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Metaheuristic Algorithms
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Metaheuristic Algorithms

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

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 47900

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 represent a rapidly growing research domain and have recently attracted a great deal of attention; they are successfully applied in engineering, transportation, planning and scheduling, logistics and supply chains, and a broad range of other domains.

Metaheuristic algorithms are widely used in combinatorial optimization to solve complex problems with non-deterministic polynomial-time hardness; they are often able to find high-quality solutions with less computational effort than other optimization methods.

This Special Issue aims at gathering recent advances in metaheuristic algorithms used for both combinatorial and continuous optimization problems. We invite authors to present their original research articles as well as review articles. This Special Issue provides a platform for researchers from academia and industry to present their novel and unpublished work in this thrilling domain.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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Published Papers (25 papers)

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Research

16 pages, 3911 KiB  
Article
Optimizing Multi-Layer Perovskite Solar Cell Dynamic Models with Hysteresis Consideration Using Artificial Rabbits Optimization
by Ahmed Saeed Abdelrazek Bayoumi, Ragab A. El-Sehiemy, Mahmoud Badawy, Mostafa Elhosseini, Mansourah Aljohani and Amlak Abaza
Mathematics 2023, 11(24), 4912; https://doi.org/10.3390/math11244912 - 09 Dec 2023
Viewed by 756
Abstract
Perovskite solar cells (PSCs) exhibit hysteresis in their J-V characteristics, complicating the identification of appropriate electrical models and the determination of the maximum power point. Given the rising prominence of PSCs due to their potential for superior performance, there is a pressing need [...] Read more.
Perovskite solar cells (PSCs) exhibit hysteresis in their J-V characteristics, complicating the identification of appropriate electrical models and the determination of the maximum power point. Given the rising prominence of PSCs due to their potential for superior performance, there is a pressing need to address this challenge. Existing solutions in the literature have not fully addressed the hysteresis issue, especially in the context of dynamic modeling. To bridge this gap, this study introduces Artificial Rabbits Optimization (ARO) as an innovative method for optimizing the parameters of an enhanced PSC dynamic model. The proposed model is constructed based on experimental J-V data sets of PSCs, ensuring that it accounts for the hysteresis characteristics observed in both forward and backward scans. The study conducted a rigorous statistical analysis to validate the Modified Two-Diode Model performance with that of the Energy Balance (MTDM_E) optimized using the innovative ARO algorithm. The performance metric utilized for validation was the Root mean square error (RMSE), a widely recognized degree of the differences between values predicted by a model and the values observed. The statistical analysis encompassed 30 independent runs to ensure the robustness and reliability of the results. The summary statistics for the MTDM_E model under the ARO algorithm demonstrated a minimum RMSE of 4.84E−04, a maximum of 6.44E−04, and a mean RMSE of 5.14E−04. The median RMSE was reported as 5.07E−04, with a standard deviation of 3.17E−05, indicating a consistent and tight clustering of results around the mean, which suggests a high level of precision in the model’s performance. Validated using root mean square error (RMSE) across 30 runs, the ARO algorithm showcased superior precision in parameter determination for the MTDM_E model, with a mean RMSE of 5.14E−04, outperforming other algorithms like GWO, PSO, SCA, and SSA. This affirms ARO’s robustness in optimizing solar cell models. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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26 pages, 7495 KiB  
Article
Propagation Search Algorithm: A Physics-Based Optimizer for Engineering Applications
by Mohammed H. Qais, Hany M. Hasanien, Saad Alghuwainem and Ka Hong Loo
Mathematics 2023, 11(20), 4224; https://doi.org/10.3390/math11204224 - 10 Oct 2023
Cited by 1 | Viewed by 1007
Abstract
For process control in engineering applications, the fewer the coding lines of optimization algorithms, the more applications there are. Therefore, this work develops a new straightforward metaheuristic optimization algorithm named the propagation search algorithm (PSA), stirred by the wave propagation of the voltage [...] Read more.
For process control in engineering applications, the fewer the coding lines of optimization algorithms, the more applications there are. Therefore, this work develops a new straightforward metaheuristic optimization algorithm named the propagation search algorithm (PSA), stirred by the wave propagation of the voltage and current along long transmission lines. The mathematical models of the voltage and current are utilized in modeling the PSA, where the voltage and current are the search agents. The propagation constant of the transmission line is the control parameter for the exploitation and exploration of the PSA. After that, the robustness of the PSA is verified using 23 famous testing functions. The statistical tests, comprising mean, standard deviation, and p-values, for 20 independent optimization experiments are utilized to confirm the robustness of the PSA to find the best result and the significant difference between the outcomes of the PSA and those of the compared algorithms. Finally, the proposed PSA is applied to find the optimum design parameters of four engineering design problems, including a three-bar truss, compression spring, pressure vessel, and welded beam. The outcomes show that the PSA converges to the best solutions very quickly, which can be applied to those applications that require a fast response. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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20 pages, 5555 KiB  
Article
Enhanced Whale Optimization Algorithm for Improved Transient Electromagnetic Inversion in the Presence of Induced Polarization Effects
by Ruiheng Li, Yi Di, Qiankun Zuo, Hao Tian and Lu Gan
Mathematics 2023, 11(19), 4164; https://doi.org/10.3390/math11194164 - 04 Oct 2023
Cited by 2 | Viewed by 748
Abstract
The transient electromagnetic (TEM) method is a non-contact technique used to identify underground structures, commonly used in mineral resource exploration. However, the induced polarization (IP) will increase the nonlinearity of TEM inversion, and it is difficult to predict the geoelectric structure from TEM [...] Read more.
