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In data acquisition scenario of edge computing, the optimization of UAV (Unmanned Aerial Vehicle) deployment is of great significance for making use of resources of UAV. We establish an optimization model of UAV cluster deployment in the edge data acquisition system. The model takes the height of UAV as the solving variable, which is more in line with the realistic characteristics. DEVIPSK-SA-FWA is proposed according to the characteristics of this model. The algorithm uses a novel coding mechanism, and uses K-Means to accelerate the convergence process of the algorithm. A variety of differential evolution mutation operators are used to form a self-adaptive strategy pool mechanism to carry out variable scale variation of population, which complete the global search well. Then fireworks algorithm searches the population locally after each round of global search. In our algorithm, global search and local search are well balanced and local optimal is effectively escaped. Finally, experimental results indicate that DEVIPSK-SA-FWA is capable of solving the model with good results, and the superiority of DEVIPSK-SA-FWA is verified through the Wilcoxon rank sum test method. In the best case, the proposed algorithm reduces energy consumption of edge data acquisition system by 32.87 %. [ABSTRACT FROM AUTHOR]

Real world problems in various domains demonstrate different characteristics of changes over time. This is why several researchers have been interested in dynamic optimisation for the last two decades. Since changes occur over time in a dynamic optimisation problem, the goal of a related algorithm becomes tracking the changing optima over time. Evolutionary algorithms and various swarm intelligence techniques have been adapted in the literature to solve dynamic optimisation problems. The Fireworks Algorithm (FWA) is a recently proposed swarm intelligence algorithm for global optimisation of complex static functions that simulates the explosion process of fireworks. Although a set of improvements over the conventional FWA are presented in the literature for the static optimisation problems, the most evident extension is the Enhanced Fireworks Algorithm (EFWA). In this paper, cost effective extensions of the EFWA are proposed for solving dynamic optimisation problems in continuous space. The performance evaluation of our EFWA-based algorithms is validated with the Moving Peaks Benchmark. Empirical studies on different benchmark instances clearly show the applicability of our extensions. Our EFWA-based extensions outperform the related work in terms of both quality of solution and computational cost for a large set of test instances of the benchmark. [ABSTRACT FROM AUTHOR]

With the increasing complexity and difficulty of numerical optimization problems in the real world, many efficient meta-heuristic optimization methods have been proposed to solve these problems. An improved Fireworks Algorithm (FWA) with elitism-based selection and optimal particle guidance strategies (EO-FWA) was proposed to address the limitations of the traditional FWA in terms of optimization accuracy and convergence speed, which not only improves the efficiency of the searching agent but also accelerates its convergence speed. In addition, by adopting boundary-based mapping rules, EO-FWA eliminates the randomness of traditional modulo operation mapping rules, which improves its stability and reliability. Twelve benchmark functions in CEC-BC-2022 are used to test the performance of EO-FWA, and the welded beam design problem is optimized at the end. The results show that EO-FWA exhibits stronger competitiveness than other algorithms in dealing with high-dimensional optimization problems and engineering optimization problem, and it can balance exploitation and exploration effectively so as to prevent the algorithm from falling into local optimal solutions. [ABSTRACT FROM AUTHOR]

As a novel intelligent algorithm, fireworks algorithm (FWA) is applied to deal with different types of optimization problems. Since FWA's search processes are relatively simple, it is inefficient. In this paper, a dynamic multi-swarm competitive fireworks algorithm (DMCFWA) is developed to enhance the search capability of FWA. Firstly, based on the scaling coefficient updated by utilizing the fitness value of the optimal firework, the dynamic explosion amplitude strategy is proposed to improve the search capability of the best firework. Secondly, utilizing the location information of the fireworks, an improved search method is designed to enhance the local search capability of firework swarms. Thirdly, a multi-swarm independent selection technique and a restart operation are adopted to boost its abilities of global exploration and local exploitation. Finally, to reduce the computational cost of FWA, a new initialization method is used and a new model for calculating the spark number is embedded in DMCFWA. By adopting these strategies, DMCFWA easily implements and does well in exploitation and exploration. CEC2017 test suite and four engineering constraint problems are used to demonstrate the performance of DMCFWA. Experimental results show that DMCFWA performs more effectively and stably than its competitors. [ABSTRACT FROM AUTHOR]

