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Mathematics
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Optimization Theory, Algorithms and Applications
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Optimization Theory, Algorithms and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 8537

Special Issue Editor

Prof. Dr. Nataliya I. Kalashnykova

E-Mail Website
Guest Editor
Postgraduate Courses in the Science Oriented to Mathematics, Autonomous University of Nuevo León (UANL), Av. Universidad s/n, Col. Ciudad Universitaria, San Nicolas de los Garza 66455, Nuevo Leon, Mexico
Interests: operations research; equilibrium in oligopoly models; numerical analysis and linear algebra for optimization problems; network problems

Special Issue Information

Dear Colleagues,

We invite you to contribute your latest theoretical and applied research to the Mathematics Special Issue on “Optimization Theory, Algorithms and Applications”. This issue aims to present the latest results in the following: (a) theoretical analyses of optimization problems; (b) design, analysis, and implementation of optimization algorithms; and (c) novel applications of optimization-driven approaches to real-life problems. We intentionally proposed a very general title to avoid restricting potential authors to specific optimization issues and hope that this will lead to the inclusion of intriguing papers on a broad range of related topics. Potential themes include, but are not limited to, continuous and discrete optimization, multilevel and multi-objective problems, optimization problems applied to decision making, manufacturing, Industry 4.0, logistics, healthcare, other operations research problems, and applications.

Prof. Dr. Nataliya I. Kalashnykova
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-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • continuous, discrete, and combinatorial optimization
  • global optimization
  • multilevel and multi-objective optimization
  • exact, heuristic, and metaheuristic algorithms
  • convergence and complexity issues
  • optimization in operations research and machine learning
  • multidisciplinary applications of optimization and operations research

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Published Papers (7 papers)

