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Nadimi-Shahraki MH, Zamani H, Asghari Varzaneh Z, Mirjalili S. A Systematic Review of the Whale Optimization Algorithm: Theoretical Foundation, Improvements, and Hybridizations. Arch Comput Methods Eng 2023; 30:1-47. [PMID: 37359740 PMCID: PMC10220350 DOI: 10.1007/s11831-023-09928-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/05/2023] [Accepted: 04/19/2023] [Indexed: 06/28/2023]
Abstract
Despite the simplicity of the whale optimization algorithm (WOA) and its success in solving some optimization problems, it faces many issues. Thus, WOA has attracted scholars' attention, and researchers frequently prefer to employ and improve it to address real-world application optimization problems. As a result, many WOA variations have been developed, usually using two main approaches improvement and hybridization. However, no comprehensive study critically reviews and analyzes WOA and its variants to find effective techniques and algorithms and develop more successful variants. Therefore, in this paper, first, the WOA is critically analyzed, then the last 5 years' developments of WOA are systematically reviewed. To do this, a new adapted PRISMA methodology is introduced to select eligible papers, including three main stages: identification, evaluation, and reporting. The evaluation stage was improved using three screening steps and strict inclusion criteria to select a reasonable number of eligible papers. Ultimately, 59 improved WOA and 57 hybrid WOA variants published by reputable publishers, including Springer, Elsevier, and IEEE, were selected as eligible papers. Effective techniques for improving and successful algorithms for hybridizing eligible WOA variants are described. The eligible WOA are reviewed in continuous, binary, single-objective, and multi/many-objective categories. The distribution of eligible WOA variants regarding their publisher, journal, application, and authors' country was visualized. It is also concluded that most papers in this area lack a comprehensive comparison with previous WOA variants and are usually compared only with other algorithms. Finally, some future directions are suggested.
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Affiliation(s)
- Mohammad H. Nadimi-Shahraki
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, 8514143131 Iran
- Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, 8514143131 Iran
| | - Hoda Zamani
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, 8514143131 Iran
- Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, 8514143131 Iran
| | - Zahra Asghari Varzaneh
- Department of Computer Science, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
| | - Seyedali Mirjalili
- Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Brisbane, 4006 Australia
- University Research and Innovation Center, Obuda University, 1034 Budapest, Hungary
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Oliva D, Ortega-Sanchez N, Navarro MA, Ramos-Michel A, El-Abd M, Mousavirad SJ, Nadimi-Shahraki MH. Segmentation of thermographies from electronic systems by using the global-best brain storm optimization algorithm. Multimed Tools Appl 2023. [DOI: 10.1007/s11042-023-15059-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2022] [Revised: 10/11/2022] [Accepted: 02/27/2023] [Indexed: 09/02/2023]
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Nadimi-Shahraki MH, Taghian S, Zamani H, Mirjalili S, Elaziz MA. MMKE: Multi-trial vector-based monkey king evolution algorithm and its applications for engineering optimization problems. PLoS One 2023; 18:e0280006. [PMID: 36595557 PMCID: PMC9810208 DOI: 10.1371/journal.pone.0280006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2022] [Accepted: 12/19/2022] [Indexed: 01/04/2023] Open
Abstract
Monkey king evolution (MKE) is a population-based differential evolutionary algorithm in which the single evolution strategy and the control parameter affect the convergence and the balance between exploration and exploitation. Since evolution strategies have a considerable impact on the performance of algorithms, collaborating multiple strategies can significantly enhance the abilities of algorithms. This is our motivation to propose a multi-trial vector-based monkey king evolution algorithm named MMKE. It introduces novel best-history trial vector producer (BTVP) and random trial vector producer (RTVP) that can effectively collaborate with canonical MKE (MKE-TVP) using a multi-trial vector approach to tackle various real-world optimization problems with diverse challenges. It is expected that the proposed MMKE can improve the global search capability, strike a balance between exploration and exploitation, and prevent the original MKE algorithm from converging prematurely during the optimization process. The performance of the MMKE was assessed using CEC 2018 test functions, and the results were compared with eight metaheuristic algorithms. As a result of the experiments, it is demonstrated that the MMKE algorithm is capable of producing competitive and superior results in terms of accuracy and convergence rate in comparison to comparative algorithms. Additionally, the Friedman test was used to examine the gained experimental results statistically, proving that MMKE is significantly superior to comparative algorithms. Furthermore, four real-world engineering design problems and the optimal power flow (OPF) problem for the IEEE 30-bus system are optimized to demonstrate MMKE's real applicability. The results showed that MMKE can effectively handle the difficulties associated with engineering problems and is able to solve single and multi-objective OPF problems with better solutions than comparative algorithms.