Objectives: Differential interferometric synthetic aperture radar (D-InSAR) has its own unique monitoring methods in acquiring surface deformation. In view of the difficulties in the application of D-InSAR technology in three-dimensional (3D) deformation monitoring of coal mine surface, this paper proposes a dynamic monitoring method based on fusion of single sight D-InSAR and Boltzmann-Knothe (BK) model. Methods: First, taking into account the characteristics of D-InSAR that it is difficult to obtain large gradient deformations, the Boltzmann function model with good boundary fit was selected, and BK model was constructed by the fusion of the Knothe time function. Second, due to the decoherence of the time-space baseline and the limitation of D-InSAR principle, it can often only obtain the short-term, one-dimensional deformation of the surface in line of sight (LOS). Therefore, based on the projection relationship between the 3D deformation and the LOS deformation, combined with the geological mining conditions of the target area, the fitness function with non-cumulative deformation was constructed. Finally, a dynamic monitoring method of surface 3D deformation of coal mine based on fusion of single sight D-InSAR and BK model was proposed by introducing the fireworks algorithm (FWA). Results and Conclusions: Simulation experiments show that the proposed method can reliably and accurately inverted all dynamic prediction parameters of mining subsidence, and the relative error of the solved parameters was between 0.11% and 7.51%. The subsidence and horizontal movement monitored by this proposed method were consistent with the real values, and the monitoring effect of the PIM-Knothe method was distorted. The results of the anti-error experiment show that under the influence of observation error or model parameter error, the overall effect of the solved parameters by the method in this paper was better, and the ability to resist errors was shown to a certain extent. The proposed method was applied to the 13121 working face of Gubei Mine in Huainan, and the surface 3D deformation of the coal mine from 2019-10-25 to 2019-12-12 was obtained. The conversion of short-term D-InSAR observation to 3D deformation dynamic monitoring based on the proposed method was realized, and the monitoring results were more consistent with the surface movement and deformation measured by the observation station. The reliability and scientificity of the dynamic prediction method for solving the surface 3D deformation of coal seam based on D-InSAR technology has been verified. [ABSTRACT FROM AUTHOR]

A mathematical model of heterogeneous task assignment problem based on mobile crowdsensing is established. This model considers the psychological and behavioral processes of participants, introduces environmental information, participants􀆳 health status, credibility, measurement time and other factors, and minimizes the total cost of task completion by finding the optimal task allocation scheme. The total task cost includes compensation cost, data loss cost and journey cost. To solve the model, a discrete fireworks algorithm with prediction information is proposed. This algorithm uses the integer coding, and the heuristic information of distance and matched-degree in the model are adopted to design the firework explosion operator. A grouping linear prediction strategy of explosion amplitude and an adaptive competition mechanism of mutation operator are proposed. Experimental results show that, compared with the existing algorithms, the proposed algorithm can find a better assignment scheme for the heterogeneous task assignment problem with mobile crowdsensing. [ABSTRACT FROM AUTHOR]

A constrained multi-objective optimization model for the low-carbon-cold chain distribution of vaccines is established to minimize the corporate transportation costs including the cost of carbon emissions and customer dissatisfaction, satisfying the constraints of the number of available vehicles, vehicle capacity and time window. A discrete two-archive-based multi-objective fireworks algorithm is proposed. The decoding method that can meet the constraints of the number of available vehicles and vehicle capacity is adopted. The partial mapping explosion operator is designed. Feasible solution archive and infeasible solution archive are set for coevolution. Feasibility search is performed on the infeasible solution archive. Experimental results show that, compared with the existing algorithms, the proposed algorithm can effectively obtain a group of Pareto non-dominated solutions with better convergence and distribution. [ABSTRACT FROM AUTHOR]

To solve the problems of low identification accuracy and complex identification methods in the Bouc-Wen model of the magnetorheological (MR) damper, a new parameter identification method using the fireworks algorithm (FWA) is proposed. According to the experimental results of the dynamic characteristics of the MR damper and the simulation data of the Bouc-Wen model, the FWA is used to identify the seven parameters of the Bouc-Wen model. On the basis of the relationship between the identification results and the command current, the current-controlled Bouc-Wen model (I-Bouc-Wen model) is constructed and compared with the experimental results under different sinusoidal excitation frequencies. Compared with the genetic algorithm (GA), differential evolution (DE) algorithm, and particle swarm optimization (PSO) algorithm, the FWA has the advantage of faster convergence, shorter calculation time, and higher stability in solving the parameter identification problem of the highly nonlinear hysteretic model. Under three harmonic excitations, the average calculation accuracies of the I-Bouc-Wen model reache 88.64 %, 90.45 %, and 81.28 %, respectively, and the dynamic characteristic curve of the model is in basic agreement with the experimental results. It can be used for the subsequent controller design and simulation research and lay a foundation for applying the parameterized model of the MR damper in vibration reduction control. [ABSTRACT FROM AUTHOR]

With the rapid advancements in processing and storage technology along with the popularity of the internet, computing capabilities have become more affordable, efficient, and widely accessible than ever before. This advancement has resulted in the emergence of a modern computing environment known as fog computing. Due to the latency-sensitiveness feature, computation of these services in fog computing is advantageous than cloud. Task scheduling is a significant issue in fog systems and substantially impacts resource utilization, task computation, and latency time. Many heuristic and meta-heuristic techniques have been applied to solve the scheduling issue. For the success of any meta-heuristic algorithm, an appropriate composition of exploration and exploitation of solution space is required to improve convergence and avoid local optima. To meet these requirements, a modified fireworks algorithm with the combination of opposition-based learning and differential evolution techniques is presented. Differential evolution operator has been utilized to avoid local optima and opposition-based learning technique has been applied for creating a diversified solution set of population. The proposed method works on the minimization of makespan and cost and improves resource utilization. The experiments have been carried out on a variety of workloads, and the findings have been compared with some recent popular metaheuristic techniques. The comparison has verified the importance of the proposed approach. [ABSTRACT FROM AUTHOR]

