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Mathematics
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Metaheuristic Algorithms, 2nd Edition
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Metaheuristic Algorithms, 2nd Edition

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 5633

Special Issue Editor

Prof. Dr. Petr Stodola

E-Mail Website
Guest Editor
Department of Tactics, University of Defence, 66210 Brno, Czech Republic
Interests: modelling and simulation; optimization; operations research; metaheuristic algorithms; combinatorial optimization problems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Metaheuristic algorithms continue to be at the forefront of research, attracting attention across various fields including engineering, transportation, planning, logistics, and beyond. These algorithms are effective for solving complex problems in combinatorial optimization, often yielding high-quality solutions with less computational effort compared to traditional optimization methods.

Building upon the success of the first edition, the Special Issue titled “Metaheuristic Algorithms, 2nd Edition” aims to showcase recent advancements in both combinatorial and continuous optimization problems.

Authors from academia and industry are invited to submit original research and review articles to share their latest findings in this dynamic and evolving domain.

Prof. Dr. Petr Stodola
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

  • swarm intelligence
  • bio-inspired algorithms
  • evolutionary algorithms
  • neighborhood search algorithms
  • hybridized algorithms
  • metaheuristics applied to combinatorial problems
  • metaheuristics applied to continuous problems
  • empirical and theoretical research on metaheuristics
  • high-impact applications of metaheuristics

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Related Special Issue

Published Papers (5 papers)

