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Axioms
Special Issues
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: 30 October 2025 | Viewed by 2690

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 100 words) can be sent to the Editorial Office for announcement on this website.

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 (4 papers)

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Research

17 pages, 306 KiB  
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
Viewed by 141
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 KiB  
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
Viewed by 502
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 KiB  
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 1 | Viewed by 329
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 KiB  
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
Viewed by 1106
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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