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A Self-Adaption butterfly optimization algorithm for Numerical optimization Problems

IEEE ACCESS 2020年 8卷 88026-88041页

作者： Fan, Yuqi Shao, Junpeng Sun, Guitao Shao, Xuan Harbin Univ Sci & Technol Sch Mech & Power Engn Key Lab Adv Mfg & Intelligent Technol Minist Educ Harbin 150080 Peoples R China

For shortcomings of poor exploaration and parameter complexities of the butterfly optimization algorithm, an improved butterfly optimization algorithm based the self-adaption method (SABOA) was proposed to extremely enhance the searching accuracy and the iteration capability. SABOA has advantages of having fewer parameters, the simple algorithm structure, and the strong precision. First, a new fragrance coefficient was added to the basic butterfly optimization algorithm. Then, new iteration and updating strategies were introduced in global searching and local searching phases. Finally, this paper tested different optimization problems including low-high functions and constrained problems, and the obtained results were compared with other well-known algorithms, this paper also drew various mathematical statistics figures to comprehensively analyze searching performances of the proposed algorithms. The experimental results show that SABOA can get less number of function evaluations compared to other considered algorithms, which illustrates that SABOA has great searching balance, large exploration, and high iterative speed.

关键词： butterfly optimization algorithm global optimization constrained problem

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An improved butterfly optimization algorithm with chaos

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017年第1期32卷 1079-1088页

作者： Arora, Sankalap Singh, Satvir IK Gujral Punjab Tech Univ Kapurthala Punjab India Shaheed Bhagat Singh State Tech Campus Ferozepur Punjab India

butterfly optimization algorithm (BOA) is a new corner in the category of nature inspired metaheuristic algorithms, inspired from food foraging behavior of the butterflies. Similar to other metaheuristic algorithms, it encounters two probable problems;(1) entrapment in local optima and (2) slow convergence speed. Chaotic maps are one of the best methods to improve the performance of metaheuristic algorithms. In the present study, chaos is introduced into BOA which increases its performance in terms of both local optima avoidance and convergence speed. Ten chaotic maps are employed to enhance the performance of the BOA. The proposed chaotic BOAs are validated on unimodal and multimodal benchmark test functions as well as on engineering design problems. The results indicate that the chaotic maps are able to significantly boost the performance of BOA.

关键词： butterfly optimization algorithm chaotic map metaheuristic optimization

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Quantum Chaotic butterfly optimization algorithm With Ranking Strategy for Constrained optimization Problems

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IEEE ACCESS 2021年 9卷 114587-114608页

作者： Prasanthi, Achikkulath Shareef, Hussain Errouissi, Rachid Asna, Madathodika Wahyudie, Addy United Arab Emirates Univ Dept Elect Engn Al Ain U Arab Emirates United Arab Emirates Univ Emirates Ctr Mobil Res Al Ain U Arab Emirates

Nature-inspired metaheuristic optimization algorithms, e.g., the butterfly optimization algorithm (BOA), have become increasingly popular. The BOA, which adapts the food foraging and social behaviors of butterflies, involves randomly defined, algorithmic-dependent parameters that affect the exploration and exploitation strategies, which negatively influences the overall performance of the algorithm. To address this issue and improve performance, this paper proposes a modified BOA, i.e., the quantum chaos BOA (QCBOA), that relies on chaos theory and quantum computing techniques. Chaos mapping of unpredictable and divergent behavior helps tune critical parameters, and the quantum wave concept helps the representative butterflies in the algorithm explore the search space more effectively. The proposed QCBOA also implements a ranking strategy to maintain balance between the exploration and exploitation phases, which is lacking in conventional BOAs. To evaluate reliability and efficiency, the proposed QCBOA is tested against a well-utilized set of 20 benchmark functions and travelling salesman problem which belongs to the class of combinatorial optimization problems. Besides, the proposed method is also adopted to photovoltaic system parameter extraction to demonstrate its application to real-word problems. An extensive comparative study was also conducted to compare the performance of QCBOA with that of the conventional BOAs, fine-tuned particle swarm optimization (PSO) algorithm, differential evolution (DE), and genetic algorithm (GA). The results demonstrate that, chaos functions with the quantum wave concept yield better performance for most tested cases and comparative results in the rest of the cases. The speed of convergence also increased compared to the conventional BOAs. The proposed QCBOA is expected to provide better results in other real-word optimization problems and benchmark functions.

