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Mashru N, Tejani GG, Patel P, Khishe M. Optimal truss design with MOHO: A multi-objective optimization perspective. PLoS One 2024; 19:e0308474. [PMID: 39159240 PMCID: PMC11332947 DOI: 10.1371/journal.pone.0308474] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2024] [Accepted: 07/22/2024] [Indexed: 08/21/2024] Open
Abstract
This research article presents the Multi-Objective Hippopotamus Optimizer (MOHO), a unique approach that excels in tackling complex structural optimization problems. The Hippopotamus Optimizer (HO) is a novel approach in meta-heuristic methodology that draws inspiration from the natural behaviour of hippos. The HO is built upon a trinary-phase model that incorporates mathematical representations of crucial aspects of Hippo's behaviour, including their movements in aquatic environments, defense mechanisms against predators, and avoidance strategies. This conceptual framework forms the basis for developing the multi-objective (MO) variant MOHO, which was applied to optimize five well-known truss structures. Balancing safety precautions and size constraints concerning stresses on individual sections and constituent parts, these problems also involved competing objectives, such as reducing the weight of the structure and the maximum nodal displacement. The findings of six popular optimization methods were used to compare the results. Four industry-standard performance measures were used for this comparison and qualitative examination of the finest Pareto-front plots generated by each algorithm. The average values obtained by the Friedman rank test and comparison analysis unequivocally showed that MOHO outperformed other methods in resolving significant structure optimization problems quickly. In addition to finding and preserving more Pareto-optimal sets, the recommended algorithm produced excellent convergence and variance in the objective and decision fields. MOHO demonstrated its potential for navigating competing objectives through diversity analysis. Additionally, the swarm plots effectively visualize MOHO's solution distribution of MOHO across iterations, highlighting its superior convergence behaviour. Consequently, MOHO exhibits promise as a valuable method for tackling complex multi-objective structure optimization issues.
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Affiliation(s)
- Nikunj Mashru
- Department of Mechanical Engineering, Faculty of Engineering and Technology, Marwadi University, Rajkot, Gujarat, India
| | | | - Pinank Patel
- Department of Mechanical Engineering, Faculty of Engineering and Technology, Marwadi University, Rajkot, Gujarat, India
| | - Mohammad Khishe
- Department of Electrical Engineering, Imam Khomeini Naval Science University of Nowshahr, Nowshahr, Iran
- Innovation Center for Artificial Intelligence Applications, Yuan Ze University, Taoyuan City, Taiwan
- Applied Science Research Center, Applied Science Private University, Amman, Jordan
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2
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Li J, Sun S, Xie L, Zhu C, He D. Multi-kernel support vector regression with improved moth-flame optimization algorithm for software effort estimation. Sci Rep 2024; 14:16892. [PMID: 39043713 PMCID: PMC11266436 DOI: 10.1038/s41598-024-67197-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2024] [Accepted: 07/09/2024] [Indexed: 07/25/2024] Open
Abstract
In this paper, a novel Moth-Flame Optimization (MFO) algorithm, namely MFO algorithm enhanced by Multiple Improvement Strategies (MISMFO) is proposed for solving parameter optimization in Multi-Kernel Support Vector Regressor (MKSVR), and the MISMFO-MKSVR model is further employed to deal with the software effort estimation problems. In MISMFO, the logistic chaotic mapping is applied to increase initial population diversity, while the mutation and flame number phased reduction mechanisms are carried out to improve the search efficiency, as well the adaptive weight adjustment mechanism is used to accelerate convergence and balance exploration and exploitation. The MISMFO model is verified on fifteen benchmark functions and CEC 2020 test set. The results show that the MISMFO has advantages over other meta-heuristic algorithms and MFO variants in terms of convergence speed and accuracy. Additionally, the MISMFO-MKSVR model is tested by simulations on five software effort datasets and the results demonstrate that the proposed model has better performance in software effort estimation problem. The Matlab code of MISMFO can be found at https://github.com/loadstar1997/MISMFO .