Simple firework algorithms get local optimal solutions easily and converge slowly, this paper adjusts the algorithm accordingly. Firstly, redefine the explosion operator by the aid of μ-law where the fitness value is converted to the degree of fitness, and the aberrance scope can be adjusted by the value of μ and the scaling factor. At the same time, the mapping strategy based on information exchange is used to enhance the search efficiency. In this paper, 12 general benchmark functions are used to compare the μFWA algorithm with other four algorithms. The experimental results show that the μFWA algorithm can obtain ideal results in the optimization of unimodal function and multimodal function which means that the algorithm can balance global search and local search well, and the convergence speed of the algorithm is improved obviously. [ABSTRACT FROM AUTHOR]

With the rapid increase in the functionality of IoT applications, the services provided by edge/IoT devices have surged in the recent past. Fog computing is gaining momentum as a contemporary computational framework for IoT-enabled smart applications that offers a latency sensitivity advantage over cloud computing. Effective task scheduling reduces application computation and latency durations while improves QoS. Many researchers have proposed a variety of heuristic and metaheuristic approaches for effective scheduling; however, there is still scope for improvement. The present work proposes a hybrid of heuristic and metaheuristic techniques for the scheduling of tasks. fireworks algorithm (FWA) is a metaheuristic algorithm, and Heterogeneous Earliest Finish Time (HEFT) is a heuristic algorithm. The bi-objective optimization approach is presented to minimize the makespan and cost factors. To compare the performance of the algorithm, the experiments have been conducted on distinct and independent scientific workflows. The results of exhaustive simulations have established the significance of the presented BH-FWA algorithm over other comparative approaches. To validate the relevance of the technique for fog computing networks, the metrics utilized for comparisons are makespan, cost, and throughput. [ABSTRACT FROM AUTHOR]

Prediction models are used to prevent and prepare for corresponding events according to various types of data generated in production. Aiming at the problems of lower predictive accuracy and slower convergent speed of the existing prediction models, a prediction model based on fireworks algorithm (FWA) and long short-term memory (LSTM) is proposed to predict time-related data. Firstly, we establish the interconnection structure model of the hidden layer nodes in the LSTM. Then, considering the diversity and concurrency of the group, we optimize the hyperparameters combination of LSTM. Finally, we improve FWA by adding three mutation operators (Gaussian mutation operator, Cauchy mutation operator, and discrete mutation operator). Based on the enhanced FWA, we achieve a better optimization effect by increasing the diversity of hyperparameters combination. The experimental results show that the performance of the proposed LSTM-enhanced FWA model has been significantly improved by comparing to the existing LSTM and LSTM-GS models. The mean absolute error (MAE) is reduced by 38.49% and 17.79%, respectively; the root mean squared error (RMSE) is reduced by 29.47% and 19.28%, respectively; and the mean absolute percentage error (MAPE) is reduced by 36.67% and 26.92%, respectively. MAE and MAPE represent the degree of deviation between the predicted value and actual value, and RMSE well reflects the precision. This means that the proposed LSTM-enhanced FWA model is better than existing LSTM and LSTM-GS models because all three types of error are reduced, meanwhile three kinds of error better reflect accuracy and precision of error. [ABSTRACT FROM AUTHOR]

In Wireless Sensor Networks (WSNs), where power consumption is a huge concern, the improvement of the network's lifetime is an area of constant study and innovation. The battery units of the sensor nodes cannot be recharged or replaced. Therefore, the need for energy efficiency in WSNs is ever-present. This paper proposes a Firework inspired Clustering Algorithm (FCA) to generate well defined and load-balanced clusters with the sensor nodes and gateways. The gateway works as cluster head (CH) for each cluster. The algorithm considers each cluster as a firework where the CH is the center of the firework and each sensor node is a 'spark' emitted by the firework. The goal of the FCA is to maximize the lifetime of the sparks which in turn will maximize the lifetime of the network. Simulations of the proposed algorithm are performed and compared with a few existing algorithms. The results show that the proposed algorithm outperforms under different evaluation metrics such as average energy consumed by sensor nodes vs number of rounds, number of active sensors vs number of rounds, first gateway die and half of the gateways die. [ABSTRACT FROM AUTHOR]

In this paper, a fireworks algorithm based Gerchberg–Saxton (GS) algorithm for the design of diffractive optical element is developed, named FW-GS algorithm, in which, the explosion mechanism of the fireworks algorithm is introduced to efficiently find the initial phase, thereby ensuring a superior phase solution for the subsequent GS algorithm. By employing this approach to shape a Gaussian beam into a square beam, the results illustrated the notable improvement of 16.10 % in RMSE and 3.29 % in diffractive efficiency when compared to the traditional GS algorithm, while exhibiting stable optimization performance. Furthermore, the proposed algorithm demonstrated adaptability to various shaping targets, with RMSE improved by about 16 % and diffractive efficiency improved by more than 3 % for shaping to circular, annular, and rectangular beams. • A fireworks algorithm based Gerchberg–Saxton (GS) algorithm for the design of beam shaping diffractive optical element is developed, named FW-GS algorithm. • Compared with the traditional GS algorithm, the FW-GS algorithm optimized RMSE and diffractive efficiency when shaping Gaussian beam into square beam, while exhibiting stable optimization performance. • The FW-GS algorithm demonstrated adaptability to various shaping targets. [ABSTRACT FROM AUTHOR]