关键词： optimization Convergence Statistics Sociology Particle swarm optimization Heuristic algorithms Genetic algorithms butterfly optimization algorithm chaos mapping optimization quantum wave exploration exploitation

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Convergence analysis of butterfly optimization algorithm

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SOFT COMPUTING 2023年第11期27卷 7245-7257页

作者： Chakraborty, Prasanjit Sharma, Sushmita Saha, Apu Kumar Natl Inst Technol Agartala Dept Math Agartala 799046 Tripura India

Convergence analysis of any random search algorithm helps to verify whether and how quickly the algorithm guarantees convergence to the point of interest. butterfly optimization algorithm (BOA) is a popular population-based stochastic optimizer introduced by mimicking the foraging behaviors of butterflies in nature. In this paper, we have developed the Markov chain model of the BOA and analyzed the convergence behavior of the algorithm. The Markov chain model of the BOA is constituted where the population sequence generated by the algorithm is found to be a finite homogenous Markov chain and the defined population state set is found to be reducible. Convergence analysis of the algorithm is performed mathematically using the Markov chain model of the algorithm with the help of global convergence theorem which is based on a random search algorithm satisfying two subtle conditions. The butterfly algorithm has been found to satisfy the conditions for the global convergence theorem to enact, whereof it guarantees the global convergence of the BOA. We have also tried to show experimentally that the convergence of the algorithm does not always have considerable impact on rate of convergence as it is influenced by various other factors. Moreover, the convergence of BOA has been compared with several state-of-the-art algorithms experimentally. Further, the effects of the parameters, namely sensory modality and power exponent on the performance of BOA, have been studied.

关键词： Metaheuristic butterfly optimization algorithm Markov chain Global convergence

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Short-term wind power prediction using a novel model based on butterfly optimization algorithm-variational mode decomposition-long short-term memory

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APPLIED ENERGY 2024年 366卷

作者： Wang, Yonggang Zhao, Kaixing Hao, Yue Yao, Yilin Shenyang Agr Univ Sch Informat & Elect Engn Shenyang 110866 Liaoning Peoples R China

The precise forecasting of wind power output is crucial for the integration of large-scale renewable energy generation into the power grid. It plays a vital role in ensuring safe and stable operation of power grid, diminishing fuel consumption, and minimizing environmental impacts. This research presents a machine learning prediction model that integrates intelligent optimization algorithms and data decomposition techniques for short-term wind power output forecasting. The initial phase of this research develops a prediction model utilizing variational mode decomposition and long short-term memory networks. To mitigate the randomness and uncertainty of wind energy, and improve prediction accuracy, the butterfly optimization algorithm is introduced to optimize the parameters of variational mode decomposition and long short-term memory networks. Several in-depth case studies are carried out on the actual wind power generation dataset in mainland China to confirm the feasibility and effectiveness of the proposed hybrid model. Experimental results demonstrate that the proposed model outperforms the compared model in terms of prediction accuracy across different seasons, showing good practicality and generalizability.