The transient electromagnetic (TEM) method is a non-contact technique used to identify underground structures, commonly used in mineral resource exploration. However, the induced polarization (IP) will increase the nonlinearity of TEM inversion, and it is difficult to predict the geoelectric structure from TEM response signals in conventional gradient inversion. We select a heuristic algorithm suitable for nonlinear inversion—a whale optimization algorithm to perform TEM inversion with an IP effect. The inverse framework is optimized by opposition-based learning (OBL) and an adaptive weighted factor (AWF). OBL improves initial population distribution for better global search, while the AWF replaces random operators to balance global and local search, enhancing solution accuracy and ensuring stable convergence. Tests on layered geoelectric models demonstrate that our improved WOA effectively reconstructs geoelectric structures, extracts IP information, and performs robustly in noisy environments. Compared to other nonlinear inversion methods, our proposed approach shows superior convergence and accuracy, effectively extracting IP information from TEM signals, with an error of less than 8%. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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42 pages, 12146 KiB  
Article
FSSSA: A Fuzzy Squirrel Search Algorithm Based on Wide-Area Search for Numerical and Engineering Optimization Problems
by Lei Chen, Bingjie Zhao and Yunpeng Ma
Mathematics 2023, 11(17), 3722; https://doi.org/10.3390/math11173722 - 29 Aug 2023
Viewed by 688
Abstract
The Squirrel Search Algorithm (SSA) is widely used due to its simple structure and efficient search ability. However, SSA exhibits relatively slow convergence speed and imbalanced exploration and exploitation. To address these limitations, this paper proposes a fuzzy squirrel search algorithm based on [...] Read more.
The Squirrel Search Algorithm (SSA) is widely used due to its simple structure and efficient search ability. However, SSA exhibits relatively slow convergence speed and imbalanced exploration and exploitation. To address these limitations, this paper proposes a fuzzy squirrel search algorithm based on a wide-area search mechanism named FSSSA. The fuzzy inference system and sine cosine mutation are employed to enhance the convergence speed. The wide-area search mechanism is introduced to achieve a better balance between exploration and exploitation, as well as improve the convergence accuracy. To evaluate the effectiveness of the proposed strategies, FSSSA is compared with SSA on 24 diverse benchmark functions, using four evaluation indexes: convergence speed, convergence accuracy, balance and diversity, and non-parametric test. The experimental results demonstrate that FSSSA outperforms SSA in all four indexes. Furthermore, a comparison with eight metaheuristic algorithms is conducted to illustrate the optimization performance of FSSSA. The results indicate that FSSSA exhibits excellent convergence speed and overall performance. Additionally, FSSSA is applied to four engineering problems, and experimental verification confirms that it maintains superior performance in realistic optimization problems, thus demonstrating its practicality. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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29 pages, 1535 KiB  
Article
A Novel Hybrid Algorithm Based on Jellyfish Search and Particle Swarm Optimization
by Husham Muayad Nayyef, Ahmad Asrul Ibrahim, Muhammad Ammirrul Atiqi Mohd Zainuri, Mohd Asyraf Zulkifley and Hussain Shareef
Mathematics 2023, 11(14), 3210; https://doi.org/10.3390/math11143210 - 21 Jul 2023
Cited by 4 | Viewed by 1051
Abstract
Metaheuristic optimization is considered one of the most efficient and powerful techniques of recent decades as it can deal effectively with complex optimization problems. The performance of the optimization technique relies on two main components: exploration and exploitation. Unfortunately, the performance is limited [...] Read more.
Metaheuristic optimization is considered one of the most efficient and powerful techniques of recent decades as it can deal effectively with complex optimization problems. The performance of the optimization technique relies on two main components: exploration and exploitation. Unfortunately, the performance is limited by a weakness in one of the components. This study aims to tackle the issue with the exploration of the existing jellyfish search optimizer (JSO) by introducing a hybrid jellyfish search and particle swarm optimization (HJSPSO). HJSPSO is mainly based on a JSO structure, but the following ocean current movement operator is replaced with PSO to benefit from its exploration capability. The search process alternates between PSO and JSO operators through a time control mechanism. Furthermore, nonlinear and time-varying inertia weight, cognitive, and social coefficients are added to the PSO and JSO operators to balance between exploration and exploitation. Sixty benchmark test functions, including 10 CEC-C06 2019 large-scale benchmark test functions with various dimensions, are used to showcase the optimization performance. Then, the traveling salesman problem (TSP) is used to validate the performance of HJSPSO for a nonconvex optimization problem. Results demonstrate that compared to existing JSO and PSO techniques, HJSPSO contributes in terms of exploration and exploitation improvements, where it outperforms other well-known metaheuristic optimization techniques that include a hybrid algorithm. In this case, HJSPSO secures the first rank in classical and large-scale benchmark test functions by achieving the highest hit rates of 64% and 30%, respectively. Moreover, HJSPSO demonstrates good applicability in solving an exemplar TSP after attaining the shortest distance with the lowest mean and best fitness at 37.87 and 36.12, respectively. Overall, HJSPSO shows superior performance in solving most benchmark test functions compared to other optimization techniques, including JSO and PSO. As a conclusion, HJSPSO is a robust technique that can be applied to solve most optimization problems with a promising solution. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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20 pages, 661 KiB  
Article
Exploring Initialization Strategies for Metaheuristic Optimization: Case Study of the Set-Union Knapsack Problem
by José García, Andres Leiva-Araos, Broderick Crawford, Ricardo Soto and Hernan Pinto
Mathematics 2023, 11(12), 2695; https://doi.org/10.3390/math11122695 - 14 Jun 2023
Cited by 2 | Viewed by 879
Abstract
In recent years, metaheuristic methods have shown remarkable efficacy in resolving complex combinatorial challenges across a broad spectrum of fields. Nevertheless, the escalating complexity of these problems necessitates the continuous development of innovative techniques to enhance the performance and reliability of these methods. [...] Read more.