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Affiliation(s)
- Jing Li
- Department of Management Engineering and Equipment Economics, Naval University of Engineering, Wuhan, 430033, China
| | - Shengxiang Sun
- Department of Management Engineering and Equipment Economics, Naval University of Engineering, Wuhan, 430033, China
| | - Li Xie
- Department of Management Engineering and Equipment Economics, Naval University of Engineering, Wuhan, 430033, China.
| | - Chen Zhu
- Department of Management Engineering and Equipment Economics, Naval University of Engineering, Wuhan, 430033, China
| | - Dubo He
- Department of Management Engineering and Equipment Economics, Naval University of Engineering, Wuhan, 430033, China
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3
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Amiri MH, Mehrabi Hashjin N, Montazeri M, Mirjalili S, Khodadadi N. Hippopotamus optimization algorithm: a novel nature-inspired optimization algorithm. Sci Rep 2024; 14:5032. [PMID: 38424229 PMCID: PMC10904400 DOI: 10.1038/s41598-024-54910-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2023] [Accepted: 02/18/2024] [Indexed: 03/02/2024] Open
Abstract
The novelty of this article lies in introducing a novel stochastic technique named the Hippopotamus Optimization (HO) algorithm. The HO is conceived by drawing inspiration from the inherent behaviors observed in hippopotamuses, showcasing an innovative approach in metaheuristic methodology. The HO is conceptually defined using a trinary-phase model that incorporates their position updating in rivers or ponds, defensive strategies against predators, and evasion methods, which are mathematically formulated. It attained the top rank in 115 out of 161 benchmark functions in finding optimal value, encompassing unimodal and high-dimensional multimodal functions, fixed-dimensional multimodal functions, as well as the CEC 2019 test suite and CEC 2014 test suite dimensions of 10, 30, 50, and 100 and Zigzag Pattern benchmark functions, this suggests that the HO demonstrates a noteworthy proficiency in both exploitation and exploration. Moreover, it effectively balances exploration and exploitation, supporting the search process. In light of the results from addressing four distinct engineering design challenges, the HO has effectively achieved the most efficient resolution while concurrently upholding adherence to the designated constraints. The performance evaluation of the HO algorithm encompasses various aspects, including a comparison with WOA, GWO, SSA, PSO, SCA, FA, GOA, TLBO, MFO, and IWO recognized as the most extensively researched metaheuristics, AOA as recently developed algorithms, and CMA-ES as high-performance optimizers acknowledged for their success in the IEEE CEC competition. According to the statistical post hoc analysis, the HO algorithm is determined to be significantly superior to the investigated algorithms. The source codes of the HO algorithm are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/160088-hippopotamus-optimization-algorithm-ho .
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Affiliation(s)
| | | | - Mohsen Montazeri
- Faculty of Electrical Engineering, Shahid Beheshti University, Tehran, Iran
| | - Seyedali Mirjalili
- Centre for Artificial Intelligence Research and Optimization, Torrens University Australia, Adelaide, Australia
- Research and Innovation Center, Obuda University, Budapest, 1034, Hungary
| | - Nima Khodadadi
- Department of Civil and Architectural Engineering, University of Miami, Coral Gables, FL, USA
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4
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Rustamaji HC, Kusuma WA, Nurdiati S, Batubara I. Community detection with Greedy Modularity disassembly strategy. Sci Rep 2024; 14:4694. [PMID: 38409331 PMCID: PMC10897298 DOI: 10.1038/s41598-024-55190-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2023] [Accepted: 02/21/2024] [Indexed: 02/28/2024] Open
Abstract
Community detection recognizes groups of densely connected nodes across networks, one of the fundamental procedures in network analysis. This research boosts the standard but locally optimized Greedy Modularity algorithm for community detection. We introduce innovative exploration techniques that include a variety of node and community disassembly strategies. These strategies include methods like non-triad creating, feeble, random as well as inadequate embeddedness for nodes, as well as low internal edge density, low triad participation ratio, weak, low conductance as well as random tactics for communities. We present a methodology that showcases the improvement in modularity across the wide variety of real-world and synthetic networks over the standard approaches. A detailed comparison against other well-known community detection algorithms further illustrates the better performance of our improved method. This study not only optimizes the process of community detection but also broadens the scope for a more nuanced and effective network analysis that may pave the way for more insights as to the dynamism and structures of its functioning by effectively addressing and overcoming the limitations that are inherently attached with the existing community detection algorithms.
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Affiliation(s)
- Heru Cahya Rustamaji
- Department of Computer Science, Faculty of Mathematics and Natural Sciences, IPB University, Bogor, Indonesia
- Department of Informatics, Faculty of Industrial Technology, UPN Veteran Yogyakarta, Yogyakarta, Indonesia
| | - Wisnu Ananta Kusuma
- Department of Computer Science, Faculty of Mathematics and Natural Sciences, IPB University, Bogor, Indonesia.
