world becomes more interconnected and data-driven, the need for efficient decision-making processes that leverage mathematical optimization techniques becomes paramount.

The development of mathematical optimization has been marked by significant advancements in theoretical research and practical applications, such as nonconvex optimization algorithms, stochastic optimization, distributionally robust optimization, discrete optimization, optimization theory, and applications in artificial intelligence, transportation, and finance. However, designing efficient algorithms and applying these novel approaches to real problems is still an open issue—particularly for nonconvex optimization, nonsmooth optimization, large-scale optimization, integer programs, and optimization under uncertainty.

This Special Issue invites researchers to report their latest research on developing all aspects of mathematical optimization and new applications in operations research. The scope includes but is not limited to convex and nonconvex optimization, nonsmooth optimization, large-scale optimization, integer program, stochastic optimization, robust optimization, computational methods, and applications of optimization techniques in various domains such as finance, logistics, energy, healthcare, transportation, and manufacturing.

Dr. Shen Peng
Dr. Jia Liu
Guest Editors

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-blind 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

  • convex and nonconvex optimization
  • nonsmooth optimization
  • large-scale optimization
  • integer program
  • stochastic optimization
  • robust optimization
  • distributionally robust optimization
  • artificial intelligence
  • operations research

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (7 papers)

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Research

16 pages, 303 KB  
Article
Outer Space Branch-and-Search Method to Tackle a Class of Linear Fractional Programming Problems and Application in Investment Decision-Making
by Xuefeng Yao, Yusi Yang and Hongwei Jiao
Axioms 2026, 15(5), 363; https://doi.org/10.3390/axioms15050363 - 13 May 2026
Abstract
This paper proposes an outer space branch-and-search method for a class of linear fractional programming problems over a polytope. First, the original problem is reformulated in an equivalent problem by applying the equivalent transformation. Second, by using a new linearization technique, a linear [...] Read more.
This paper proposes an outer space branch-and-search method for a class of linear fractional programming problems over a polytope. First, the original problem is reformulated in an equivalent problem by applying the equivalent transformation. Second, by using a new linearization technique, a linear programming relaxation problem of the equivalent problem is constructed. Third, lower bounds are obtained by solving a sequence of linear programming relaxation problems. Fourth, the convergence of the proposed algorithm is proved, and its worst-case computational complexity is estimated. Finally, numerical experimental results are reported to demonstrate the effectiveness of the algorithm. Additionally, an investment decision-making problem was solved to validate the applicability of the method proposed in this paper. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
22 pages, 440 KB  
Article
Expected Maximization of a Concave Utility Function Under Threshold-Based Activation
by Guangming Li, Yufei Li, Shengjie Chen, Mou Sun and Wushuaijun Zhang
Axioms 2026, 15(3), 169; https://doi.org/10.3390/axioms15030169 - 27 Feb 2026
Viewed by 363
Abstract
Maximizing the expected value of a concave and strictly increasing utility function defines a fundamental class of discrete optimization problems. Among them, coverage decision problems with diminishing marginal returns under uncertainty, typically modeled via a set-union operator, have been extensively studied. In the [...] Read more.
Maximizing the expected value of a concave and strictly increasing utility function defines a fundamental class of discrete optimization problems. Among them, coverage decision problems with diminishing marginal returns under uncertainty, typically modeled via a set-union operator, have been extensively studied. In the classical framework, an item becomes active once it is covered by at least one chosen meta-item. Motivated by increasing robustness requirements in applications such as automated systems, social networks, and emergency response planning, we extend this setting by introducing threshold-based activation. The resulting generalized problem can be formulated as a mixed-integer nonlinear programming problem, for which we further propose three exact algorithms. The first two methods linearize the utility function using submodular cuts (SC) and outer-approximation (OA) techniques, respectively, resulting in formulations that can be solved exactly by off-the-shelf mixed-integer linear programming solvers. The third method builds upon the OA framework and further employs Benders decomposition (BD) to project out the item-related variables, which enables superior performance on ultra-large-scale instances. Extensive computational experiments show that, compared with the SC and BD methods, the OA method exhibits a substantial speed advantage on instances with a size of around 40,000, which can be solved within 100 s. In contrast, for ultra-large-scale instances with more than 100,000 items, the BD method demonstrates superior computational efficiency. These results provide practical guidance for algorithmic strategy selection and further demonstrate the computational tractability of this broader class of utility maximization problems under threshold-based activation. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
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12 pages, 265 KB  
Article
Existence of Weakly Pareto–Nash Equilibrium for Multiobjective Games with Infinitely Many Players
by Huaxin Chen and Wensheng Jia
Axioms 2025, 14(7), 517; https://doi.org/10.3390/axioms14070517 - 4 Jul 2025
Cited by 1 | Viewed by 841
Abstract
Our work proves the existence of weakly Pareto–Nash equilibrium (PNE) in multiobjective games (MGs) with infinitely many players. First, we demonstrate the existence of weakly PNE under compactness assumptions by using the intersection theorem. Then, we extend the intersection theorem to the non-compact [...] Read more.
Our work proves the existence of weakly Pareto–Nash equilibrium (PNE) in multiobjective games (MGs) with infinitely many players. First, we demonstrate the existence of weakly PNE under compactness assumptions by using the intersection theorem. Then, we extend the intersection theorem to the non-compact case and obtain a new intersection theorem. Finally, we prove the existence of weakly PNE in MGs with infinitely many players without compactness assumptions. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