In recent years, metaheuristic methods have shown remarkable efficacy in resolving complex combinatorial challenges across a broad spectrum of fields. Nevertheless, the escalating complexity of these problems necessitates the continuous development of innovative techniques to enhance the performance and reliability of these methods. This paper aims to contribute to this endeavor by examining the impact of solution initialization methods on the performance of a hybrid algorithm applied to the set union knapsack problem (SUKP). Three distinct solution initialization methods, random, greedy, and weighted, have been proposed and evaluated. These have been integrated within a sine cosine algorithm employing k-means as a binarization procedure. Through testing on medium- and large-sized SUKP instances, the study reveals that the solution initialization strategy influences the algorithm’s performance, with the weighted method consistently outperforming the other two. Additionally, the obtained results were benchmarked against various metaheuristics that have previously solved SUKP, showing favorable performance in this comparison. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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35 pages, 5942 KiB  
Article
Bio-Inspired Multi-UAV Path Planning Heuristics: A Review
by Faten Aljalaud, Heba Kurdi and Kamal Youcef-Toumi
Mathematics 2023, 11(10), 2356; https://doi.org/10.3390/math11102356 - 18 May 2023
Cited by 4 | Viewed by 2007
Abstract
Despite the rapid advances in autonomous guidance and navigation techniques for unmanned aerial vehicle (UAV) systems, there are still many challenges in finding an optimal path planning algorithm that allows outlining a collision-free navigation route from the vehicle’s current position to a goal [...] Read more.
Despite the rapid advances in autonomous guidance and navigation techniques for unmanned aerial vehicle (UAV) systems, there are still many challenges in finding an optimal path planning algorithm that allows outlining a collision-free navigation route from the vehicle’s current position to a goal point. The challenges grow as the number of UAVs involved in the mission increases. Therefore, this work provides a comprehensive systematic review of the literature on the path planning algorithms for multi-UAV systems. In particular, the review focuses on biologically inspired (bio-inspired) algorithms due to their potential in overcoming the challenges associated with multi-UAV path planning problems. It presents a taxonomy for classifying existing algorithms and describes their evolution in the literature. The work offers a structured and accessible presentation of bio-inspired path planning algorithms for researchers in this subject, especially as no previous review exists with a similar scope. This classification is significant as it facilitates studying bio-inspired multi-UAV path planning algorithms under one framework, shows the main design features of the algorithms clearly to assist in a detailed comparison between them, understanding current research trends, and anticipating future directions. Our review showed that bio-inspired algorithms have a high potential to approach the multi-UAV path planning problem and identified challenges and future research directions that could help improve this dynamic research area. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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47 pages, 12334 KiB  
Article
Chaotic Sand Cat Swarm Optimization
by Farzad Kiani, Sajjad Nematzadeh, Fateme Aysin Anka and Mine Afacan Findikli
Mathematics 2023, 11(10), 2340; https://doi.org/10.3390/math11102340 - 17 May 2023
Cited by 12 | Viewed by 2085
Abstract
In this study, a new hybrid metaheuristic algorithm named Chaotic Sand Cat Swarm Optimization (CSCSO) is proposed for constrained and complex optimization problems. This algorithm combines the features of the recently introduced SCSO with the concept of chaos. The basic aim of the [...] Read more.
In this study, a new hybrid metaheuristic algorithm named Chaotic Sand Cat Swarm Optimization (CSCSO) is proposed for constrained and complex optimization problems. This algorithm combines the features of the recently introduced SCSO with the concept of chaos. The basic aim of the proposed algorithm is to integrate the chaos feature of non-recurring locations into SCSO’s core search process to improve global search performance and convergence behavior. Thus, randomness in SCSO can be replaced by a chaotic map due to similar randomness features with better statistical and dynamic properties. In addition to these advantages, low search consistency, local optimum trap, inefficiency search, and low population diversity issues are also provided. In the proposed CSCSO, several chaotic maps are implemented for more efficient behavior in the exploration and exploitation phases. Experiments are conducted on a wide variety of well-known test functions to increase the reliability of the results, as well as real-world problems. In this study, the proposed algorithm was applied to a total of 39 functions and multidisciplinary problems. It found 76.3% better responses compared to a best-developed SCSO variant and other chaotic-based metaheuristics tested. This extensive experiment indicates that the CSCSO algorithm excels in providing acceptable results. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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17 pages, 3483 KiB  
Article
Shapley-Value-Based Hybrid Metaheuristic Multi-Objective Optimization for Energy Efficiency in an Energy-Harvesting Cognitive Radio Network
by Shalley Bakshi, Surbhi Sharma and Rajesh Khanna
Mathematics 2023, 11(7), 1656; https://doi.org/10.3390/math11071656 - 30 Mar 2023
Cited by 1 | Viewed by 955
Abstract
Energy efficiency and throughput are concerns for energy-harvesting cognitive radio networks. However, attaining the maximum level of both requires optimization of sensing duration, harvested energy, and transmission time. To obtain the optimal values of these multiple parameters and to maximize the average throughput [...] Read more.
Energy efficiency and throughput are concerns for energy-harvesting cognitive radio networks. However, attaining the maximum level of both requires optimization of sensing duration, harvested energy, and transmission time. To obtain the optimal values of these multiple parameters and to maximize the average throughput and energy efficiency, a new hybrid technique for multi-objective optimization is proposed. This hybrid optimization algorithm incorporates a Shapley value and a game theoretic concept into metaheuristics. Here, particle swarm optimization grey wolf optimization (PSOGWO) is selected as the source for the advanced hybrid algorithm. The concept of the unbiased nature of wolves is also added to PSOGWO to make it more efficient. Multi-objective optimization is formulated by taking a deep look into combined spectrum sensing and energy harvesting in a cognitive radio network (CSSEH). The Pareto optimal solutions for the multi-objective optimization problem of energy efficiency and throughput can be obtained using PSOGWO by updating the velocity with the weights. In the proposed Shapley hybrid multi-objective optimization algorithm, we used Shapley values to set up the weights that, in turn, updated the velocities of the particles. This updated velocity increased the ability of particles to reach a global optimum rather than becoming trapped in local optima. The solution obtained with this hybrid algorithm is the Shapley–Pareto optimal solution. The proposed algorithm is also compared with state-of-the-art PSOGWO, unbiased PSOGWO, and GWO. The results show a significant level of improvement in terms of energy efficiency by 3.56% while reducing the sensing duration and increasing the average throughput by 21.83% in comparison with standard GWO. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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24 pages, 2794 KiB  
Article
A Discrete-Event Simheuristic for Solving a Realistic Storage Location Assignment Problem
by Jonas F. Leon, Yuda Li, Mohammad Peyman, Laura Calvet and Angel A. Juan
Mathematics 2023, 11(7), 1577; https://doi.org/10.3390/math11071577 - 24 Mar 2023
Cited by 3 | Viewed by 1812
Abstract
In the context of increasing complexity in manufacturing and logistic systems, the combination of optimization and simulation can be considered a versatile tool for supporting managerial decision-making. An informed storage location assignment policy is key for improving warehouse operations, which play a vital [...] Read more.