- Tropical Biopharmaca Research Center, IPB University, Bogor, Indonesia.
| | - Sri Nurdiati
- Department of Mathematics, Faculty of Mathematics and Natural Sciences, IPB University, Bogor, Indonesia
| | - Irmanida Batubara
- Department of Chemistry, Faculty of Mathematics and Natural Sciences, IPB University, Bogor, Indonesia
- Tropical Biopharmaca Research Center, IPB University, Bogor, Indonesia
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5
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Premalatha M, Jayasudha M, Čep R, Priyadarshini J, Kalita K, Chatterjee P. A comparative evaluation of nature-inspired algorithms for feature selection problems. Heliyon 2024; 10:e23571. [PMID: 38187288 PMCID: PMC10770462 DOI: 10.1016/j.heliyon.2023.e23571] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2023] [Revised: 12/02/2023] [Accepted: 12/06/2023] [Indexed: 01/09/2024] Open
Abstract
Feature selection is a critical component of machine learning and data mining which addresses challenges like irrelevance, noise, redundancy in large-scale data etc., which often result in the curse of dimensionality. This study employs a K-nearest neighbour wrapper to implement feature selection using six nature-inspired algorithms, derived from human behaviour and mammal-inspired techniques. Evaluated on six real-world datasets, the study aims to compare the performance of these algorithms in terms of accuracy, feature count, fitness, convergence and computational cost. The findings underscore the efficacy of the Human Learning Optimization, Poor and Rich Optimization and Grey Wolf Optimizer algorithms across multiple performance metrics. For instance, for mean fitness, Human Learning Optimization outperforms the others, followed by Poor and Rich Optimization and Harmony Search. The study suggests the potential of human-inspired algorithms, particularly Poor and Rich Optimization, in robust feature selection without compromising classification accuracy.
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Affiliation(s)
- Mariappan Premalatha
- School of Computer Science & Engineering, Vellore Institute of Technology, Chennai 600 127, India
| | - Murugan Jayasudha
- School of Computer Science & Engineering, Vellore Institute of Technology, Chennai 600 127, India
| | - Robert Čep
- Department of Machining, Assembly and Engineering Metrology, Faculty of Mechanical Engineering, VSB-Technical University of Ostrava, 17. Listopadu 2172/15, 708 00 Ostrava, Czech Republic
| | - Jayaraju Priyadarshini
- School of Computer Science & Engineering, Vellore Institute of Technology, Chennai 600 127, India
| | - Kanak Kalita
- University Centre for Research & Development, Chandigarh University, Mohali, 140413, India
| | - Prasenjit Chatterjee
- Chief Research Fellow, Faculty of Civil Engineering, Institute of Sustainable Construction, Laboratory of Smart Building Systems, Vilnius Gediminas Technical University, Vilnius, Lithuania
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Houssein EH, Oliva D, Samee NA, Mahmoud NF, Emam MM. Liver Cancer Algorithm: A novel bio-inspired optimizer. Comput Biol Med 2023; 165:107389. [PMID: 37678138 DOI: 10.1016/j.compbiomed.2023.107389] [Citation(s) in RCA: 32] [Impact Index Per Article: 32.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Revised: 08/04/2023] [Accepted: 08/25/2023] [Indexed: 09/09/2023]
Abstract
This paper introduces a new bio-inspired optimization algorithm named the Liver Cancer Algorithm (LCA), which mimics the liver tumor growth and takeover process. It uses an evolutionary search approach that simulates the behavior of liver tumors when taking over the liver organ. The tumor's ability to replicate and spread to other organs inspires the algorithm. LCA algorithm is developed using genetic operators and a Random Opposition-Based Learning (ROBL) strategy to efficiently balance local and global searches and explore the search space. The algorithm's efficiency is tested on the IEEE Congress of Evolutionary Computation in 2020 (CEC'2020) benchmark functions and compared to seven widely used metaheuristic algorithms, including Genetic Algorithm (GA), particle swarm optimization (PSO), Differential Evolution (DE), Adaptive Guided Differential Evolution Algorithm (AGDE), Improved Multi-Operator Differential Evolution (IMODE), Harris Hawks Optimization (HHO), Runge-Kutta Optimization Algorithm (RUN), weIghted meaN oF vectOrs (INFO), and Coronavirus Herd Immunity Optimizer (CHIO). The statistical results of the convergence curve, boxplot, parameter space, and qualitative metrics show that the LCA algorithm performs competitively compared to well-known algorithms. Moreover, the versatility of the LCA algorithm extends beyond mathematical benchmark problems. It was also successfully applied to tackle the feature selection problem and optimize the support vector machine for various biomedical data classifications, resulting in the creation of the LCA-SVM model. The LCA-SVM model was evaluated in a total of twelve datasets, among which the MonoAmine Oxidase (MAO) dataset stood out, showing the highest performance compared to the other datasets. In particular, the LCA-SVM model achieved an impressive accuracy of 98.704% on the MAO dataset. This outstanding result demonstrates the efficacy and potential of the LCA-SVM approach in handling complex datasets and producing highly accurate predictions. The experimental results indicate that the LCA algorithm surpasses other methods to solve mathematical benchmark problems and feature selection.
