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A hybrid-strategy-improved butterfly optimization algorithm applied to the node coverage problem of wireless sensor networks

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MATHEMATICAL BIOSCIENCES AND ENGINEERING 2022年第4期19卷 3928-3952页

作者： Ma, Donghui Duan, Qianqian Shanghai Univ Engn Sci Dept Elect & Elect Engn Shanghai 201620 Peoples R China

To increase the node coverage of wireless sensor networks (WSN) more effectively, in this paper, we propose a hybrid-strategy-improved butterfly optimization algorithm (H-BOA). First, we introduce Kent chaotic map to initialize the population to ensure a more uniform search space. Second, a new inertial weight modified from the Sigmoid function is introduced to balance the global and local search capacities. Third, we comprehensively use elite-fusion and elite-oriented local mutation strategies to raise the population diversity. Then, we introduce a perturbation based on the standard normal distribution to reduce the possibility of the algorithm falling into premature. Finally, the simulated annealing process is introduced to evaluate the solution's quality and improve the algorithm's ability, which is helpful to jump out of the local optimal value. Through numerous experiments of the international benchmark functions, the results show the performance of H-BOA has been significantly raised. We apply it to the WSN nodes coverage problem. The results show that H-BOA improves the WSN maximum coverage and it is far more than other optimization algorithms.

关键词： butterfly optimization algorithm wireless sensor networks hybrid strategy optimized coverage

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A balanced butterfly optimization algorithm for numerical optimization and feature selection

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SOFT COMPUTING 2022年第21期26卷 11505-11523页

作者： Long, Wen Jiao, Jianjun Wu, Tiebin Xu, Ming Cai, Shaohong Guizhou Univ Finance & Econ Key Lab Big Data Stat Anal Guiyang 550025 Peoples R China Guizhou Univ Finance & Econ Key Lab Econ Syst Simulat Guiyang 550025 Peoples R China Guizhou Univ Finance & Econ Sch Math & Stat Guiyang 550025 Peoples R China Hunan Univ Humanities Sci & Technol Sch Energy & Elect Engn Loudi 417000 Peoples R China

butterfly optimization algorithm (BOA) is a relatively novel optimization technique for solving function optimization as well as real-world applications. However, the paramount challenge in BOA is that it is prone to stagnation in local optima. The purpose of this study is to balance the exploration and exploitation abilities of BOA when two new strategies are introduced. The dynamic inertia weight based on Logistic model as the first strategy is introduced to modify the position updating equation. Another strategy is the opposition-based learning. A new variant of BOA called BBOA based on these two strategies is proposed. Ten widely used benchmark test functions and 30 complex benchmarks from CEC 2014 are selected to verify the effectiveness of BBOA. The used benchmark problems are composed of unimodal, multimodal, rotated, shifted, hybrid and composite functions. The experimental results and analysis show that the proposed BBOA has better exploration ability than the conventional BOA when solving different characteristics functions. Finally, BBOA is applied to solve three real-world engineering applications and sixteen feature selection problems. The results demonstrate that BBOA can outperform other competitors in terms of the accuracy of solution on constrained engineering design and feature selection problems.

关键词： butterfly optimization algorithm Inertia weight Logistic model Opposition-based learning Engineering design problem Feature selection

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An improved butterfly optimization algorithm for training the feed-forward artificial neural networks

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SOFT COMPUTING 2023年第7期27卷 3887-3905页

作者： Irmak, Busra Karakoyun, Murat Gulcu, Saban Necmettin Erbakan Univ Dept Comp Engn Konya Turkey

Artificial neural network (ANN) which is an information processing technique developed by modeling the nervous system of the human brain is one of the most powerful learning methods today. One of the factors that make ANN successful is its training algorithm. In this paper, an improved butterfly optimization algorithm (IBOA) based on the butterfly optimization algorithm was proposed for training the feed-forward artificial neural networks. The IBOA algorithm has the chaotic property which helps optimization algorithms to explore the search space more dynamically and globally. In the experiments, ten chaotic maps were used. The success of the IBOA algorithm was tested on 13 benchmark functions which are well known to those working on global optimization and are frequently used for testing and analysis of optimization algorithms. The Tent-mapped IBOA algorithm outperformed the other algorithms in most of the benchmark functions. Moreover, the success of the IBOA-MLP algorithm also has been tested on five classification datasets (xor, balloon, iris, breast cancer, and heart) and the IBOA-MLP algorithm was compared with four algorithms in the literature. According to the statistical performance metrics (sensitivity, specificity, precision, F1-score, and Friedman test), the IBOA-MLP outperformed the other algorithms and proved to be successful in training the feed-forward artificial neural networks.