In the context of increasing complexity in manufacturing and logistic systems, the combination of optimization and simulation can be considered a versatile tool for supporting managerial decision-making. An informed storage location assignment policy is key for improving warehouse operations, which play a vital role in the efficiency of supply chains. Traditional approaches in the literature to solve the storage location assignment problem present some limitations, such as excluding the stochastic variability of processes or the interaction among different warehouse activities. This work addresses those limitations by proposing a discrete-event simheuristic framework that ensures robust solutions in the face of real-life warehouse conditions. The approach followed embraces the complexity of the problem by integrating the order sequence and picking route in the solution construction and uses commercial simulation software to reduce the impact of stochastic events on the quality of the solution. The implementation of this type of novel methodology within a warehouse management system can enhance warehouse efficiency without requiring an increase in automation level. The method developed is tested under a number of computational experiments that show its convenience and point toward future lines of research. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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25 pages, 593 KiB  
Article
A Formulation for the Stochastic Multi-Mode Resource-Constrained Project Scheduling Problem Solved with a Multi-Start Iterated Local Search Metaheuristic
by Alfredo S. Ramos, Pablo A. Miranda-Gonzalez, Samuel Nucamendi-Guillén and Elias Olivares-Benitez
Mathematics 2023, 11(2), 337; https://doi.org/10.3390/math11020337 - 09 Jan 2023
Cited by 1 | Viewed by 1675
Abstract
This research introduces a stochastic version of the multi-mode resource-constrained project scheduling problem (MRCPSP) and its mathematical model. In addition, an efficient multi-start iterated local search (MS-ILS) algorithm, capable of solving the deterministic MRCPSP, is adapted to deal with the proposed stochastic version [...] Read more.
This research introduces a stochastic version of the multi-mode resource-constrained project scheduling problem (MRCPSP) and its mathematical model. In addition, an efficient multi-start iterated local search (MS-ILS) algorithm, capable of solving the deterministic MRCPSP, is adapted to deal with the proposed stochastic version of the problem. For its deterministic version, the MRCPSP is an NP-hard optimization problem that has been widely studied. The problem deals with a trade-off between the amount of resources that each project activity requires and its duration. In the case of the proposed stochastic formulation, the execution times of the activities are uncertain. Benchmark instances of projects with 10, 20, 30, and 50 activities from well-known public libraries were adapted to create test instances. The adapted algorithm proved to be capable and efficient for solving the proposed stochastic problem. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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30 pages, 4045 KiB  
Article
Metaheuristic Optimization for Improving Weed Detection in Wheat Images Captured by Drones
by El-Sayed M. El-Kenawy, Nima Khodadadi, Seyedali Mirjalili, Tatiana Makarovskikh, Mostafa Abotaleb, Faten Khalid Karim, Hend K. Alkahtani, Abdelaziz A. Abdelhamid, Marwa M. Eid, Takahiko Horiuchi, Abdelhameed Ibrahim and Doaa Sami Khafaga
Mathematics 2022, 10(23), 4421; https://doi.org/10.3390/math10234421 - 23 Nov 2022
Cited by 21 | Viewed by 2797
Abstract
Background and aim: Machine learning methods are examined by many researchers to identify weeds in crop images captured by drones. However, metaheuristic optimization is rarely used in optimizing the machine learning models used in weed classification. Therefore, this research targets developing a new [...] Read more.
Background and aim: Machine learning methods are examined by many researchers to identify weeds in crop images captured by drones. However, metaheuristic optimization is rarely used in optimizing the machine learning models used in weed classification. Therefore, this research targets developing a new optimization algorithm that can be used to optimize machine learning models and ensemble models to boost the classification accuracy of weed images. Methodology: This work proposes a new approach for classifying weed and wheat images captured by a sprayer drone. The proposed approach is based on a voting classifier that consists of three base models, namely, neural networks (NNs), support vector machines (SVMs), and K-nearest neighbors (KNN). This voting classifier is optimized using a new optimization algorithm composed of a hybrid of sine cosine and grey wolf optimizers. The features used in training the voting classifier are extracted based on AlexNet through transfer learning. The significant features are selected from the extracted features using a new feature selection algorithm. Results: The accuracy, precision, recall, false positive rate, and kappa coefficient were employed to assess the performance of the proposed voting classifier. In addition, a statistical analysis is performed using the one-way analysis of variance (ANOVA), and Wilcoxon signed-rank tests to measure the stability and significance of the proposed approach. On the other hand, a sensitivity analysis is performed to study the behavior of the parameters of the proposed approach in achieving the recorded results. Experimental results confirmed the effectiveness and superiority of the proposed approach when compared to the other competing optimization methods. The achieved detection accuracy using the proposed optimized voting classifier is 97.70%, F-score is 98.60%, specificity is 95.20%, and sensitivity is 98.40%. Conclusion: The proposed approach is confirmed to achieve better classification accuracy and outperforms other competing approaches. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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13 pages, 1813 KiB  
Article
A Global Neighborhood with Hill-Climbing Algorithm for Fuzzy Flexible Job Shop Scheduling Problem
by Juan Carlos Seck-Tuoh-Mora, Nayeli Jazmín Escamilla-Serna, Leonardo Javier Montiel-Arrieta, Irving Barragan-Vite and Joselito Medina-Marin
Mathematics 2022, 10(22), 4233; https://doi.org/10.3390/math10224233 - 12 Nov 2022
Cited by 2 | Viewed by 1458
Abstract
The Flexible Job Shop Scheduling Problem (FJSSP) continues to be studied extensively to test new metaheuristics and because of its closeness to current production systems. A variant of the FJSSP uses fuzzy processing times instead of fixed times. This paper proposes a new [...] Read more.