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Affiliation(s)
- Essam H Houssein
- Faculty of Computers and Information, Minia University, Minia, Egypt.
| | - Diego Oliva
- Depto. Innovación Basada en la Información y el Conocimiento, Universidad de Guadalajara, CUCEI, Guadalajara, Jal, Mexico.
| | - Nagwan Abdel Samee
- Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
| | - Noha F Mahmoud
- Rehabilitation Sciences Department, Health and Rehabilitation Sciences College, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
| | - Marwa M Emam
- Faculty of Computers and Information, Minia University, Minia, Egypt.
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Emam MM, Samee NA, Jamjoom MM, Houssein EH. Optimized deep learning architecture for brain tumor classification using improved Hunger Games Search Algorithm. Comput Biol Med 2023; 160:106966. [PMID: 37141655 DOI: 10.1016/j.compbiomed.2023.106966] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2023] [Revised: 04/05/2023] [Accepted: 04/19/2023] [Indexed: 05/06/2023]
Abstract
One of the worst diseases is a brain tumor, which is defined by abnormal development of synapses in the brain. Early detection of brain tumors is essential for improving prognosis, and classifying tumors is a vital step in the disease's treatment. Different classification strategies using deep learning have been presented for the diagnosis of brain tumors. However, several challenges exist, such as the need for a competent specialist in classifying brain cancers by deep learning models and the problem of building the most precise deep learning model for categorizing brain tumors. We propose an evolved and highly efficient model based on deep learning and improved metaheuristic algorithms to address these challenges. Specifically, we develop an optimized residual learning architecture for classifying multiple brain tumors and propose an improved variant of the Hunger Games Search algorithm (I-HGS) based on combining two enhancing strategies: Local Escaping Operator (LEO) and Brownian motion. These two strategies balance solution diversity and convergence speed, boosting the optimization performance and staying away from the local optima. First, we have evaluated the I-HGS algorithm on the IEEE Congress on Evolutionary Computation held in 2020 (CEC'2020) test functions, demonstrating that I-HGS outperformed the basic HGS and other popular algorithms regarding statistical convergence, and various measures. The suggested model is then applied to the optimization of the hyperparameters of the Residual Network 50 (ResNet50) model (I-HGS-ResNet50) for brain cancer identification, proving its overall efficacy. We utilize several publicly available, gold-standard datasets of brain MRI images. The proposed I-HGS-ResNet50 model is compared with other existing studies as well as with other deep learning architectures, including Visual Geometry Group 16-layer (VGG16), MobileNet, and Densely Connected Convolutional Network 201 (DenseNet201). The experiments demonstrated that the proposed I-HGS-ResNet50 model surpasses the previous studies and other well-known deep learning models. I-HGS-ResNet50 acquired an accuracy of 99.89%, 99.72%, and 99.88% for the three datasets. These results efficiently prove the potential of the proposed I-HGS-ResNet50 model for accurate brain tumor classification.
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Affiliation(s)
- Marwa M Emam
- Faculty of Computers and Information, Minia University, Minia, Egypt.
| | - Nagwan Abdel Samee
- Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.
| | - Mona M Jamjoom
- Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia.
| | - Essam H Houssein
- Faculty of Computers and Information, Minia University, Minia, Egypt.
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Rajwar K, Deep K, Das S. An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges. Artif Intell Rev 2023; 56:1-71. [PMID: 37362893 PMCID: PMC10103682 DOI: 10.1007/s10462-023-10470-y] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2023]
Abstract
As the world moves towards industrialization, optimization problems become more challenging to solve in a reasonable time. More than 500 new metaheuristic algorithms (MAs) have been developed to date, with over 350 of them appearing in the last decade. The literature has grown significantly in recent years and should be thoroughly reviewed. In this study, approximately 540 MAs are tracked, and statistical information is also provided. Due to the proliferation of MAs in recent years, the issue of substantial similarities between algorithms with different names has become widespread. This raises an essential question: can an optimization technique be called 'novel' if its search properties are modified or almost equal to existing methods? Many recent MAs are said to be based on 'novel ideas', so they are discussed. Furthermore, this study categorizes MAs based on the number of control parameters, which is a new taxonomy in the field. MAs have been extensively employed in various fields as powerful optimization tools, and some of their real-world applications are demonstrated. A few limitations and open challenges have been identified, which may lead to a new direction for MAs in the future. Although researchers have reported many excellent results in several research papers, review articles, and monographs during the last decade, many unexplored places are still waiting to be discovered. This study will assist newcomers in understanding some of the major domains of metaheuristics and their real-world applications. We anticipate this resource will also be useful to our research community.