17 pages, 306 KB  
Article
Minimizing Makespan Scheduling on a Single Machine with General Positional Deterioration Effects
by Yu Sun, Hongyu He, Yanzhi Zhao and Ji-Bo Wang
Axioms 2025, 14(4), 290; https://doi.org/10.3390/axioms14040290 - 12 Apr 2025
Cited by 13 | Viewed by 1414
Abstract
This work studies single-machine scheduling with general position-dependent deterioration, where job processing times are general non-decreasing functions dependent on their positions in a sequence. The goal is to find a job sequence such that makespan is minimized. The problem can be extended to [...] Read more.
This work studies single-machine scheduling with general position-dependent deterioration, where job processing times are general non-decreasing functions dependent on their positions in a sequence. The goal is to find a job sequence such that makespan is minimized. The problem can be extended to deal with green scheduling environment where processing time increases due to additional carbon-reduction procedure. Under some optimal properties, we prove that the problem is solved by the largest processing time (denoted by LPT) first rule. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
24 pages, 1929 KB  
Article
Robust Optimization for Cooperative Task Assignment of Heterogeneous Unmanned Aerial Vehicles with Time Window Constraints
by Zhichao Gao, Mingfa Zheng, Haitao Zhong and Yu Mei
Axioms 2025, 14(3), 184; https://doi.org/10.3390/axioms14030184 - 2 Mar 2025
Cited by 1 | Viewed by 1823
Abstract
The cooperative task assignment problem with time windows for heterogeneous multiple unmanned aerial vehicles is an attractive complex combinatorial optimization problem. In reality, unmanned aerial vehicles’ fuel consumption exhibits uncertainty due to environmental factors or operational maneuvers, and accurately determining the probability distributions [...] Read more.
The cooperative task assignment problem with time windows for heterogeneous multiple unmanned aerial vehicles is an attractive complex combinatorial optimization problem. In reality, unmanned aerial vehicles’ fuel consumption exhibits uncertainty due to environmental factors or operational maneuvers, and accurately determining the probability distributions for these uncertainties remains challenging. This paper investigates the heterogeneous multiple unmanned aerial vehicle cooperative task assignment model that incorporates time window constraints under uncertain environments. To model the time window constraints, we employ the big-M method. To address the uncertainty in fuel consumption, we apply an adjustable robust optimization approach combined with duality theory, which allows us to derive the robust equivalent form and transform the model into a deterministic mixed-integer linear programming problem. We conduct a series of numerical experiments to compare the optimization results across different objectives, including maximizing task profit, minimizing total distance, minimizing makespan, and incorporating three different time window constraints. The numerical results demonstrate that the robust optimization-based heterogeneous multiple unmanned aerial vehicle cooperative task assignment model effectively mitigates the impact of parameter uncertainty, while achieving a balanced trade-off between robustness and the optimality of task assignment objectives. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
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21 pages, 309 KB  
Article
Research on Group Scheduling with General Logarithmic Deterioration Subject to Maximal Completion Time Cost
by Jin-Da Miao, Dan-Yang Lv, Cai-Min Wei and Ji-Bo Wang
Axioms 2025, 14(3), 153; https://doi.org/10.3390/axioms14030153 - 20 Feb 2025
Cited by 10 | Viewed by 892
Abstract
Single-machine group scheduling with general logarithmic deterioration is investigated, where the actual job processing (resp. group setup) time is a non-decreasing function of the sum of the logarithmic job processing (resp. group setup) times of the jobs (resp. groups) already processed. Under some [...] Read more.
Single-machine group scheduling with general logarithmic deterioration is investigated, where the actual job processing (resp. group setup) time is a non-decreasing function of the sum of the logarithmic job processing (resp. group setup) times of the jobs (resp. groups) already processed. Under some optimal properties, it is shown that the maximal completion time (i.e., makespan) cost is solved in polynomial time and the optimal algorithm is presented. In addition, an extension of the general weighted deterioration model is given. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
33 pages, 53062 KB  
Article
An Improved MOEA/D with an Auction-Based Matching Mechanism
by Guangjian Li, Mingfa Zheng, Guangjun He, Yu Mei, Gaoji Sun and Haitao Zhong
Axioms 2024, 13(9), 644; https://doi.org/10.3390/axioms13090644 - 20 Sep 2024
Cited by 4 | Viewed by 2655
Abstract
Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing [...] Read more.
Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing these subproblems in a collaborative manner. However, most existing MOEA/Ds maintain population diversity by limiting the replacement region or scale, which come at the cost of decreasing convergence. To better balance convergence and diversity, we introduce auction theory into algorithm design and propose an auction-based matching (ABM) mechanism to coordinate the replacement procedure in MOEA/D. In the ABM mechanism, each subproblem can be associated with its preferred individual in a competitive manner by simulating the auction process in economic activities. The integration of ABM into MOEA/D forms the proposed MOEA/D-ABM. Furthermore, to make the appropriate distribution of weight vectors, a modified adjustment strategy is utilized to adaptively adjust the weight vectors during the evolution process, where the trigger timing is determined by the convergence activity of the population. Finally, MOEA/D-ABM is compared with six state-of-the-art multi-objective evolutionary algorithms (MOEAs) on some benchmark problems with two to ten objectives. The experimental results show the competitiveness of MOEA/D-ABM in the performance of diversity and convergence. They also demonstrate that the use of the ABM mechanism can greatly improve the convergence rate of the algorithm. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
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