关键词： Artificial neural networks butterfly optimization algorithm Chaos Multilayer perceptron Training artificial neural networks

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A Hybrid Feature Selection Method Using an Improved Binary butterfly optimization algorithm and Adaptive ß-Hill Climbing

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IEEE ACCESS 2023年 11卷 93511-93537页

作者： Tiwari, Anurag Thapar Inst Engn & Technol Patiala 147004 Punjab India

The butterfly optimization algorithm (BOA) is a recently proposed nature-inspired metaheuristic algorithm mimicking the food-foraging behavior of butterflies. Its abilities include simplicity, good convergence rate towards local optima, and avoiding the local optima stagnation problem to some extent. In earlier studies, the performance of Binary BOA (BBOA) is shown to be superior to various stateof-the-art methods in different optimization issues, such as search space reduction and solving classical engineering problems. Here, BBOA expands the original search space with all possibilities (Exploration) and seeks to determine the best one from all the produced solutions (Exploitation). Generally, the global performance of BBOA depends on the tradeoff between the Exploration and Exploitation phase and hence, produces quality solutions when a suitable tradeoff is maintained. This study introduces an improved and computationally effective variant of conventionalBBOAby improving the local search ability of the butterfly optimization algorithm. Initially, twelve binary variants were produced using three different transfer functions (S, U, V-shaped), and solution quality is evaluated in terms of respective fitness function scores. Next, we explored the local search ability of BOA by another recently developed optimization technique, namely, Adaptive ss-Hill Climbing, to compute quality solutions. This optimization process employed two stochastic operators: N -operator (Neighborhood operator) and ss -operator (Mutation operator) to generate improved offspring compared to parent solutions. This phase is iteratively implemented until the desired level of binary pattern with suitable classification accuracy is obtained. We validated the proposed approach on twenty datasets with eleven state-of-the-art feature selection algorithms. The overall results suggest that the proposed improvements increase the classification accuracy with fewer features on most datasets. In addition, th

关键词： butterfly optimization algorithm classification accuracy convergence rate feature selection local optima transfer function

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Enhanced butterfly optimization algorithm for reliability optimization problems

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JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2021年第7期12卷 7595-7619页

作者： Sharma, Tarun K. Shobhit Univ Gangoh Dept CSE Saharanpur India

In this study a recently introduced algorithm, based on foraging process of butterflies known as butterfly optimization algorithm (BOA) is explored and a modified variant is introduced. The framework of BOA is based on the fragrance emitted by the butterflies, which helps other butterflies in searching food as well as in identifying a mating partner. BOA performs both the local and global search while seeking for the global optimal solution for the problem. Despite this BOA sometime stuck in a local optima which results in a slow or poor convergence. This study embeds the bidirectional search in the structure of BOA. This helps to perform the local search in forward as well as backward direction. Greedy selection is performed, while selecting the direction. If the solution improves while traversing backward then backward traverse is adapted otherwise forward. The proposed variant is termed as bidirectional butterfly optimization algorithm (BBOA). This modification facilitate in accelerating the convergence rate of BOA, which is verified and validated by statistical and comparative results on a set of CEC2006 and CEC2014 benchmark problems. Non-parametric statistical tests are performed to analyze the results. Further the method is investigated to solve eight reliability optimization problems. Experimental results demonstrate the competitiveness of BBOA.

关键词： Bidirectional search butterfly optimization algorithm Reliability optimization problems Constrained optimization optimization

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A mixed sine cosine butterfly optimization algorithm for global optimization and its application

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CLUSTER COMPUTING-THE JOURNAL OF NETWORKS SOFTWARE TOOLS AND APPLICATIONS 2022年第6期25卷 4573-4600页

作者： Sharma, Sushmita Saha, Apu Kumar Roy, Susmita Mirjalili, Seyedali Nama, Sukanta Natl Inst Technol Agartala Dept Math Agartala 799046 Tripura India Torrens Univ Australia Ctr Artificial Intelligence Res & Optimisat Brisbane Qld 4006 Australia Yonsei Univ Yonsei Frontier Lab Seoul South Korea Gomati Dist Polytech Dept Sci & Humanities Udaipur 799013 Tripura India