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Affiliation(s)
- Mohammad H. Nadimi-Shahraki
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
- Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran
- Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Adelaide, Australia
- * E-mail: ,
| | - Shokooh Taghian
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
- Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran
| | - Hoda Zamani
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
- Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran
| | - Seyedali Mirjalili
- Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Adelaide, Australia
- Yonsei Frontier Lab, Yonsei University, Seoul, South Korea
| | - Mohamed Abd Elaziz
- Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt
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Nadimi-Shahraki MH, Zamani H, Mirjalili S. Enhanced whale optimization algorithm for medical feature selection: A COVID-19 case study. Comput Biol Med 2022; 148:105858. [PMID: 35868045 DOI: 10.1016/j.compbiomed.2022.105858] [Citation(s) in RCA: 38] [Impact Index Per Article: 19.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2022] [Revised: 06/15/2022] [Accepted: 07/08/2022] [Indexed: 01/01/2023]
Abstract
The whale optimization algorithm (WOA) is a prominent problem solver which is broadly applied to solve NP-hard problems such as feature selection. However, it and most of its variants suffer from low population diversity and poor search strategy. Introducing efficient strategies is highly demanded to mitigate these core drawbacks of WOA particularly for dealing with the feature selection problem. Therefore, this paper is devoted to proposing an enhanced whale optimization algorithm named E-WOA using a pooling mechanism and three effective search strategies named migrating, preferential selecting, and enriched encircling prey. The performance of E-WOA is evaluated and compared with well-known WOA variants to solve global optimization problems. The obtained results proved that the E-WOA outperforms WOA's variants. After E-WOA showed a sufficient performance, then, it was used to propose a binary E-WOA named BE-WOA to select effective features, particularly from medical datasets. The BE-WOA is validated using medical diseases datasets and compared with the latest high-performing optimization algorithms in terms of fitness, accuracy, sensitivity, precision, and number of features. Moreover, the BE-WOA is applied to detect coronavirus disease 2019 (COVID-19) disease. The experimental and statistical results prove the efficiency of the BE-WOA in searching the problem space and selecting the most effective features compared to comparative optimization algorithms.
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Affiliation(s)
- Mohammad H Nadimi-Shahraki
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran; Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran; Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Brisbane, Australia.
| | - Hoda Zamani
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran; Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran
| | - Seyedali Mirjalili
- Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Brisbane, Australia; Yonsei Frontier Lab, Yonsei University, Seoul, Republic of Korea
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Nadimi-Shahraki MH, Fatahi A, Zamani H, Mirjalili S, Abualigah L. An Improved Moth-Flame Optimization Algorithm with Adaptation Mechanism to Solve Numerical and Mechanical Engineering Problems. Entropy (Basel) 2021; 23:1637. [PMID: 34945943 PMCID: PMC8700729 DOI: 10.3390/e23121637] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/10/2021] [Revised: 11/18/2021] [Accepted: 11/25/2021] [Indexed: 11/16/2022]
Abstract
Moth-flame optimization (MFO) algorithm inspired by the transverse orientation of moths toward the light source is an effective approach to solve global optimization problems. However, the MFO algorithm suffers from issues such as premature convergence, low population diversity, local optima entrapment, and imbalance between exploration and exploitation. In this study, therefore, an improved moth-flame optimization (I-MFO) algorithm is proposed to cope with canonical MFO's issues by locating trapped moths in local optimum via defining memory for each moth. The trapped moths tend to escape from the local optima by taking advantage of the adapted wandering around search (AWAS) strategy. The efficiency of the proposed I-MFO is evaluated by CEC 2018 benchmark functions and compared against other well-known metaheuristic algorithms. Moreover, the obtained results are statistically analyzed by the Friedman test on 30, 50, and 100 dimensions. Finally, the ability of the I-MFO algorithm to find the best optimal solutions for mechanical engineering problems is evaluated with three problems from the latest test-suite CEC 2020. The experimental and statistical results demonstrate that the proposed I-MFO is significantly superior to the contender algorithms and it successfully upgrades the shortcomings of the canonical MFO.
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Affiliation(s)
- Mohammad H. Nadimi-Shahraki
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 8514143131, Iran; (A.F.); (H.Z.)
- Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 8514143131, Iran
| | - Ali Fatahi
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 8514143131, Iran; (A.F.); (H.Z.)
- Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 8514143131, Iran
| | - Hoda Zamani
- Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 8514143131, Iran; (A.F.); (H.Z.)
- Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 8514143131, Iran
| | - Seyedali Mirjalili
- Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Brisbane 4006, Australia
- Yonsei Frontier Lab, Yonsei University, Seoul 03722, Korea
| | - Laith Abualigah
- Faculty of Computer Sciences and Informatics, Amman Arab University, Amman 11953, Jordan;
- School of Computer Sciences, Universiti Sains Malaysia, Pulau Pinang 11800, Malaysia
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Nadimi-Shahraki MH, Taghian S, Mirjalili S, Faris H. MTDE: An effective multi-trial vector-based differential evolution algorithm and its applications for engineering design problems. Appl Soft Comput 2020. [DOI: 10.1016/j.asoc.2020.106761] [Citation(s) in RCA: 47] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Dehkordi MR, Seifzadeh H, Beydoun G, Nadimi-Shahraki MH. Success prediction of android applications in a novel repository using neural networks. COMPLEX INTELL SYST 2020. [DOI: 10.1007/s40747-020-00154-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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