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Research

19 pages, 595 KB  
Article
Research on Spare Parts Configuration Method for Marine Equipment Based on Spare Parts Utilization Rate
by Zhengxuan Gu, Yali Zhai and Songshi Shao
Mathematics 2026, 14(1), 35; https://doi.org/10.3390/math14010035 - 22 Dec 2025
Abstract
An optimization method for the spare parts configuration of marine equipment is investigated based on spare parts support probability and utilization rate indicators. First, a general expression for the spare parts utilization rate is presented, and analytical expressions for the spare parts support [...] Read more.
An optimization method for the spare parts configuration of marine equipment is investigated based on spare parts support probability and utilization rate indicators. First, a general expression for the spare parts utilization rate is presented, and analytical expressions for the spare parts support probability and utilization rate are derived for Gamma-type spare parts with non-exponential life distributions, which are commonly found in marine spare parts. The relationship between two calculation methods for the utilization rate of exponential-type spare parts, as a special case of Gamma-type spare parts, is discussed. Second, as the analytical expression for the Gamma-type spare parts utilization rate is relatively complex, an approximate calculation method for the spare parts utilization rate is provided. Under the condition of given support probability requirements, the spare parts utilization rate is calculated through three approaches: theoretical calculation, approximate calculation, and simulation experiment. The calculation results demonstrate the validity of the analytical expression for the spare parts utilization rate and the applicability of the approximate algorithm. Furthermore, an approximate algorithm for the Weibull-type spare parts utilization rate is presented and verified through simulation calculations. Subsequently, considering both spare parts support probability requirements and utilization rate requirements, a spare parts configuration optimization model is established with the objective of maximizing the cost ratio, and the calculation procedures are provided. Finally, the feasibility of the spare parts configuration optimization model is illustrated through case analysis. Full article
(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)
17 pages, 1742 KB  
Article
Hessian-Enhanced Likelihood Optimization for Gravitational Wave Parameter Estimation: A Second-Order Approach to Machine Learning-Based Inference
by Zhuopeng Peng and Fan Zhang
Mathematics 2025, 13(24), 4014; https://doi.org/10.3390/math13244014 - 17 Dec 2025
Viewed by 151
Abstract
We introduce a new method for estimating gravitational wave parameters. This approach uses a second-order likelihood optimization framework built into a machine learning system (JimGW). Current methods often rely on first-order approximations, which can miss important details, while our method incorporates the full [...] Read more.
We introduce a new method for estimating gravitational wave parameters. This approach uses a second-order likelihood optimization framework built into a machine learning system (JimGW). Current methods often rely on first-order approximations, which can miss important details, while our method incorporates the full Hessian matrix of the likelihood function. This allows us to better capture the shape of the parameter space for gravitational waves. Our theoretical framework demonstrates that the trace of the Hessian matrix, when properly normalized, provides a coordinate-invariant measure of the local likelihood geometry that significantly enhances parameter recovery accuracy for gravitational wave sources. We test our second-order method using data from the three gravitational wave events. Take GW150914 as an example; the results show large gains in precision for parameter estimation, with accuracy gains exceeding 93% across all inferred parameters compared to standard first-order implementations. We use Jensen–Shannon divergence to compare the resulting posterior distributions. The JSD values range from 0.366 to 0.948, which correlate directly with improved parameter recovery as validated through injection studies. The method remains computationally efficient with only a 20% increase in runtime. At the same time, it produces seven times more effective samples. Our results show that machine learning methods using only first-order information can lead to systematic errors in gravitational wave parameter estimation. The incorporation of second-order corrections emerges not as an optional refinement but as a necessary component for achieving theoretically optimal inference. It also matters for ongoing gravitational wave analyses, future detector networks, and the broader application of machine learning methods in precision scientific measurement. Full article
(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)
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21 pages, 2695 KB  
Article
Ship Spare Parts Optimization Model Based on Ideal Point Method and Improved Ant Colony Algorithm
by Tianyu Ma, Huiling Sun, Rui Qi and Xiangjun Li
Mathematics 2025, 13(23), 3862; https://doi.org/10.3390/math13233862 - 2 Dec 2025
Viewed by 196
Abstract
This study proposes an optimization approach for ship spare parts allocation by integrating the ideal point method (IPM) with an improved ant colony algorithm. The traditional R/C (Reliability–Cost Ratio) model is constrained by single-objective formulations that fail to reconcile cost efficiency with system [...] Read more.