In recent years, the fireworks algorithm (FWA) has attracted more and more attention due to its strong ability to solve optimization problems. However, the global performance of FWA is significantly affected by the explosion amplitude. In this paper, a dynamic fireworks algorithm with particle swarm optimization (DFWPSO) is developed to improve the global performance of FWA. In DFWPSO, a dynamic explosion amplitude mechanism based on the evolution speed of population, which is dynamically adjusted by evaluating the evolution speed of fitness in each iteration process, is designed to control the global and local searching information. Moreover, a new nonlinear minimal amplitude check strategy based on function decreasing is designed to obtain appropriate amplitude. Furthermore, a new firework updating mechanism based on particle swarm optimization (PSO) is implemented to accelerate the convergence of algorithm and cut down on computing resources. In addition, the selection operator of FWA is abandoned and all fireworks are updated by velocity and current location in each iteration process. To verify the performance of the proposed DFWPSO algorithm, three groups of the benchmark functions are used and tested for experiments. Compared with other variants of FWA and PSO variants, results show that the proposed algorithm performs competitively and effectively. [ABSTRACT FROM AUTHOR]

To solve the problems of the waste of resources caused by the small explosion amplitude (even close to 0) of the best firework in the conventional fireworks algorithm (FWA), and the relatively weak local search ability caused by the minimal explosion amplitude check method in the enhanced fireworks algorithm (EFWA), this paper proposes two improved strategies for FWA. First, based on the heuristic information of the distance between the best firework and other fireworks, an adaptive explosion amplitude strategy is proposed to search the local area accurately at the final phase of the FWA. Second, the highly random Lévy flight strategy is adopted instead of the Gaussian sparks strategy to generate mutation sparks in the EFWA to enhance the diversity of local search. Simulation results on 12 standard benchmark functions and their shifted functions indicate that the proposed algorithm improves the optimization precision and obtains better performance in high-dimensional complex optimization problems compared with the EFWA, the hybrid fireworks algorithm with differential evolution operator (FWADE), and the particle swarm optimization algorithm (PSO). [ABSTRACT FROM AUTHOR]

The fireworks algorithm, which is inspired from the phenomenon of fireworks explosion, is a special kind of swarm intelligence algorithm proposed in 2010. Since then, it has been attracting more and more research interest and has been widely employed in many real-world problems due to its unique search manner and high efficiency. In this article, we present a comprehensive review of its advances and applications. We begin with an introduction to the original fireworks algorithm. Then we review its algorithmic research work for single objective and multi-objective optimization problems. After that, we present the theoretical analyses of the fireworks algorithm. Finally, we give a brief overview of its applications and implementations. Hopefully, this article could provide a useful road map for researchers and practitioners who are interested in this algorithm and inspire new ideas for its further development. [ABSTRACT FROM AUTHOR]

For the characteristics of nonlinear and multi-phase in the batch process, a self-adaptive multi-phase batch process fault diagnosis method is proposed in this paper. Firstly, kernel entropy component analysis (KECA) method is used to achieve multi-phase partition adaptively, which makes the process data mapped into the high-dimensional feature space and then constructs the core entropy and the angular structure similarity. Then a multi-phase KECA failure monitoring model is developed by using the angular structure similarity as the statistic, which is based on the partitioned phases and the effective failure features by the KECA feature extraction method. A multi-phase batch process fault diagnosis method, which applies the multi-class support vector machines (MSVM) and fireworks algorithm (FWA), is proposed to recognize each sub-phase fault diagnosis automatically. The effectiveness and advantages of the proposed multi-phase fault diagnosis method are illustrated with a case study on a fed-batch penicillin fermentation process. [ABSTRACT FROM AUTHOR]

Unnatural control chart patterns (CCPs) can be associated with the quality problems of the production process. It is quite critical to detect and identify these patterns effectively based on process data. Various machine learning techniques to CCPs recognition have been studied on the process only suffer from basic CCPs of unnatural patterns. Practical production process data may be the combination of two or more basic patterns simultaneously in reality. This paper proposes a mixture CCPs recognition method based on fusion feature reduction (FFR) and fireworks algorithm-optimized multiclass support vector machine (MSVM). FFR algorithm consists of three main sub-networks: statistical and shape features, features fusion and kernel principal component analysis feature dimensionality reduction, which make the features more effective. In MSVM classifier algorithm, the kernel function parameters play a very significant role in mixture CCPs recognition accuracy. Therefore, fireworks algorithm is proposed to select the two-dimensional parameters of the classifier. The results of the proposed algorithm are benchmarked with popular genetic algorithm and particle swarm optimization methods. Simulation results demonstrate that the proposed method can gain the higher recognition accuracy and significantly reduce the running time. [ABSTRACT FROM AUTHOR]

As a new variant of swarm intelligence algorithm, fireworks algorithm (FWA) exhibits promising performance on a wide set of optimization problems, for which the fireworks algorithm has been concentrated on and investigated by researchers recently. This paper aims to improve the performance of the FWA by exploiting updating information of the core firework to guide the algorithm's searching process. Based on this mentality, this paper ameliorated the explosion strategy of core firework of dynamic fireworks algorithm (dynFWA). The proposed algorithm, named dynPgFWA in this paper, improved FWA from two aspects: amplifying the explosion amplitude on the direction on which core firework is updated, and making more sparks which are generated by core firework distributed on this direction to enhance the algorithm's searching ability on updating direction. A numerical experiment on CEC2015 and CEC2017 test suite was implemented to verify the performance of the proposed algorithm. Results of the experiment indicated that dynPgFWA outperformed the compared evolutionary algorithms in the quality of solutions. [ABSTRACT FROM AUTHOR]