The Flexible Job Shop Scheduling Problem (FJSSP) continues to be studied extensively to test new metaheuristics and because of its closeness to current production systems. A variant of the FJSSP uses fuzzy processing times instead of fixed times. This paper proposes a new algorithm for FJSSP with fuzzy processing times called the global neighborhood with hill-climbing algorithm (GN-HC). This algorithm performs solution exploration using simple operators concurrently for global search neighborhood handling. For local search, random restart hill-climbing is applied at each solution to find the best machine for each operation. For the selection of operations in hill climbing, a record of the operations defining the fuzzy makespan is employed to use them as a critical path. Finally, an estimation of the crisp makespan with the longest processing times in hill climbing is made to improve the speed of the GN-HC. The GN-HC is compared with other recently proposed methods recognized for their excellent performance, using 6 FJSSP instances with fuzzy times. The obtained results show satisfactory competitiveness for GN-HC compared to state-of-the-art algorithms. The GN-HC implementation was performed in Matlab and can be found on GitHub (check Data Availability Statement at the end of the paper). Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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63 pages, 12070 KiB  
Article
Light Spectrum Optimizer: A Novel Physics-Inspired Metaheuristic Optimization Algorithm
by Mohamed Abdel-Basset, Reda Mohamed, Karam M. Sallam and Ripon K. Chakrabortty
Mathematics 2022, 10(19), 3466; https://doi.org/10.3390/math10193466 - 23 Sep 2022
Cited by 29 | Viewed by 4565
Abstract
This paper introduces a novel physical-inspired metaheuristic algorithm called “Light Spectrum Optimizer (LSO)” for continuous optimization problems. The inspiration for the proposed algorithm is the light dispersions with different angles while passing through rain droplets, causing the meteorological phenomenon of the colorful rainbow [...] Read more.
This paper introduces a novel physical-inspired metaheuristic algorithm called “Light Spectrum Optimizer (LSO)” for continuous optimization problems. The inspiration for the proposed algorithm is the light dispersions with different angles while passing through rain droplets, causing the meteorological phenomenon of the colorful rainbow spectrum. In order to validate the proposed algorithm, three different experiments are conducted. First, LSO is tested on solving CEC 2005, and the obtained results are compared with a wide range of well-regarded metaheuristics. In the second experiment, LSO is used for solving four CEC competitions in single objective optimization benchmarks (CEC2014, CEC2017, CEC2020, and CEC2022), and its results are compared with eleven well-established and recently-published optimizers, named grey wolf optimizer (GWO), whale optimization algorithm (WOA), and salp swarm algorithm (SSA), evolutionary algorithms like differential evolution (DE), and recently-published optimizers including gradient-based optimizer (GBO), artificial gorilla troops optimizer (GTO), Runge–Kutta method (RUN) beyond the metaphor, African vultures optimization algorithm (AVOA), equilibrium optimizer (EO), grey wolf optimizer (GWO), Reptile Search Algorithm (RSA), and slime mold algorithm (SMA). In addition, several engineering design problems are solved, and the results are compared with many algorithms from the literature. The experimental results with the statistical analysis demonstrate the merits and highly superior performance of the proposed LSO algorithm. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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26 pages, 2424 KiB  
Article
Meta-Heuristic Optimization and Keystroke Dynamics for Authentication of Smartphone Users
by El-Sayed M. El-Kenawy, Seyedali Mirjalili, Abdelaziz A. Abdelhamid, Abdelhameed Ibrahim, Nima Khodadadi and Marwa M. Eid
Mathematics 2022, 10(16), 2912; https://doi.org/10.3390/math10162912 - 13 Aug 2022
Cited by 42 | Viewed by 2351
Abstract
Personal Identification Numbers (PIN) and unlock patterns are two of the most often used smartphone authentication mechanisms. Because PINs have just four or six characters, they are subject to shoulder-surfing attacks and are not as secure as other authentication techniques. Biometric authentication methods, [...] Read more.
Personal Identification Numbers (PIN) and unlock patterns are two of the most often used smartphone authentication mechanisms. Because PINs have just four or six characters, they are subject to shoulder-surfing attacks and are not as secure as other authentication techniques. Biometric authentication methods, such as fingerprint, face, or iris, are now being studied in a variety of ways. The security of such biometric authentication is based on PIN-based authentication as a backup when the maximum defined number of authentication failures is surpassed during the authentication process. Keystroke-dynamics-based authentication has been studied to circumvent this limitation, in which users were categorized by evaluating their typing patterns as they input their PIN. A broad variety of approaches have been proposed to improve the capacity of PIN entry systems to discriminate between normal and abnormal users based on a user’s typing pattern. To improve the accuracy of user discrimination using keystroke dynamics, we propose a novel approach for improving the parameters of a Bidirectional Recurrent Neural Network (BRNN) used in classifying users’ keystrokes. The proposed approach is based on a significant modification to the Dipper Throated Optimization (DTO) algorithm by employing three search leaders to improve the exploration process of the optimization algorithm. To assess the effectiveness of the proposed approach, two datasets containing keystroke dynamics were included in the conducted experiments. In addition, we propose a feature selection algorithm for selecting the proper features that enable better user classification. The proposed algorithms are compared to other optimization methods in the literature, and the results showed the superiority of the proposed algorithms. Moreover, a statistical analysis is performed to measure the stability and significance of the proposed methods, and the results confirmed the expected findings. The best classification accuracy achieved by the proposed optimized BRNN is 99.02% and 99.32% for the two datasets. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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20 pages, 577 KiB  
Article
A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem
by Juan F. Gomez, Javier Panadero, Rafael D. Tordecilla, Juliana Castaneda and Angel A. Juan
Mathematics 2022, 10(14), 2405; https://doi.org/10.3390/math10142405 - 09 Jul 2022
Cited by 5 | Viewed by 1531
Abstract
The capacitated dispersion problem is a variant of the maximum diversity problem in which a set of elements in a network must be determined. These elements might represent, for instance, facilities in a logistics network or transmission devices in a telecommunication network. Usually, [...] Read more.