This study proposes an optimization approach for ship spare parts allocation by integrating the ideal point method (IPM) with an improved ant colony algorithm. The traditional R/C (Reliability–Cost Ratio) model is constrained by single-objective formulations that fail to reconcile cost efficiency with system reliability, often producing the paradoxical result that fewer spare parts correspond to higher reliability. To address this limitation, a multi-objective model was constructed for reliability–cost optimization, while the enhanced ant colony algorithm identifies optimal spare part configurations that achieve balanced trade-offs. Nine representative scenarios were analyzed, with simulation outcomes compared between the IPM and R/C model approaches. Sensitivity analyses of critical parameters were conducted, and the effectiveness of both approaches was evaluated. The results demonstrate that the IPM consistently achieves higher reliability, particularly under stringent reliability requirements and tighter spare parts constraints. The findings provide a robust analytical foundation for evidence-based decision-making in ship equipment support. Full article
(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)
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19 pages, 498 KB  
Article
Optimization of Direct Convolution Algorithms on ARM Processors for Deep Learning Inference
by Shang Li, Fei Yu, Shankou Zhang, Huige Yin and Hairong Lin
Mathematics 2025, 13(5), 787; https://doi.org/10.3390/math13050787 - 27 Feb 2025
Cited by 1 | Viewed by 2426
Abstract
In deep learning, convolutional layers typically bear the majority of the computational workload and are often the primary contributors to performance bottlenecks. The widely used convolution algorithm is based on the IM2COL transform to take advantage of the highly optimized GEMM (General Matrix [...] Read more.
In deep learning, convolutional layers typically bear the majority of the computational workload and are often the primary contributors to performance bottlenecks. The widely used convolution algorithm is based on the IM2COL transform to take advantage of the highly optimized GEMM (General Matrix Multiplication) kernel acceleration, using the highly optimized BLAS (Basic Linear Algebra Subroutine) library, which tends to incur additional memory overhead. Recent studies have indicated that direct convolution approaches can outperform traditional convolution implementations without additional memory overhead. In this paper, we propose a high-performance implementation of the direct convolution algorithm for inference that preserves the channel-first data layout of the convolutional layer inputs/outputs. We evaluate the performance of our proposed algorithm on a multi-core ARM CPU platform and compare it with state-of-the-art convolution optimization techniques. Experimental results demonstrate that our new algorithm performs better across the evaluated scenarios and platforms. Full article
(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)
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46 pages, 9513 KB  
Article
Multi-Strategy Improved Binary Secretarial Bird Optimization Algorithm for Feature Selection
by Fuqiang Chen, Shitong Ye, Jianfeng Wang and Jia Luo
Mathematics 2025, 13(4), 668; https://doi.org/10.3390/math13040668 - 18 Feb 2025
Cited by 4 | Viewed by 1306
Abstract
With the rapid development of large model technology, data storage as well as collection is very important to improve the accuracy of model training, and Feature Selection (FS) methods can greatly eliminate redundant features in the data warehouse and improve the interpretability of [...] Read more.
With the rapid development of large model technology, data storage as well as collection is very important to improve the accuracy of model training, and Feature Selection (FS) methods can greatly eliminate redundant features in the data warehouse and improve the interpretability of the model, which makes it particularly important in the field of large model training. In order to better reduce redundant features in data warehouses, this paper proposes an enhanced Secretarial Bird Optimization Algorithm (SBOA), called BSFSBOA, by combining three learning strategies. First, for the problem of insufficient algorithmic population diversity in SBOA, the best-rand exploration strategy is proposed, which utilizes the randomness and optimality of random individuals as well as optimal individuals to effectively improve the population diversity of the algorithm. Second, to address the imbalance in the exploration/exploitation phase of SBOA, the segmented balance strategy is proposed to improve the balance by segmenting the individuals in the population, targeting individuals of different natures with different degrees of exploration and exploitation performance, and improving the quality of the FS subset when the algorithm is solved. Finally, for the problem of insufficient exploitation performance of SBOA, a four-role exploitation strategy is proposed, which strengthens the effective exploitation ability of the algorithm and enhances the classification accuracy of the FS subset by different degrees of guidance through the four natures of individuals in the population. Subsequently, the proposed BSFSBOA-based FS method is applied to solve 36 FS problems involving low, medium, and high dimensions, and the experimental results show that, compared to SBOA, BSFSBOA improves the performance of classification accuracy by more than 60%, also ranks first in feature subset size, obtains the least runtime, and confirms that the BSFSBOA-based FS method is a robust FS method with efficient solution performance, high stability, and high practicality. Full article
(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)