Fireworks algorithm (FWA) is a swarm intelligent algorithm inspired by fireworks explosion. Based on the analysis of the shortcoming of Gaussian mutant operator, a fireworks algorithm based on differential mutant operator (DEFWA) is proposed, and a dynamic spark explosion strategy is adopted for optimal fireworks. Experiments on the benchmark function set show that the proposed DEFWA based algorithm outperforms several improved fireworks algorithms in the solution accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

To promote energy saving, high efficiency and quality production in mechanical manufacturing industry, a large number of studies have been conducted on parameters optimisation, especially for turning. However, most of the approaches have focused on single objective model and unidirectional turning (UDT). This paper presents a multi-objective parameter optimisation method for energy consumption, cutting time and surface roughness using new process of forward-and-reverse multidirectional turning (MDT). Firstly, the composition characteristics of cutting parameters for energy consumption, cutting time and surface roughness of MDT are analyzed to establish the corresponding models through nonlinear regression fitting, respectively. Then taking the minimum energy consumption, cutting time and surface roughness as the optimisation objectives, the improved fireworks algorithm can generate nearly 100 groups of optimal solutions. The most suitable processing parameters solution needs to be selected according to different machining requirements. In application scenarios, most relative errors of the models are within 10%. Comparing the machining performance of MDT and UDT under the same cutting parameters, the processing efficiency is increased by 25.97% and energy consumption is reduced by 12.38%, using the MDT. This study provides a multi-objective optimisation approach and models for MDT to reduce energy consumption, improve production efficiency and quality. [Display omitted] • Proposing a multi-objective optimisation method for multidirectional turning. • Establishing multi-objective optimisation models. • Addressing solutions based on improved fireworks algorithm considering energy, efficiency and quality. • Analyzing the practicability of the optimisation models and method in the case. [ABSTRACT FROM AUTHOR]

How to choose a chaotic sequence to construct a chaotic S-box is a key factor to determine the performance of the S-box. In this paper, a construction method for chaotic S-box based on fireworks algorithm is proposed, in which the fireworks algorithm is used to search for the optimal solution in the solution space of the Lorenz chaotic system. The performances of S-box are tested through the nonlinearity, differential uniformity, strict avalanche criterion, output bits independence criterion and bijectivity, and compared with the existing classical S-boxes based on the Lorenz chaotic system. The results indicate that the S-box in this paper has more excellent cryptographic characteristics, which will provide a new idea for the efficient generation of chaotic S-box. [ABSTRACT FROM AUTHOR]

Due to the low efficiency of cloud computing resource task scheduling and uneven resource allocation, this paper combined the improved fireworks algorithm and artificial bee colony algorithm into IFWA-ABC. Firstly, this paper described the cloud computing resource task scheduling. Secondly, it used the chaotic reverse learning and Cauchy distribution to optimize the FWA initialization. It optimized the radii of the core fireworks and the non-core fireworks respectively. It obtained the optimal individuals in the FWA by improving the ABC algorithm. Finally, it used the IFWA-ABC algorithm for cloud computing task scheduling. In the simulation experiment, IFWA-ABC has obvious advantages compared with FWA and ABC in terms of execution time, consumption cost and energy consumption index, which can effectively improve cloud computing resource allocation efficiency . [ABSTRACT FROM AUTHOR]

In order to pick out the service composition that meets the complex application requirements of users and the high comprehensive performance in the large-scale Web service environment, we propose an improved fireworks algorithm mixing chaotic mechanism and Levy mutation. Firstly, the chaos theory is used to generate the initial fireworks population and avoid uneven dispersion of individuals which can result in repeated local optimization. Then the Levy mutation operator is introduced to the search process to enhance the global search capability of the algorithm and avoid premature convergence. Finally, the elite selection strategy is adopted to reduce the time expenses of the algorithm in the process of selecting next generation fireworks population. Experimental results verify the optimization performance and stability of the algorithm. [ABSTRACT FROM AUTHOR]

BBO is one of the emerging meta-heuristic optimizer. It is based on sharing the features among islands. This study proposes a hybrid algorithm obtained by incorporating fireworks explosion concept of Fireworks Algorithm into biogeography-based optimization. The hybrid algorithm is named as fireworks-inspired biogeography-based optimization (FBBO). The key feature in the proposed FBBO algorithm is the hybridization of two different searching skills to improve solution quality. FBBO provides a better balance between solution diversification and intensification. The proposed algorithm is tested on CEC 2014 benchmark problems. Numerical experiments demonstrate its effectiveness and accuracy. [ABSTRACT FROM AUTHOR]

BBO is one of the emerging meta-heuristic optimizer. It is based on sharing the features among islands. This study proposes a hybrid algorithm obtained by incorporating fireworks explosion concept of Fireworks Algorithm into biogeography-based optimization. The hybrid algorithm is named as fireworks-inspired biogeography-based optimization (FBBO). The key feature in the proposed FBBO algorithm is the hybridization of two different searching skills to improve solution quality. FBBO provides a better balance between solution diversification and intensification. The proposed algorithm is tested on CEC 2014 benchmark problems. Numerical experiments demonstrate its effectiveness and accuracy. [ABSTRACT FROM AUTHOR]