关键词： Short-term wind power prediction butterfly optimization algorithm Long short-term memory network Variational mode decomposition

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Identifying top-k influential nodes in social networks: a discrete hybrid optimizer by integrating butterfly optimization algorithm with differential evolution

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JOURNAL OF SUPERCOMPUTING 2024年第13期80卷 19624-19668页

作者： Tang, Jianxin Zhu, Hongyu Han, Lihong Song, Shihui Lanzhou Univ Technol Sch Comp & Commun Lanzhou 730050 Peoples R China Lanzhou Univ Finance & Econ Sch Stat Lanzhou 730020 Peoples R China

The most challenge of influence maximization (IM) is to locate a finite set of influencers while maximizing the influence dissemination in a social network. Due to the increasingly widespread and complex application scenarios of IM problem, how to solve the problem effectively remains as a prominent research hotspot. However, most of the existing IM algorithms tend to prioritize either lightweight computational time or solution accuracy, which are hard to be acquired simultaneously. Therefore, considering the trade-off between efficiency and effectiveness, a novel discrete hybrid optimizer by integrating butterfly optimization algorithm (BOA) with differential evolution (DE), named DBOA-DE, is proposed in this paper. An adaptive probability is designed to guide the two operations in the hybrid optimizer, where BOA shows excellent exploratory characteristics by simulating the behavior of butterfly swarms, while DE performs local exploitation through mutation and crossover procedures. Furthermore, in expectation of enhancing the solution accuracy, an improved local search policy is conceived to avoid DBOA-DE from falling into local optimum. Extensive experiments on six real-world social networks show that DBOA-DE outperforms baseline algorithms on influence propagation while maintaining acceptable efficiency, which validate the promising effectiveness and efficiency of the proposed algorithm for IM problems.

关键词： Social networks Influence maximization Discrete hybrid optimizer butterfly optimization algorithm Differential evolution

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Improved butterfly optimization algorithm applied to prediction of combined cycle power plant

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MATHEMATICS AND COMPUTERS IN SIMULATION 2023年 204卷 337-353页

作者： Wang, Xiao Sun, Xiao-Xue Chu, Shu-Chuan Watada, Junzo Pan, Jeng-Shyang Shandong Univ Sci & Technol Coll Comp Sci & Engn Qingdao Peoples R China Waseda Univ Grad Sch Informat Prod & Syst Kitakyushu Japan Chaoyang Univ Technol Dept Informat Management Taichung Taiwan

The electricity output is worth monitoring because of the rising electricity demand. Ambient temperature, air pressure, relative humidity, and exhaust pressure all impact the production output of a combined cycle power plant. This study proposes the BOAPPE algorithm, which combines the butterfly optimization algorithm (BOA) with the phasmatodea population evolution algorithm (PPE) to estimate power output better and reduce excessive cost waste. When used in conjunction with a support vector regression (SVR) model, such as BOAPPE-SVR, for estimating the power output of a power plant under basic load, it not only enhances the model's prediction accuracy but also successfully avoids the problem of the model entering local optimization too soon. The parallel strategy of the BOAPPE algorithm in this research improves convergence speed, while the random walk strategy prevents the model from sliding into local optimization. The results reveal that the model paired with the BOAPPE algorithm is more accurate and better than the other models in this research when comparing the performance of the parameters such as mean square error, relative error, and correlation coefficient. As a result, the BOAPPE-SVR model is a viable model for power load forecasting. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： butterfly optimization algorithm Phasmatodea population evolution algorithm Support vector regression Combined cycle power plant

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butterfly optimization algorithm based methodology for enhancing the shaded photovoltaic array extracted power via reconfiguration process

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ENERGY CONVERSION AND MANAGEMENT 2020年 220卷 113115-113115页

作者： Fathy, Ahmed Jouf Univ Fac Engn Dept Elect Engn Sakaka Saudi Arabia Zagazig Univ Elect Power & Machine Dept Fac Engn Zagazig Egypt