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22 pages, 1918 KB  
Article
Research on Multi-Center Path Optimization for Emergency Events Based on an Improved Particle Swarm Optimization Algorithm
by Zeyu Zou, Hui Zeng, Xiaodong Zheng and Junming Chen
Mathematics 2025, 13(4), 654; https://doi.org/10.3390/math13040654 - 17 Feb 2025
Cited by 1 | Viewed by 1266
Abstract
Emergency events pose critical challenges to national and social stability, requiring efficient and timely responses to mitigate their impact. In the initial stages of an emergency, decision-makers face the dual challenge of minimizing transportation costs while adhering to stringent rescue time constraints. To [...] Read more.
Emergency events pose critical challenges to national and social stability, requiring efficient and timely responses to mitigate their impact. In the initial stages of an emergency, decision-makers face the dual challenge of minimizing transportation costs while adhering to stringent rescue time constraints. To address these issues, this study proposes a two-stage optimization model aimed at ensuring the equitable distribution of disaster relief materials across multiple distribution centers. The model seeks to minimize the overall cost, encompassing vehicle dispatch expenses, fuel consumption, and time window penalty costs, thereby achieving a balance between efficiency and fairness. To solve this complex optimization problem, a hybrid algorithm combining genetic algorithms and particle swarm optimization was designed. This hybrid approach leverages the global exploration capability of genetic algorithms and the fast convergence of particle swarm optimization to achieve superior performance in solving real-world logistics challenges. Case studies were conducted to evaluate the feasibility and effectiveness of both the proposed model and the algorithm. Results indicate that the model accurately reflects the dynamics of emergency logistics operations, while the hybrid algorithm exhibits strong local optimization capabilities and robust performance in handling diverse and complex scenarios. Experimental findings underscore the potential of the proposed approach in optimizing emergency response logistics. The hybrid algorithm consistently achieves significant reductions in total cost while maintaining fairness in material distribution. These results demonstrate the algorithm’s applicability to a wide range of disaster scenarios, offering a reliable and efficient tool for emergency planners. This study not only contributes to the body of knowledge in emergency logistics optimization but also provides practical insights for policymakers and practitioners striving to improve disaster response strategies. Full article
(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)
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37 pages, 9637 KB  
Article
An Optimized Method for Solving the Green Permutation Flow Shop Scheduling Problem Using a Combination of Deep Reinforcement Learning and Improved Genetic Algorithm
by Yongxin Lu, Yiping Yuan, Jiarula Yasenjiang, Adilanmu Sitahong, Yongsheng Chao and Yunxuan Wang
Mathematics 2025, 13(4), 545; https://doi.org/10.3390/math13040545 - 7 Feb 2025
Cited by 4 | Viewed by 2447
Abstract
This paper tackles the green permutation flow shop scheduling problem (GPFSP) with the goal of minimizing both the maximum completion time and energy consumption. It introduces a novel hybrid approach that combines end-to-end deep reinforcement learning with an improved genetic algorithm. Firstly, the [...] Read more.
This paper tackles the green permutation flow shop scheduling problem (GPFSP) with the goal of minimizing both the maximum completion time and energy consumption. It introduces a novel hybrid approach that combines end-to-end deep reinforcement learning with an improved genetic algorithm. Firstly, the PFSP is modeled using an end-to-end deep reinforcement learning (DRL) approach, named PFSP_NET, which is designed based on the characteristics of the PFSP, with the actor–critic algorithm employed to train the model. Once trained, this model can quickly and directly produce relatively high-quality solutions. Secondly, to further enhance the quality of the solutions, the outputs from PFSP_NET are used as the initial population for the improved genetic algorithm (IGA). Building upon the traditional genetic algorithm, the IGA utilizes three crossover operators, four mutation operators, and incorporates hamming distance, effectively preventing the algorithm from prematurely converging to local optimal solutions. Then, to optimize energy consumption, an energy-saving strategy is proposed that reasonably adjusts the job scheduling order by shifting jobs backward without increasing the maximum completion time. Finally, extensive experimental validation is conducted on the 120 test instances of the Taillard standard dataset. By comparing the proposed method with algorithms such as the standard genetic algorithm (SGA), elite genetic algorithm (EGA), hybrid genetic algorithm (HGA), discrete self-organizing migrating algorithm (DSOMA), discrete water wave optimization algorithm (DWWO), and hybrid monkey search algorithm (HMSA), the results demonstrate the effectiveness of the proposed method. Optimal solutions are achieved in 28 test instances, and the latest solutions are updated in instances Ta005 and Ta068 with values of 1235 and 5101, respectively. Additionally, experiments on 30 instances, including Taillard 20-10, Taillard 50-10, and Taillard 100-10, indicate that the proposed energy strategy can effectively reduce energy consumption. Full article
(This article belongs to the Special Issue Optimization Theory, Algorithms and Applications)
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