The integration of energy internet (EI) and electric power system has a profound influence on electric power system planning. Therefore, this paper mainly resolves the EI-oriented multi-stage generation and transmission coordinated planning problem with a modified fireworks algorithm. Firstly, we combined with Stackelberg game theory and focused on subject game theory, system low carbon characteristic and renewable energy generation, a multi-stage generation and transmission coordinated planning model for electric power system is proposed. The model has a main objective function of maximizing the social welfare and two secondary objective functions of maximizing individual profits in the operation stage and maximizing overall profits of generation companies in the planning stage. Then, a modified fireworks algorithm (MFWA) is proposed with good expandability, convergence and adaptability to solve the problem. The MFWA is modified by introducing Gaussian Mutation to improve global search capability. The basic coding method and solution procedure of the MFWA are depicted. Finally, an improved IEEE-24 bus system is used to test the proposed planning method and MFWA. By comparing three scenarios and analysing results, we can verify the validity and feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Aiming at the problem of multi-agent path planning in dynamic environments，we propose an improved dynamic path planning method by combining the ant colony algorithm and fireworks algorithm. This method accelerates the iteration speed of the algorithm by adapting the pheromone intensity value and the pheromone reduction factor ? and uses the fireworks algorithm to solve the deadlock problem in the path planning process and avoid falling into a local optimum. In the process o£ multi-agent dynamic collision avoidance，corresponding collision avoidance strategies are made according to whether the motion trajectory between dynamic obstacles and multi-agent intersects，and the path collision function is used to solve the multi-agent frontal collision problem. Simulation results show that the proposed algorithm is superior to the traditional ant colony algorithm. It can effectively solve the collision problem in multi-agent path planning，and quickly find the optimal collision-free path. [ABSTRACT FROM AUTHOR]

Learning a classifier from imbalanced data is a challenging problem in Machine learning. A dataset is said to be imbalanced when the number of instances belonging to one class is much less than the number of instances belonging to the other class. Classifiers that proves efficient on standard data fail when the data is imbalanced as they are over trained by the majority class instances. Since class imbalance is a common characteristic of real-world data, the need for better classifiers becomes essential. This paper proposes a novel instance-based classification algorithm called Weighted Pattern Matching based Classification (PMC+) for classifying imbalanced data. PMC+ classifies unlabelled instances by computing the absolute difference between the feature values of the instances in the dataset and the unlabelled instance. PMC+ employs a simple classification procedure with weights and shows reasonably good performance. To improve the performance of PMC+, Fireworks based Feature and Weight Selection algorithm based on the idea of PMC+ has been proposed. PMC+ is evaluated on 44 binary imbalanced datasets and 15 multiclass imbalanced datasets. Although PMC+ does not employ a resampling or cost-sensitive method, experiments show that PMC+ is effective for classification of imbalanced data. The results of the experiments were validated using various non-parametric statistical tests. [ABSTRACT FROM AUTHOR]

Abstract As a relatively new swarm intelligence algorithm, the fireworks algorithm (FWA) has been applied to solve lots of real-world optimization problem. However, there are still some shortcomings in the FWA algorithms. The search equation of FWA is relatively simple. Since the search mechanism of FWA mainly relies on the explosion sparks, the exploration and exploitation abilities of the algorithm are limited. In order to improve the performance of FWA, a simplified hybrid fireworks algorithm (SHFWA) is proposed in this paper. In SHFWA, to enhance the exploitation ability, a modified search formula is designed for core firework swarm. To enhance the exploration ability, for each firework swarm, another way of generating sparks–harmony spark is designed. In the conventional fireworks algorithm, the calculation of the number of sparks generated by each firework and the calculation of amplitude of explosion for each firework are very complex. In SHFWA, a simplified method is employed to compute these two variables. By introducing these methods, SHFWA is easy to implement and is good at exploration and exploitation. The proposed algorithm is tested on 40 benchmark functions. The experimental results demonstrate that SHFWA performs effectively and competitively when compared with several reported algorithms. [ABSTRACT FROM AUTHOR]

Since community detection is an important tool for understanding the complex structure of social networks, an improved fireworks algorithm is proposed in this paper. The algorithm generates the initial population with the Affinity Propagation approach to have high initialization quality. The algorithm optimizes the modularity density as objective function by calculating the amplitude, the number of sparks and exploring the sparks. One firework is mutated twice, randomly and according to the label of its neighbors. Experiments on both real and synthetic networks show that the proposed algorithm achieves more accurate results in terms of modularity and normalized mutual information. [ABSTRACT FROM AUTHOR]

We present a new swarm intelligent optimization algorithm called popcorn algorithm. The popcorn algorithm learns from the advantage of the explosion mechanism of the fireworks algorithm and takes advantage of the individual particle’s fitness value in the optimization process to adjust the number of offspring dynamically. The better the individual particle’s fitness value is, the larger of the offspring population, and the more of the offspring searching in the vicinity of the individual particle. The algorithm adjusts the number of offspring dynamically to control the balance between local search and global search. In addition, it uses the memory mechanism of the particle swarm optimization algorithm as reference, and introduces the best individual particle and the best global particle to construct a new explosion radius, so that it can adjust the step size dynamically in the optimization process. The Gaussian perturbation is performed on the best global particle to increase the diversity of the population. Experimental results show that compared with other optimization algorithms such as the bat algorithm, standard particle swarm optimization algorithm and fireworks algorithm, the overall performance of the proposed popcorn algorithm is better. [ABSTRACT FROM AUTHOR]