The capacitated dispersion problem is a variant of the maximum diversity problem in which a set of elements in a network must be determined. These elements might represent, for instance, facilities in a logistics network or transmission devices in a telecommunication network. Usually, it is considered that each element is limited in its servicing capacity. Hence, given a set of possible locations, the capacitated dispersion problem consists of selecting a subset that maximizes the minimum distance between any pair of elements while reaching an aggregated servicing capacity. Since this servicing capacity is a highly usual constraint in real-world problems, the capacitated dispersion problem is often a more realistic approach than is the traditional maximum diversity problem. Given that the capacitated dispersion problem is an NP-hard problem, whenever large-sized instances are considered, we need to use heuristic-based algorithms to obtain high-quality solutions in reasonable computational times. Accordingly, this work proposes a multi-start biased-randomized algorithm to efficiently solve the capacitated dispersion problem. A series of computational experiments is conducted employing small-, medium-, and large-sized instances. Our results are compared with the best-known solutions reported in the literature, some of which have been proven to be optimal. Our proposed approach is proven to be highly competitive, as it achieves either optimal or near-optimal solutions and outperforms the non-optimal best-known solutions in many cases. Finally, a sensitive analysis considering different levels of the minimum aggregate capacity is performed as well to complete our study. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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41 pages, 5668 KiB  
Article
A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural Network
by Syed Anayet Karim, Mohd Shareduwan Mohd Kasihmuddin, Saratha Sathasivam, Mohd. Asyraf Mansor, Siti Zulaikha Mohd Jamaludin and Md Rabiol Amin
Mathematics 2022, 10(12), 1963; https://doi.org/10.3390/math10121963 - 07 Jun 2022
Cited by 10 | Viewed by 1573
Abstract
Hybridized algorithms are commonly employed to improve the performance of any existing method. However, an optimal learning algorithm composed of evolutionary and swarm intelligence can radically improve the quality of the final neuron states and has not received creative attention yet. Considering this [...] Read more.
Hybridized algorithms are commonly employed to improve the performance of any existing method. However, an optimal learning algorithm composed of evolutionary and swarm intelligence can radically improve the quality of the final neuron states and has not received creative attention yet. Considering this issue, this paper presents a novel metaheuristics algorithm combined with several objectives—introduced as the Hybrid Election Algorithm (HEA)—with great results in solving optimization and combinatorial problems over a binary search space. The core and underpinning ideas of this proposed HEA are inspired by socio-political phenomena, consisting of creative and powerful mechanisms to achieve the optimal result. A non-systematic logical structure can find a better phenomenon in the study of logic programming. In this regard, a non-systematic structure known as Random k Satisfiability (RANkSAT) with higher-order is hosted here to overcome the interpretability and dissimilarity compared to a systematic, logical structure in a Discrete Hopfield Neural Network (DHNN). The novelty of this study is to introduce a new multi-objective Hybrid Election Algorithm that achieves the highest fitness value and can boost the storage capacity of DHNN along with a diversified logical structure embedded with RANkSAT representation. To attain such goals, the proposed algorithm tested four different types of algorithms, such as evolutionary types (Genetic Algorithm (GA)), swarm intelligence types (Artificial Bee Colony algorithm), population-based (traditional Election Algorithm (EA)) and the Exhaustive Search (ES) model. To check the performance of the proposed HEA model, several performance metrics, such as training–testing, energy, similarity analysis and statistical analysis, such as the Friedman test with convergence analysis, have been examined and analyzed. Based on the experimental and statistical results, the proposed HEA model outperformed all the mentioned four models in this research. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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23 pages, 3401 KiB  
Article
Design of Aquila Optimization Heuristic for Identification of Control Autoregressive Systems
by Khizer Mehmood, Naveed Ishtiaq Chaudhary, Zeshan Aslam Khan, Muhammad Asif Zahoor Raja, Khalid Mehmood Cheema and Ahmad H. Milyani
Mathematics 2022, 10(10), 1749; https://doi.org/10.3390/math10101749 - 20 May 2022
Cited by 19 | Viewed by 1520
Abstract
Swarm intelligence-based metaheuristic algorithms have attracted the attention of the research community and have been exploited for effectively solving different optimization problems of engineering, science, and technology. This paper considers the parameter estimation of the control autoregressive (CAR) model by applying a novel [...] Read more.