This paper proposes a hybrid sine cosine butterfly optimization algorithm (m-SCBOA), in which a modified butterfly optimization algorithm is combined with sine cosine algorithm to achieve superior exploratory and exploitative search capabilities. The newly suggested m-SCBOA algorithm has been tested on 39 benchmark functions and compared with seven state-of-the-art algorithms. Moreover, it is tested with the CEC 2017 test suite, and the results are compared with seven more algorithms. Experimental results have demonstrated superior results of the proposed algorithm in nearly 75% of occasions on average whereas, similar results in nearly 20% of cases. Simulation results and convergence graphs show the supremacy of the m-SCBOA over the compared algorithms. The Friedman rank test validates that the m-SCBOA is statistically the best among the experiments. Additionally, four real-world engineering design problems and a priori multi-objective problem called parameter optimization of Al-4.5% Cu-TiC metal matrix composite are solved and the outcomes are compared to a wide range of algorithms. The results of these case studies establish the merits of m-SCBOA in solving challenging, real-world problems with unknown global optima.

关键词： optimization butterfly optimization algorithm Sine cosine algorithm Analytic hierarchy process

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EABOA: Enhanced adaptive butterfly optimization algorithm for numerical optimization and engineering design problems

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ALEXANDRIA ENGINEERING JOURNAL 2024年 87卷 543-573页

作者： He, Kai Zhang, Yong Wang, Yu-Kun Zhou, Rong-He Zhang, Hong-Zhi Univ Sci & Technol Liaoning Sch Elect & Informat Engn Anshan 114051 Peoples R China

The butterfly optimization algorithm (BOA) is a meta -heuristic algorithm that mimics foraging and mating behavior of butterflies. In order to alleviate the problems of slow convergence, local optimum and lack of population diversity of BOA, an enhanced adaptive butterfly optimization algorithm (EABOA) is proposed in this paper. First, a new adaptive fragrance model is designed, which provided a finer fragrance perception way and effectively enhanced the convergence speed and accuracy. Second, Levy flight with high -frequency short -step jumping and low -frequency long -step walking is adopted to help the algorithm jump out of the local optimum. Third, the dimension learning -based hunting is employed to enhance information exchange by creating neighbors for each butterfly, thus improving the balance between local and global search and maintaining population diversity. In addition, the Fitness -Distance -Constraint (FDC) method is introduced to enhance constraint handling in EABOA (named FDC-EABOA). The proposed EABOA is compared with 8 well-known algorithms and 8 BOA variants in CEC 2022 test suite and the results were statistically analyzed using Friedman, Friedman aligned rank, Wilcoxon signed rank, Quade rank and multiple comparisons, analysis of variance (ANOVA) and range analysis. Finally, EABOA and FDC-EABOA are applied to seven engineering problems (parameter identification of photovoltaic module model, speed reducer design, tension/compression spring design, pressure vessel design, gear train design, welded beam design, SOPWM for 3 -level inverters), and metrics such as Improvement Index (IF) and Mean Constraint Violation (MV) confirm that the proposed algorithms are satisfactory. Experimental results and statistical analysis show that the proposed algorithms outperform the comparison algorithms and demonstrate the strong potential for solving numerical optimization and engineering design problems.

关键词： butterfly optimization algorithm Adaptive fragrance Levy flight Dimension learning-based hunting Numerical optimization Engineering design problems

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A ship motion forecasting approach based on empirical mode decomposition method hybrid deep learning network and quantum butterfly optimization algorithm

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NONLINEAR DYNAMICS 2022年第3期107卷 2447-2467页

作者： Li, Ming-Wei Xu, Dong-Yang Geng, Jing Hong, Wei-Chiang Harbin Engn Univ Coll Shipbldg Engn Harbin 150001 Heilongjiang Peoples R China Asia Eastern Univ Sci & Technol Dept Informat Management 58Sec 2Sichuan Rd New Taipei 22064 Taiwan