Aiming at the high complexity, strong nonlinearity and strong time characteristics of intermittent process, this paper proposed a new method based on kernel entropy component analysis (KECA) to reduce the dimensionality of the KECA characteristic variables, and used the fireworks algorithm (FWA) to optimize the support vector machine (SVM) parameters for the intermittent process of division fault diagnosis method. Firstly, it carried out multi-directional kernel principal component analysis (MKPCA) for the on-line fault monitoring and output the fault data. Second, it used K-means method to divide the batch process into several sub-periods. It used KECA to reduce characteristic variable dimensionality according to the contribution rate of entropy to determine the number of selected elements and extracted feature information in depth. Finally, it constructed FWA optimized SVM parameter fault diagnosis model in each sub-period, put the reduced dimension processed fault data into their own sub-period FWA-SVM diagnostic model for fault diagnosis. Through a variety of comparative experimental study based on penicillin simulation data, it verifies the feasibility and effectiveness of this method. [ABSTRACT FROM AUTHOR]

The decision of intelligent minefield attacking tank forces is a complex multi-constraint and multi-objective nonlinear optimization problem. Aiming at the common defects of commonly used intelligent algorithms and combining with the characteristics of fireworks algorithm, this paper proposed an adaptive fireworks algorithm to deal with it. In this paper, we first established the mathematical model of this problem and transformed the model into an unconstrained single-objective extremum by using the external penalty function method. Furthermore, the adaptive fireworks algorithm is used to solve the model. In order to verify the superiority of adaptive fireworks algorithm to deal with this problem, experimental results show that the adaptive fireworks algorithm has faster convergence speed and shorter computation time than the other algorithms, and the results can intuitively describe the reasonable task allocation scheme of the complex situation, which provides a foundation for studying the force control. [ABSTRACT FROM AUTHOR]

Abstract In this paper, strength of recently introduced nature inspired heuristic computing technique named fireworks algorithms (FWA) and its variants are exploited in the field of system identification based on active noise control (ANC) systems. Residual error based fitness function is constructed for ANC system and optimization of parameter is carried out with the help of fireworks, enhance fireworks and adaptive fireworks algorithms. The design scheme is applied to number of scenarios of ANC system for different primary and secondary paths. The designed methodology is evaluated for three different noise interferences based on sinusoidal and random signals. The scheme validated by means of accuracy and convergence operators through the results of statistics based on ample number of independent trails. The comparative study of results is also made for three variants of FWA to establish their worth in terms of precision, stability and complexity measures. [ABSTRACT FROM AUTHOR]

In order to enable low-latency computation-intensive applications for mobile user equipments (UEs), computation offloading becomes critical necessary. We tackle the computation offloading problem in a mixed fog and cloud computing system, which is composed of an long term evolution-advanced (LTE-A) small-cell based fog node, a powerful cloud center, and a group of UEs. The optimization problem is formulated into a mixed-integer non-linear programming problem, and through a joint optimization of offloading decision making, computation resource allocation, resource block (RB) assignment, and power distribution, the maximum delay among all the UEs is minimized. Due to its mixed combinatory, we propose a low-complexity iterative suboptimal algorithm called BTFA based joint computation offloading and resource allocation algorithm (FAJORA) to solve it. In FAJORA, first, offloading decisions are obtained via binary tailored fireworks algorithm; then computation resources are allocated by bisection algorithm. Limited by the uplink LTE-A constraints, we allocate feasible RB patterns instead of RBs, and then distribute transmit power among the RBs of each pattern, where Lagrangian dual decomposition is adopted. Since one UE may be allocated with multiple feasible patterns, we propose a novel heuristic algorithm for each UE to extract the optimal pattern from its allocated patterns. Simulation results verify the convergence of the proposed iterative algorithms, and exhibit significant performance gains could be obtained compared with other algorithms. [ABSTRACT FROM AUTHOR]

In this paper we propose an enhanced fireworks algorithm for locating the critical slip surface giving the minimum safety factor in slope stability analysis, and we employ a concise algorithm of the Morgenstern and Price method to calculate the safety factor. To demonstrate its applicability and to illustrate the reliability and effectiveness of the proposed method, we present three benchmark examples with varying complex slopes. By comparing the minimum safety factor and the total number of iterations, the proposed method is proved to be highly competitive in terms of efficiency and accuracy. [ABSTRACT FROM AUTHOR]

As a new variant of swarm intelligence algorithm, fireworks algorithm (FWA) has significant performance on solving single objective problems, and has been applied broadly on a number of fields. To further improve its performance, a best firework updating information guided adaptive fireworks algorithm (PgAFWA) is proposed, in which the evolving process is guided by the direction from previous best firework to the current best firework from two aspects: amplifying the explosion amplitude on the direction that the best firework is updated, and making more sparks which are generated by the best firework distributed on this direction to further enhance the exploring ability on it. Numerical experiment on CEC2015 test suite was implemented to verify performance of the proposed algorithm. The experiment results indicated that the PgAFWA outperformed the compared algorithms in terms of both convergence speed and solving quality. [ABSTRACT FROM AUTHOR]