Swarm intelligence-based metaheuristic algorithms have attracted the attention of the research community and have been exploited for effectively solving different optimization problems of engineering, science, and technology. This paper considers the parameter estimation of the control autoregressive (CAR) model by applying a novel swarm intelligence-based optimization algorithm called the Aquila optimizer (AO). The parameter tuning of AO is performed statistically on different generations and population sizes. The performance of the AO is investigated statistically in various noise levels for the parameters with the best tuning. The robustness and reliability of the AO are carefully examined under various scenarios for CAR identification. The experimental results indicate that the AO is accurate, convergent, and robust for parameter estimation of CAR systems. The comparison of the AO heuristics with recent state of the art counterparts through nonparametric statistical tests established the efficacy of the proposed scheme for CAR estimation. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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27 pages, 2597 KiB  
Article
Non-Systematic Weighted Satisfiability in Discrete Hopfield Neural Network Using Binary Artificial Bee Colony Optimization
by Siti Syatirah Muhammad Sidik, Nur Ezlin Zamri, Mohd Shareduwan Mohd Kasihmuddin, Habibah A. Wahab, Yueling Guo and Mohd. Asyraf Mansor
Mathematics 2022, 10(7), 1129; https://doi.org/10.3390/math10071129 - 01 Apr 2022
Cited by 26 | Viewed by 2174
Abstract
Recently, new variants of non-systematic satisfiability logic were proposed to govern Discrete Hopfield Neural Network. This new variant of satisfiability logical rule will provide flexibility and enhance the diversity of the neuron states in the Discrete Hopfield Neural Network. However, there is no [...] Read more.
Recently, new variants of non-systematic satisfiability logic were proposed to govern Discrete Hopfield Neural Network. This new variant of satisfiability logical rule will provide flexibility and enhance the diversity of the neuron states in the Discrete Hopfield Neural Network. However, there is no systematic method to control and optimize the logical structure of non-systematic satisfiability. Additionally, the role of negative literals was neglected, reducing the expressivity of the information that the logical structure holds. This study proposed an additional optimization layer of Discrete Hopfield Neural Network called the logic phase that controls the distribution of negative literals in the logical structure. Hence, a new variant of non-systematic satisfiability named Weighted Random 2 Satisfiability was formulated. Thus, a proposed searching technique called the binary Artificial Bee Colony algorithm will ensure the correct distribution of the negative literals. It is worth mentioning that the binary Artificial Bee Colony has flexible and less free parameters where the modifications tackled on the objective function. Specifically, this study utilizes a binary Artificial Bee Colony algorithm by modifying the updating rule equation by using not and (NAND) logic gate operator. The performance of the binary Artificial Bee Colony will be compared with other variants of binary Artificial Bee Colony algorithms of different logic gate operators and conventional binary algorithms such as the Particle Swarm Optimization, Exhaustive Search, and Genetic Algorithm. The experimental results and comparison show that the proposed algorithm is compatible in finding the correct logical structure according to the initiate ratio of negative literal. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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19 pages, 3413 KiB  
Article
Multi-Objective Artificial Bee Colony Algorithm with Minimum Manhattan Distance for Passive Power Filter Optimization Problems
by Nien-Che Yang, Danish Mehmood and Kai-You Lai
Mathematics 2021, 9(24), 3187; https://doi.org/10.3390/math9243187 - 10 Dec 2021
Cited by 5 | Viewed by 2541
Abstract
Passive power filters (PPFs) are most effective in mitigating harmonic pollution from power systems; however, the design of PPFs involves several objectives, which makes them a complex multiple-objective optimization problem. This study proposes a method to achieve an optimal design of PPFs. We [...] Read more.
Passive power filters (PPFs) are most effective in mitigating harmonic pollution from power systems; however, the design of PPFs involves several objectives, which makes them a complex multiple-objective optimization problem. This study proposes a method to achieve an optimal design of PPFs. We have developed a new multi-objective optimization method based on an artificial bee colony (ABC) algorithm with a minimum Manhattan distance. Four different types of PPFs, namely, single-tuned, second-order damped, third-order damped, and C-type damped order filters, and their characteristics were considered in this study. A series of case studies have been presented to prove the efficiency and better performance of the proposed method over previous well-known algorithms. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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17 pages, 4699 KiB  
Article
Optimization of Fuzzy Logic Based Virtual Pilot for Wargaming
by Alexandr Stefek and Petr Frantis
Mathematics 2021, 9(24), 3169; https://doi.org/10.3390/math9243169 - 09 Dec 2021
Cited by 3 | Viewed by 1833
Abstract
This paper deals with the design of an autopilot based on a set of fuzzy controllers. The model of the aircraft that the autopilot controls is defined as a model with 6 degrees of freedom, where the inputs to this model are the [...] Read more.
This paper deals with the design of an autopilot based on a set of fuzzy controllers. The model of the aircraft that the autopilot controls is defined as a model with 6 degrees of freedom, where the inputs to this model are the settings of the engine thrust (DX), rudder rotation (Dl) and elevators (Dm and Dn). The fuzzy controllers are of the Mamdani type, where the set of parameters defining the controller allow the derivation of membership functions of the input variables and membership functions of the output variables. The parameters of fuzzy controllers are determined by the optimization process. For the purpose of optimization, a fitness function is defined, which derives the simulation parameters from its parameter (vector), and the simulation subsequently performed and evaluated determines whether it is a feasible solution in addition the value of this solution. By this optimization process, the sub-optimal solution is found and is then used to define the settings of the fuzzy controllers and, therefore, the autopilot. This paper contains a description of each step of the solution of the described problem, and with the help of the obtained results, it is determined that the presented procedure allows us to find an autopilot capable of controlling the defined model of the aircraft. In addition, there is a brief description regarding the misconceptions explored during the development of the experiment. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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40 pages, 10246 KiB  
Article
Blood Coagulation Algorithm: A Novel Bio-Inspired Meta-Heuristic Algorithm for Global Optimization
by Drishti Yadav
Mathematics 2021, 9(23), 3011; https://doi.org/10.3390/math9233011 - 24 Nov 2021
Cited by 13 | Viewed by 2570
Abstract
This paper introduces a novel population-based bio-inspired meta-heuristic optimization algorithm, called Blood Coagulation Algorithm (BCA). BCA derives inspiration from the process of blood coagulation in the human body. The underlying concepts and ideas behind the proposed algorithm are the cooperative behavior of thrombocytes [...] Read more.
