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Mathematics
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Advances in Metaheuristic Optimization Algorithms
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Advances in Metaheuristic Optimization Algorithms

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E1: Mathematics and Computer Science".

Deadline for manuscript submissions: 30 October 2026 | Viewed by 5931

Special Issue Editor

Prof. Alma Rodríguez

E-Mail Website
Guest Editor
Electronics department, University of Guadalajara, CUCEI. Av. Revolución 1500, Guadalajara, Jal C.P 44430, Mexico
Interests: artificial intelligence algorithms

Special Issue Information

Dear Colleagues,

Metaheuristic optimization algorithms have seen significant advancements in recent decades, driven by their ability to tackle complex and diverse optimization problems across various domains. These algorithms, inspired by natural and artificial processes, have provided robust and flexible solutions for intricate computational challenges. Therefore, this Special Issue aims to highlight the latest developments, innovative methodologies, and practical applications of these algorithms.

We seek papers that explore novel metaheuristic approaches, hybrid algorithms, and their theoretical foundations. Contributions that demonstrate the application of metaheuristic optimization in real-world problems, including but not limited to engineering design, logistics, bioinformatics, finance, and artificial intelligence, are highly encouraged. Additionally, we welcome studies that compare the performance of different metaheuristic techniques, investigate parameter tuning strategies, and propose new benchmarks for algorithm evaluation.

This Special Issue aims to serve as a comprehensive resource for researchers and practitioners, fostering a deeper understanding of metaheuristic optimization and its potential to solve complex problems in various scientific and industrial fields.

Prof. Alma Rodríguez
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

  • metaheuristics
  • swarm intelligence
  • evolutionary computation
  • artificial intelligence
  • bio-inspired optimization methods
  • applied optimization

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Published Papers (5 papers)