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Affiliation(s)
- Kanchan Rajwar
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667 India
| | - Kusum Deep
- Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667 India
| | - Swagatam Das
- Electronics and Communication Sciences Unit, Indian Statistical Institute, Kolkata, West Bengal 700108 India
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Jati GK, Kuwanto G, Hashmi T, Widjaja H. Discrete komodo algorithm for traveling salesman problem. Appl Soft Comput 2023. [DOI: 10.1016/j.asoc.2023.110219] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/22/2023]
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10
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Emam MM, Houssein EH, Ghoniem RM. A modified reptile search algorithm for global optimization and image segmentation: Case study brain MRI images. Comput Biol Med 2023; 152:106404. [PMID: 36521356 DOI: 10.1016/j.compbiomed.2022.106404] [Citation(s) in RCA: 20] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2022] [Revised: 10/29/2022] [Accepted: 12/03/2022] [Indexed: 12/12/2022]
Abstract
In this paper, we proposed an enhanced reptile search algorithm (RSA) for global optimization and selected optimal thresholding values for multilevel image segmentation. RSA is a recent metaheuristic optimization algorithm depending on the hunting behavior of crocodiles. RSA is inclined to inadequate diversity, local optima, and unbalanced exploitation abilities as other metaheuristic algorithms. The RUNge Kutta optimizer (RUN) is a novel metaheuristic algorithm that has demonstrated effectiveness in solving real-world optimization problems. The enhanced solution quality (ESQ) in RUN utilizes the thus-far best solution to promote the quality of solutions, improve the convergence speed, and effectively balance the exploration and exploitation steps. Also, the Scale factor (SF) has a randomized adaptation nature, which helps RUN in further improving the exploration and exploitation steps. This parameter ensures a smooth transition from exploration to exploitation. In order to mitigate the drawbacks of the RSA algorithm, this paper proposed a modified RSA (mRSA), which combines the RSA algorithm with the RUN. The ESQ mechanism and the scale factor boost the original RSA's performance, enhance convergence speed, bypass local optimum, and enhance the balance between exploitation and exploration. The validity of mRSA was verified using two experimental sequences. First, we applied mRSA to CEC'2020 benchmark functions of various types and dimensions, showing that mRSA has more robust search capabilities than the original RSA and popular counterpart algorithms concerning statistical, convergence, and diversity measurements. The second experiment evaluated mRSA for a real-world application to solve magnetic resonance imaging (MRI) brain image segmentation. Overall experimental results confirm that the mRSA has a strong optimization ability. Also, mRSA method is a more successful multilevel thresholding segmentation and outperforms comparison methods according to different performance measures.
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Affiliation(s)
- Marwa M Emam
- Faculty of Computers and Information, Minia University, Minia, Egypt.
| | - Essam H Houssein
- Faculty of Computers and Information, Minia University, Minia, Egypt.
| | - Rania M Ghoniem
- Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia; Department of Computer, Mansoura University, Mansoura, Egypt.
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11
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A critical problem in benchmarking and analysis of evolutionary computation methods. NAT MACH INTELL 2022. [DOI: 10.1038/s42256-022-00579-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
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12
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Circle Search Algorithm: A Geometry-Based Metaheuristic Optimization Algorithm. MATHEMATICS 2022. [DOI: 10.3390/math10101626] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
This paper presents a novel metaheuristic optimization algorithm inspired by the geometrical features of circles, called the circle search algorithm (CSA). The circle is the most well-known geometric object, with various features including diameter, center, perimeter, and tangent lines. The ratio between the radius and the tangent line segment is the orthogonal function of the angle opposite to the orthogonal radius. This angle plays an important role in the exploration and exploitation behavior of the CSA. To evaluate the robustness of the CSA in comparison to other algorithms, many independent experiments employing 23 famous functions and 3 real engineering problems were carried out. The statistical results revealed that the CSA succeeded in achieving the minimum fitness values for 21 out of the tested 23 functions, and the p-value was less than 0.05. The results evidence that the CSA converged to the minimum results faster than the comparative algorithms. Furthermore, high-dimensional functions were used to assess the CSA’s robustness, with statistical results revealing that the CSA is robust to high-dimensional problems. As a result, the proposed CSA is a promising algorithm that can be used to easily handle a wide range of optimization problems.
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