The operation of the photovoltaic (PV) array under partial shadow conditions (PSCs) has negative effects on the extracted global maximum power (GMP) which is decreased due to the presence of power loss. Rearranging the shaded panels in the array is essential to enhance the GMP and diminish the effect of shadow, this process is known as PV array reconfiguration. Most of reported approaches did not guarantee the GMP and applicable to specific dimension of the PV array. Therefore, this paper proposes a novel methodology incorporated recent metaheuristic approach of butterfly optimization algorithm (BOA) to reconfigure the shaded PV array optimally and extract the GMP. BOA is selected due to its multiple advantages like ease of implementation, simple in construction, requirement of less controlling parameters, and effectiveness in solving real-time problems. Five shadow patterns are studied and the obtained results via BOA are compared to series-parallel total-cross-tied (SP-TCT), novel structure (NS) puzzle pattern, shade dispersion with NS and grey wolf optimizer (GWO) based arrangements. The proposed BOA succeeded in achieving maximum GMP enhancement of 27.43% compared to SP-TCT configuration. Moreover, Wilcoxon test is investigated for the results of the proposed BOA and GWO. Furthermore, the statistical parameters of both approaches are calculated. The obtained results confirmed the availability of the proposed BOA in reconfiguring the PV array operated under PSCs optimally.

关键词： Reconfiguration of PV array butterfly optimization algorithm Global maximum power

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Reverse guidance butterfly optimization algorithm integrated with information cross-sharing

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021年第2期41卷 3463-3484页

作者： Luo, Jun Tian, Qin Xu, Meng Chongqing Univ Key Lab Optoelect Technol & Syst Minist Educ Chongqing Peoples R China Chongqing Univ Sci & Technol Sch Mech & Power Engn Chongqing Peoples R China

Aiming at the disadvantages of slow convergence and the premature phenomenon of the butterfly optimization algorithm (BOA), this paper proposes a modified BOA (MBOA) called reverse guidance butterfly optimization algorithm integrated with information cross-sharing. First, the quasi-opposition concept is employed in the global search phase that lacks local exploitation capabilities to broaden the search space. Second, the neighborhood search weight factor is added in the local search stage to balance exploration and exploitation. Finally, the information cross-sharing mechanism is introduced to enhance the ability of the algorithm to jump out of the local optima. The proposed MBOA is tested in fourteen benchmark functions and three constrained engineering problems. The series of experimental results indicate that MBOA shows better performance in terms of convergence speed, convergence accuracy, stability as well as robustness.

关键词： butterfly optimization algorithm benchmark function information cross-sharing neighborhood search weight factor reverse guidance

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Optimal Cooperative Spectrum Sensing Based on butterfly optimization algorithm

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Computers, Materials & Continua 2022年第4期71卷 369-387页

作者： Noor Gul Saeed Ahmed Atif Elahi Su Min Kim Junsu Kim Department of Electronics Engineering Korea Polytechnic University15073Gyeonggi-doKorea Department of Electronics University of Peshawar25120Pakistan Department of Electrical Engineering Mirpur University of Science of TechnologyAJ&K10250Pakistan Department of Electrical Engineering International Islamic UniversityIslamabad 44000Pakistan

Since the introduction of the Internet of Things(IoT),several researchers have been exploring its productivity to utilize and organize the spectrum *** radio(CR)technology is characterized as the best aspirant for wireless communications to augment IoT *** the CR networks,secondary users(SUs)opportunistically get access to the primary users(PUs)spectrum through spectrum *** multipath issues in the wireless channel can fluster the sensing ability of the individual ***,several cooperative SUs are engaged in cooperative spectrum sensing(CSS)to ensure reliable sensing *** CSS,security is still a major concern for the researchers to safeguard the fusion center(FC)against abnormal sensing reports initiated by the malicious users(MUs).In this paper,butterfly optimization algorithm(BOA)-based soft decision method is proposed to find an optimized weighting coefficient vector correlated to the SUs sensing *** coefficient vector is utilized in the soft decision rule at the FC before making any global *** effectiveness of the proposed scheme is compared for a variety of parameters with existing schemes through simulation *** results confirmed the supremacy of the proposed BOA scheme in both the normal SUs’environment and when lower and higher SNRs information is carried by the different categories of MUs.

关键词： Internet of Things cognitive radio network butterfly optimization algorithm particle swarm optimization malicious users genetic algorithm

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