This paper introduces a novel population-based bio-inspired meta-heuristic optimization algorithm, called Blood Coagulation Algorithm (BCA). BCA derives inspiration from the process of blood coagulation in the human body. The underlying concepts and ideas behind the proposed algorithm are the cooperative behavior of thrombocytes and their intelligent strategy of clot formation. These behaviors are modeled and utilized to underscore intensification and diversification in a given search space. A comparison with various state-of-the-art meta-heuristic algorithms over a test suite of 23 renowned benchmark functions reflects the efficiency of BCA. An extensive investigation is conducted to analyze the performance, convergence behavior and computational complexity of BCA. The comparative study and statistical test analysis demonstrate that BCA offers very competitive and statistically significant results compared to other eminent meta-heuristic algorithms. Experimental results also show the consistent performance of BCA in high dimensional search spaces. Furthermore, we demonstrate the applicability of BCA on real-world applications by solving several real-life engineering problems. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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41 pages, 1255 KiB  
Article
A Novel Learning-Based Binarization Scheme Selector for Swarm Algorithms Solving Combinatorial Problems
by José Lemus-Romani, Marcelo Becerra-Rozas, Broderick Crawford, Ricardo Soto, Felipe Cisternas-Caneo, Emanuel Vega, Mauricio Castillo, Diego Tapia, Gino Astorga, Wenceslao Palma, Carlos Castro and José García
Mathematics 2021, 9(22), 2887; https://doi.org/10.3390/math9222887 - 12 Nov 2021
Cited by 12 | Viewed by 1817
Abstract
Currently, industry is undergoing an exponential increase in binary-based combinatorial problems. In this regard, metaheuristics have been a common trend in the field in order to design approaches to successfully solve them. Thus, a well-known strategy includes the employment of continuous swarm-based algorithms [...] Read more.
Currently, industry is undergoing an exponential increase in binary-based combinatorial problems. In this regard, metaheuristics have been a common trend in the field in order to design approaches to successfully solve them. Thus, a well-known strategy includes the employment of continuous swarm-based algorithms transformed to perform in binary environments. In this work, we propose a hybrid approach that contains discrete smartly adapted population-based strategies to efficiently tackle binary-based problems. The proposed approach employs a reinforcement learning technique, known as SARSA (State–Action–Reward–State–Action), in order to utilize knowledge based on the run time. In order to test the viability and competitiveness of our proposal, we compare discrete state-of-the-art algorithms smartly assisted by SARSA. Finally, we illustrate interesting results where the proposed hybrid outperforms other approaches, thus, providing a novel option to tackle these types of problems in industry. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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19 pages, 371 KiB  
Article
A Binary Machine Learning Cuckoo Search Algorithm Improved by a Local Search Operator for the Set-Union Knapsack Problem
by José García, José Lemus-Romani, Francisco Altimiras, Broderick Crawford, Ricardo Soto, Marcelo Becerra-Rozas, Paola Moraga, Alex Paz Becerra, Alvaro Peña Fritz, Jose-Miguel Rubio and Gino Astorga
Mathematics 2021, 9(20), 2611; https://doi.org/10.3390/math9202611 - 16 Oct 2021
Cited by 9 | Viewed by 2394
Abstract
Optimization techniques, specially metaheuristics, are constantly refined in order to decrease execution times, increase the quality of solutions, and address larger target cases. Hybridizing techniques are one of these strategies that are particularly noteworthy due to the breadth of applications. In this article, [...] Read more.
Optimization techniques, specially metaheuristics, are constantly refined in order to decrease execution times, increase the quality of solutions, and address larger target cases. Hybridizing techniques are one of these strategies that are particularly noteworthy due to the breadth of applications. In this article, a hybrid algorithm is proposed that integrates the k-means algorithm to generate a binary version of the cuckoo search technique, and this is strengthened by a local search operator. The binary cuckoo search algorithm is applied to the NP-hard Set-Union Knapsack Problem. This problem has recently attracted great attention from the operational research community due to the breadth of its applications and the difficulty it presents in solving medium and large instances. Numerical experiments were conducted to gain insight into the contribution of the final results of the k-means technique and the local search operator. Furthermore, a comparison to state-of-the-art algorithms is made. The results demonstrate that the hybrid algorithm consistently produces superior results in the majority of the analyzed medium instances, and its performance is competitive, but degrades in large instances. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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17 pages, 3653 KiB  
Article
A Metaheuristic Algorithm for Flexible Energy Storage Management in Residential Electricity Distribution Grids
by Ovidiu Ivanov, Bogdan-Constantin Neagu, Gheorghe Grigoras, Florina Scarlatache and Mihai Gavrilas
Mathematics 2021, 9(19), 2375; https://doi.org/10.3390/math9192375 - 24 Sep 2021
Cited by 11 | Viewed by 1607
Abstract
The global climate change mitigation efforts have increased the efforts of national governments to incentivize local households in adopting PV panels for local electricity generation. Since PV generation is available during the daytime, at off-peak hours, the optimal management of such installations often [...] Read more.
The global climate change mitigation efforts have increased the efforts of national governments to incentivize local households in adopting PV panels for local electricity generation. Since PV generation is available during the daytime, at off-peak hours, the optimal management of such installations often considers local storage that can defer the use of local generation to a later time. The energy stored in batteries located in optimal places in the network can be used by the utility to improve the operation conditions in the network. This paper proposes a metaheuristic approach based on a genetic algorithm that considers three different scenarios of using energy storage for reducing the energy losses in the network. Two cases considers the battery placement and operation under the direct control of the network operator, with single and multiple bus and phase placement locations. Here, the aim was to maximize the benefit for the whole network. The third case considers selfish prosumer battery management, where the storage owner uses the batteries only for their own benefit. The optimal design of the genetic algorithm and of the solution encoding allows for a comparative study of the results, highlighting the important strengths and weaknesses of each scenario. A case study is performed in a real distribution system. Full article
(This article belongs to the Special Issue Metaheuristic Algorithms)
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