Ship motion (SHM) forecasting value is an important parameter for ship navigation and operation. However, due to the coupling effect of wind, wave, and current, its time series has strong nonlinear characteristics, so it is a great challenge to obtain accurate forecasting results. Therefore, considering the strong nonlinear of SHM time series, firstly, this paper decomposes the original time series into multiple intrinsic mode functions (IMF) using empirical mode decomposition (EMD) technology and then establishes a hybrid deep learning network for each IMF based on convolutional neural network (CNN) and gated recurrent unit (GRU) according to the characteristics of SHM time series. On this basis, the EMD-CNN-GRU (ECG) hybrid forecasting model of SHM is constructed by integrating a component forecasting model. Secondly, considering the difficulty of hyper-parameters selection of ECG model, this paper improves the butterfly optimization algorithm (BOA) based on quantum theory, designs the quantum coding rules of butterfly spatial position, establishes the optimization process of butterfly algorithm based on quantum coding, and then proposes the quantum butterfly optimization algorithm (QBOA). Finally, a hybrid forecasting approach integrating ECG and QBOA is proposed, namely ECG & QBOA. To evaluate the feasibility and performance of the proposed approach. A prediction experiment was carried out with the SHM data of a real ship. The results indicate that, compared with the other comparison models selected in this paper, ECG-based models have significant higher forecasting accuracy (with MAPE values of 10.86% and 12.69% in two experiments, respectively, and with significant accuracy improvement of at least 10% than other compared models), and the QBOA has obtained more appropriate hyper-parameters combination of ECG model.

关键词： Ship motion forecasting Deep learning model Empirical mode decomposition Quantum computation butterfly optimization algorithm

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MPBOA-A novel hybrid butterfly optimization algorithm with symbiosis organisms search for global optimization and image segmentation

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MULTIMEDIA TOOLS AND APPLICATIONS 2021年第8期80卷 12035-12076页

作者： Sharma, Sushmita Saha, Apu Kumar Majumder, Arindam Nama, Sukanta Natl Inst Technol Agartala Dept Math Agartala 799046 India Natl Inst Technol Agartala Dept Mech Engn Agartala 799046 India

The conventional butterfly optimization algorithm (BOA) does not appropriately balance the exploration and exploitation characteristics of an algorithm to solve present-day challenging optimization problems. For the same, in this paper, a novel hybrid BOA (MPBOA, in short) is suggested, where the BOA is combined with mutualism and parasitism phases of the Symbiosis Organisms Search (SOS) algorithm to enhance the search behaviour (both global and local) of BOA. The mutualism phase is applied with the global phase of BOA, and the parasitism phase is added with the local phase of BOA to ensure a better trade-off between the global and local search of the proposed algorithm. A suit of twenty-five benchmark functions is employed to investigate its performance with several other state-of-the-art algorithms available in the literature. Also, to check its performance statistically, the Friedman rank test and t-test are carried out. The consistency of the proposed algorithm is tested with a boxplot diagram. Also, four real-world problems are solved to check the efficiency of the algorithm in solving industrial problems. Finally, the proposed MPBOA is utilized to obtain the optimal threshold in the multilevel thresholding problem of the segmentation of individual images. From the obtained results, it is found that the overall performance of the newly introduced MPBOA is satisfactory in terms of its search behaviour and convergence time to obtain global optima.

关键词： optimization techniques butterfly optimization algorithm Symbiosis organisms search Mutualism phase Parasitism phase MPBOA Benchmark function Image segmentation

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Unknown area exploration for robots with energy constraints using a modified butterfly optimization algorithm

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SOFT COMPUTING 2023年第7期27卷 3785-3804页

作者： Bendahmane, Amine Tlemsani, Redouane Univ Sci & Technol Oran Mohamed Boudiaf Comp Sci Dept Signal Image Parole SIMPA Lab BP 1505 Bir El Djir 31000 Oran Algeria

butterfly optimization algorithm (BOA) is a recent metaheuristic that has been used in several optimization problems. In this paper, we propose a new version of the algorithm (xBOA) based on the crossover operator and compare its results to the original BOA and 3 other variants recently introduced in the literature. We also proposed a framework for solving the unknown area exploration problem with energy constraints using metaheuristics in both single- and multi-robot scenarios. This framework allowed us to benchmark the performances of different metaheuristics for the robotics exploration problem. We conducted several experiments to validate this framework and used it to compare the effectiveness of xBOA with well-known metaheuristics used in the literature through 5 evaluation criteria. Although BOA and xBOA are not optimal in all these criteria, we found that BOA can be a good alternative to many metaheuristics in terms of the exploration time, while xBOA is more robust to local optima;has better fitness convergence;and achieves better exploration rates than the original BOA and its other variants.

关键词： Robotics Exploration butterfly optimization algorithm Crossover operator Metaheuristics Multi-robot systems

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