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Research

29 pages, 4179 KiB  
Article
Solving the Economic Load Dispatch Problem by Attaining and Refining Knowledge-Based Optimization
by Pravesh Kumar and Musrrat Ali
Mathematics 2025, 13(7), 1042; https://doi.org/10.3390/math13071042 - 23 Mar 2025
Viewed by 265
Abstract
The Static Economic Load Dispatch (SELD) problem is a paramount optimization challenge in power engineering that seeks to optimize the allocation of power between generating units to meet imposed constraints while minimizing energy requirements. Recently, researchers have employed numerous meta-heuristic approaches to tackle [...] Read more.
The Static Economic Load Dispatch (SELD) problem is a paramount optimization challenge in power engineering that seeks to optimize the allocation of power between generating units to meet imposed constraints while minimizing energy requirements. Recently, researchers have employed numerous meta-heuristic approaches to tackle this challenging, non-convex problem. This work introduces an innovative meta-heuristic algorithm, named “Attaining and Refining Knowledge-based Optimization (ARKO)”, which uses the ability of humans to learn from their surroundings by leveraging the collective knowledge of a population. The ARKO algorithm consists of two distinct phases: attaining and refining. In the attaining phase, the algorithm gathers knowledge from the population’s top candidates, while the refining phase enhances performance by leveraging the knowledge of other selected candidates. This innovative way of learning and improving with the help of top candidates provides a robust exploration and exploitation capability for this algorithm. To validate the efficacy of ARKO, we conduct a comprehensive evaluation against eleven other established meta-heuristic algorithms using a diverse set of 41 test functions of the CEC-2017 and CEC-2022 test suites, and then, three real-life applications also verify its practical ability. Subsequently, we implement ARKO to optimize the SELD problem considering several instances. The examination of the numerical and statistical results confirms the remarkable efficiency and potential practical ability of ARKO in complex optimization tasks. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)
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30 pages, 2330 KiB  
Article
A New Hybrid Improved Kepler Optimization Algorithm Based on Multi-Strategy Fusion and Its Applications
by Zhenghong Qian, Yaming Zhang, Dongqi Pu, Gaoyuan Xie, Die Pu and Mingjun Ye
Mathematics 2025, 13(3), 405; https://doi.org/10.3390/math13030405 - 26 Jan 2025
Viewed by 888
Abstract
The Kepler optimization algorithm (KOA) is a metaheuristic algorithm based on Kepler’s laws of planetary motion and has demonstrated outstanding performance in multiple test sets and for various optimization issues. However, the KOA is hampered by the limitations of insufficient convergence accuracy, weak [...] Read more.
The Kepler optimization algorithm (KOA) is a metaheuristic algorithm based on Kepler’s laws of planetary motion and has demonstrated outstanding performance in multiple test sets and for various optimization issues. However, the KOA is hampered by the limitations of insufficient convergence accuracy, weak global search ability, and slow convergence speed. To address these deficiencies, this paper presents a multi-strategy fusion Kepler optimization algorithm (MKOA). Firstly, the algorithm initializes the population using Good Point Set, enhancing population diversity. Secondly, Dynamic Opposition-Based Learning is applied for population individuals to further improve its global exploration effectiveness. Furthermore, we introduce the Normal Cloud Model to perturb the best solution, improving its convergence rate and accuracy. Finally, a new position-update strategy is introduced to balance local and global search, helping KOA escape local optima. To test the performance of the MKOA, we uses the CEC2017 and CEC2019 test suites for testing. The data indicate that the MKOA has more advantages than other algorithms in terms of practicality and effectiveness. Aiming at the engineering issue, this study selected three classic engineering cases. The results reveal that the MKOA demonstrates strong applicability in engineering practice. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)
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13 pages, 1770 KiB  
Article
Prediction of Carbon Emissions Level in China’s Logistics Industry Based on the PSO-SVR Model
by Liang Chen, Yitong Pan and Dongqing Zhang
Mathematics 2024, 12(13), 1980; https://doi.org/10.3390/math12131980 - 26 Jun 2024
Cited by 6 | Viewed by 1622
Abstract
Adjusting the energy structure of various industries is crucial for achieving China’s carbon peak and carbon neutrality goals. Given the significant proportion of carbon emissions from the logistics industry in the tertiary sector, the research on predicting the carbon emissions of the logistics [...] Read more.
Adjusting the energy structure of various industries is crucial for achieving China’s carbon peak and carbon neutrality goals. Given the significant proportion of carbon emissions from the logistics industry in the tertiary sector, the research on predicting the carbon emissions of the logistics industry is of great significance for China to achieve its “Dual carbon” target. In this paper, the gray relational analysis (GRA) methodology is adopted to screen the influencing factors of carbon emissions in the logistics industry firstly. Then, the particle swarm optimization (PSO) algorithm was used to optimize the penalty coefficientand kernel function range parameter of the support vector regression (SVR) model (i.e. PSO- SVR model). The data from 2000 to 2021 regarding carbon emissions and related influencing factors in China’s logistics industry are analyzed, and the mean absolute percentage error (MAPE) of the PSO-SVR model is 0.82%, which shows that the proposed PSO-SVR model in this paper is effective. Finally, instructive suggestions are provided for China to achieve the “Dual Carbon” goal and upgrading of the logistics industry. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)
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21 pages, 1929 KiB  
Article
An Agile Adaptive Biased-Randomized Discrete-Event Heuristic for the Resource-Constrained Project Scheduling Problem
by Xabier A. Martin, Rosa Herrero, Angel A. Juan and Javier Panadero
Mathematics 2024, 12(12), 1873; https://doi.org/10.3390/math12121873 - 16 Jun 2024
Cited by 1 | Viewed by 1034
Abstract
In industries such as aircraft or train manufacturing, large-scale manufacturing companies often manage several complex projects. Each of these projects includes multiple tasks that share a set of limited resources. Typically, these tasks are also subject to time dependencies among them. One frequent [...] Read more.
In industries such as aircraft or train manufacturing, large-scale manufacturing companies often manage several complex projects. Each of these projects includes multiple tasks that share a set of limited resources. Typically, these tasks are also subject to time dependencies among them. One frequent goal in these scenarios is to minimize the makespan, or total time required to complete all the tasks within the entire project. Decisions revolve around scheduling these tasks, determining the sequence in which they are processed, and allocating shared resources to optimize efficiency while respecting the time dependencies among tasks. This problem is known in the scientific literature as the Resource-Constrained Project Scheduling Problem (RCPSP). Being an NP-hard problem with time dependencies and resource constraints, several optimization algorithms have already been proposed to tackle the RCPSP. In this paper, a novel discrete-event heuristic is introduced and later extended into an agile biased-randomized algorithm complemented with an adaptive capability to tune the parameters of the algorithm. The results underscore the effectiveness of the algorithm in finding competitive solutions for this problem within short computing times. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)
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19 pages, 665 KiB  
Article
A Learnheuristic Algorithm Based on Thompson Sampling for the Heterogeneous and Dynamic Team Orienteering Problem
by Antonio R. Uguina, Juan F. Gomez, Javier Panadero, Anna Martínez-Gavara and Angel A. Juan
Mathematics 2024, 12(11), 1758; https://doi.org/10.3390/math12111758 - 5 Jun 2024
Viewed by 1236
Abstract
The team orienteering problem (TOP) is a well-studied optimization challenge in the field of Operations Research, where multiple vehicles aim to maximize the total collected rewards within a given time limit by visiting a subset of nodes in a network. With the goal [...] Read more.
The team orienteering problem (TOP) is a well-studied optimization challenge in the field of Operations Research, where multiple vehicles aim to maximize the total collected rewards within a given time limit by visiting a subset of nodes in a network. With the goal of including dynamic and uncertain conditions inherent in real-world transportation scenarios, we introduce a novel dynamic variant of the TOP that considers real-time changes in environmental conditions affecting reward acquisition at each node. Specifically, we model the dynamic nature of environmental factors—such as traffic congestion, weather conditions, and battery level of each vehicle—to reflect their impact on the probability of obtaining the reward when visiting each type of node in a heterogeneous network. To address this problem, a learnheuristic optimization framework is proposed. It combines a metaheuristic algorithm with Thompson sampling to make informed decisions in dynamic environments. Furthermore, we conduct empirical experiments to assess the impact of varying reward probabilities on resource allocation and route planning within the context of this dynamic TOP, where nodes might offer a different reward behavior depending upon the environmental conditions. Our numerical results indicate that the proposed learnheuristic algorithm outperforms static approaches, achieving up to 25% better performance in highly dynamic scenarios. Our findings highlight the effectiveness of our approach in adapting to dynamic conditions and optimizing decision-making processes in transportation systems. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms, 2nd Edition)
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