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Research

50 pages, 5419 KB  
Article
MSAPO: A Multi-Strategy Fusion Artificial Protozoa Optimizer for Solving Real-World Problems
by Hanyu Bo, Jiajia Wu and Gang Hu
Mathematics 2025, 13(17), 2888; https://doi.org/10.3390/math13172888 - 6 Sep 2025
Viewed by 817
Abstract
Artificial protozoa optimizer (APO), as a newly proposed meta-heuristic algorithm, is inspired by the foraging, dormancy, and reproduction behaviors of protozoa in nature. Compared with traditional optimization algorithms, APO demonstrates strong competitive advantages; nevertheless, it is not without inherent limitations, such as slow [...] Read more.
Artificial protozoa optimizer (APO), as a newly proposed meta-heuristic algorithm, is inspired by the foraging, dormancy, and reproduction behaviors of protozoa in nature. Compared with traditional optimization algorithms, APO demonstrates strong competitive advantages; nevertheless, it is not without inherent limitations, such as slow convergence and a proclivity towards local optimization. In order to enhance the efficacy of the algorithm, this paper puts forth a multi-strategy fusion artificial protozoa optimizer, referred to as MSAPO. In the initialization stage, MSAPO employs the piecewise chaotic opposition-based learning strategy, which results in a uniform population distribution, circumvents initialization bias, and enhances the global exploration capability of the algorithm. Subsequently, cyclone foraging strategy is implemented during the heterotrophic foraging phase. enabling the algorithm to identify the optimal search direction with greater precision, guided by the globally optimal individuals. This reduces random wandering, significantly accelerating the optimization search and enhancing the ability to jump out of the local optimal solutions. Furthermore, the incorporation of hybrid mutation strategy in the reproduction stage enables the algorithm to adaptively transform the mutation patterns during the iteration process, facilitating a strategic balance between rapid escape from local optima in the initial stages and precise convergence in the subsequent stages. Ultimately, crisscross strategy is incorporated at the conclusion of the algorithm’s iteration. This not only enhances the algorithm’s global search capacity but also augments its capability to circumvent local optima through the integrated application of horizontal and vertical crossover techniques. This paper presents a comparative analysis of MSAPO with other prominent optimization algorithms on the three-dimensional CEC2017 and the highest-dimensional CEC2022 test sets, and the results of numerical experiments show that MSAPO outperforms the compared algorithms, and ranks first in the performance evaluation in a comprehensive way. In addition, in eight real-world engineering design problem experiments, MSAPO almost always achieves the theoretical optimal value, which fully confirms its high efficiency and applicability, thus verifying the great potential of MSAPO in solving complex optimization problems. Full article
(This article belongs to the Special Issue Advances in Metaheuristic Optimization Algorithms)
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37 pages, 5365 KB  
Article
Prediction of Sulfur Dioxide Emissions in China Using Novel CSLDDBO-Optimized PGM(1, N) Model
by Lele Cui, Gang Hu and Abdelazim G. Hussien
Mathematics 2025, 13(17), 2846; https://doi.org/10.3390/math13172846 - 3 Sep 2025
Viewed by 572
Abstract
Sulfur dioxide not only affects the ecological environment and endangers health but also restricts economic development. The reasonable prediction of sulfur dioxide emissions is beneficial for formulating more comprehensive energy use strategies and guiding social policies. To this end, this article uses a [...] Read more.
Sulfur dioxide not only affects the ecological environment and endangers health but also restricts economic development. The reasonable prediction of sulfur dioxide emissions is beneficial for formulating more comprehensive energy use strategies and guiding social policies. To this end, this article uses a multiparameter combination optimization gray prediction model (PGM(1, N)), which not only defines the difference between the sequences represented by variables but also optimizes the order of all variables. To this end, this article proposes an improved algorithm for the Dung Beetle Optimization (DBO) algorithm, namely, CSLDDBO, to optimize two important parameters in the model, namely, the smoothing generation coefficient and the order of the gray generation operators. In order to overcome the shortcomings of DBO, four improvement strategies have been introduced. Firstly, the use of a chain foraging strategy is introduced to guide the ball-rolling beetle to update its position. Secondly, the rolling foraging strategy is adopted to fully conduct adaptive searches in the search space. Then, learning strategies are adopted to improve the global search capabilities. Finally, based on the idea of differential evolution, the convergence speed of the algorithm was improved, and the ability to escape from local optima was enhanced. The superiority of CSLDDBO was verified on the CEC2022 test set. Finally, the optimized PGM(1, N) model was used to predict China’s sulfur dioxide emissions. From the results, it can be seen that the error of the PGM(1, N) model is the smallest at 0.1117%, and the prediction accuracy is significantly higher than that of other prediction models. Full article
(This article belongs to the Special Issue Advances in Metaheuristic Optimization Algorithms)
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40 pages, 14071 KB  
Article
Adapted Multi-Strategy Fractional-Order Relative Pufferfish Optimization Algorithm for Feature Selection
by Lukui Xu, Jiajun Lv and Youling Yu
Mathematics 2025, 13(17), 2799; https://doi.org/10.3390/math13172799 - 31 Aug 2025
Viewed by 730
Abstract
In the development of artificial intelligence (AI) technology, utilizing datasets for model instruction to achieve higher predictive and reasoning efficacy has become a common technical approach. However, primordial datasets often contain a significant number of redundant features (RF), which can compromise the prediction [...] Read more.
In the development of artificial intelligence (AI) technology, utilizing datasets for model instruction to achieve higher predictive and reasoning efficacy has become a common technical approach. However, primordial datasets often contain a significant number of redundant features (RF), which can compromise the prediction accuracy and generalization ability of models. To effectively reduce RF in datasets, this work advances a new version of the Pufferfish Optimization Algorithm (POA), termed AMFPOA. Firstly, by considering the knowledge disparities among different groups of members and incorporating the concept of adaptive learning, an adaptive exploration strategy is introduced to enhance the algorithm’s Global Exploration (GE) capability. Secondly, by dividing the entire swarm into multiple subswarms, a three-swarm search strategy is advanced. This allows for targeted optimization schemes for different subswarms, effectively achieving a good balance across various metrics for the algorithm. Lastly, leveraging the historical memory property of Fractional-Order theory and the member weighting of Bernstein polynomials, a Fractional-Order Bernstein exploitation strategy is advanced, which significantly augments the algorithm’s local exploitation (LE) capability. Subsequent experimental results on 23 real-world Feature Selection (FS) problems demonstrate that AMFPOA achieves an average success rate exceeding 87.5% in fitness function value (FFV), along with ideal efficacy rates of 86.5% in Classification Accuracy (CA) and 60.1% in feature subset size reduction. These results highlight its strong capability for RF elimination, establishing AMFPOA as a promising FS method. Full article
(This article belongs to the Special Issue Advances in Metaheuristic Optimization Algorithms)
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19 pages, 4169 KB  
Article
Magnetic Coil’s Performance Optimization with Nonsmooth Search Algorithms
by Igor Reznichenko, Primož Podržaj and Aljoša Peperko
Mathematics 2025, 13(15), 2490; https://doi.org/10.3390/math13152490 - 2 Aug 2025
Viewed by 768
Abstract
This research is concerned with design optimization of control systems. Our case study deals with magnetic levitation, in which an essential part is a solenoid. Its dimensions, along with controller parameters, form the optimization variables. We present a novel way of writing the [...] Read more.
This research is concerned with design optimization of control systems. Our case study deals with magnetic levitation, in which an essential part is a solenoid. Its dimensions, along with controller parameters, form the optimization variables. We present a novel way of writing the explicit expression of the solenoid’s force acting on a magnetic dipole, as well as its first derivatives. Numerical tests using non-gradient search algorithms show the difference in optimal designs provided by these methods. Since such optimization depends on output signals, a comparison of step response analysis methods is presented. Full article
(This article belongs to the Special Issue Advances in Metaheuristic Optimization Algorithms)
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54 pages, 2429 KB  
Article
A Novel Bio-Inspired Optimization Algorithm Based on Mantis Shrimp Survival Tactics
by José Alfonso Sánchez Cortez, Hernán Peraza Vázquez and Adrián Fermin Peña Delgado
Mathematics 2025, 13(9), 1500; https://doi.org/10.3390/math13091500 - 1 May 2025
Cited by 5 | Viewed by 2095
Abstract
This paper presents a novel meta-heuristic algorithm inspired by the visual capabilities of the mantis shrimp (Gonodactylus smithii), which can detect linearly and circularly polarized light signals to determine information regarding the polarized light source emitter. Inspired by these unique visual [...] Read more.
This paper presents a novel meta-heuristic algorithm inspired by the visual capabilities of the mantis shrimp (Gonodactylus smithii), which can detect linearly and circularly polarized light signals to determine information regarding the polarized light source emitter. Inspired by these unique visual characteristics, the Mantis Shrimp Optimization Algorithm (MShOA) mathematically covers three visual strategies based on the detected signals: random navigation foraging, strike dynamics in prey engagement, and decision-making for defense or retreat from the burrow. These strategies balance exploitation and exploration procedures for local and global search over the solution space. MShOA’s performance was tested with 20 testbench functions and compared against 14 other optimization algorithms. Additionally, it was tested on 10 real-world optimization problems taken from the IEEE CEC2020 competition. Moreover, MShOA was applied to solve three studied cases related to the optimal power flow problem in an IEEE 30-bus system. Wilcoxon and Friedman’s statistical tests were performed to demonstrate that MShOA offered competitive, efficient solutions in benchmark tests and real-world applications. Full article
(This article belongs to the Special Issue Advances in Metaheuristic Optimization Algorithms)
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