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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: 31 August 2025 | Viewed by 2446

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

Published Papers (4 papers)

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Research

19 pages, 498 KiB  
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
Viewed by 553
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 KiB  
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 1 | Viewed by 424
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 KiB  
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
Viewed by 414
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 KiB  
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
Viewed by 843
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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