Abstract The fireworks algorithm, which is inspired by the explosion of fireworks, is a new swarm-based meta-heuristic algorithm for global optimization. This work proposes an improved fireworks optimization algorithm (IFWA) based on the enhanced fireworks algorithm (EFWA). Three aspects of improvement are presented after an analysis of the drawbacks of EFWA. These improvements are a new explosion scheme, GS-Gaussian explosion operator, and deep information exchange strategy. The proposed IFWA is tested on 23 benchmark function optimization problems and a real engineering problem, namely, optimal controller design for automotive active suspension. Optimization results prove that IFWA has competitive advantage compared with EFWA and other popular meta-heuristic algorithms and demonstrates the potential to solve real problems effectively. [ABSTRACT FROM AUTHOR]

In this article, an efficient Discrete CoFFWA method is proposed to deal with distribution network reconfigurations. It is useful for minimizing the active power network losses by switching on/off sectionalizing switches and shunt capacitors. The mathematical formulation may be expressed as one of combinatorial optimization problems. This article presents a discrete version of cooperative framework for fireworks algorithm (CoFFWA) of advanced metaheuristics to solve distribution network reconfigurations efficiently. It is one of the efficient Fireworks Algorithms that imitate the behavior of firework explosion. To improve the solution accuracy, CoFFWA makes use of new strategies such as the independent selection method and the crowdness‐avoiding cooperative strategy. The proposed method transforms CoFFWA into discrete one with multipoint mutation. The proposed method is successfully applied to the IEEE 69‐node and 119‐node distribution networks. [ABSTRACT FROM AUTHOR]

The fireworks algorithm (FWA), a newly introduced metaheuristic algorithm, has exhibited remarkable performance in a variety of optimization problems. However, FWA still has some shortcomings that need to be addressed. In the present study, an improved fireworks algorithm (IFWA) is proposed to mitigate the drawbacks of the original algorithm. In the IFWA, the possibility of interaction among different solutions during the optimization process is provided. Moreover, a strategy is considered to decrease the computational effort of the algorithm. The IFWA is used to deal with the discrete structural optimization problems of steel trusses and frames. The results demonstrate the efficiency of the proposed IFWA compared with other well-known metaheuristics in the literature, in terms of the optimum solutions and the convergence rate. [ABSTRACT FROM AUTHOR]

In order to solve the problem of the waste of resources due to the small explosion amplitude with best fitness(even close to 0) in the conventional fireworks algorithm(FWA) and the problem of the relatively weak local search ability owing to the novel minimal explosion amplitude check method used in enhanced fireworks algorithm(EFWA), this paper provided two strategies to improve the performance of the EFWA. Firstly, it introduced an adaptive dynamic explosion amplitude update strategy based on the heuristic information of distance between the current best firework and other fireworks to balance the global and local search of the EFWA. And then, it used Lévy flight strategy with strong randomness to generate explosion sparks to enhance the diversity of local search. The experimental results on twelve standard benchmark functions and their shifted functions indicate that the proposed algorithm outperforms EFWA in terms of optimization accuracy and convergence abilities on complex high-dimension optimization. [ABSTRACT FROM AUTHOR]

Fireworks algorithm (FWA) is one of the recently developed meta-heuristic techniques, which has shown potential to solve non-shifted optimization functions. However, several engineering optimization problems have shifted optima where the performance of the algorithm heavily degrades owing to the intrinsic limitations of FWA. This paper proposes an Improved FWA with Chaotic Sequence Operator (IFWA-CSO) to efficiently solve diverse engineering optimization problems having shifted optima. The proposed algorithm is validated on benchmark mathematical functions. The IFWA-CSO algorithm is then proposed to solve complex economic dispatch problem of power systems considering several practical constraints such as valve-point loading effect, ramp rate limits, prohibited operating zones, etc. The application results of the proposed method on 140 generator system are presented and compared with existing methods available in literature. [ABSTRACT FROM AUTHOR]

In order to reduce the damages of transmission line icing, an effective ice accretion forecasting can be used to guide the de‐icing work. The ice accretion on transmission lines varies slowly over time, and the icing data series is characteristic of timing sequence and autocorrelation. Time‐series analysis is suitable for analysing the similar data series, and fireworks algorithm (FA) is used to determine the autoregressive order and the moving average order of time‐series analysis. Then a short‐term ice accretion forecasting for transmission lines with modified time‐series analysis by FA is built. The ice accretion experiments were done in artificial icing laboratory. The results show that the modified time‐series analysis model by the FA has higher accuracy than another five models, whose relative errors are <1.3% and closer to the experimental data. Field applications also show that the modified time‐series analysis model has higher accuracy than the traditional one for the short‐term ice accretion forecasting, whose average error rates are separately 2.6723 and 5.2654%. [ABSTRACT FROM AUTHOR]

Wireless sensor networks have a wide range of applications, however, how to effectively deploy wireless sensor nodes, improve the utilization of nodes and network coverage, is still an urgent problem to be solved. Traditional wireless sensor network deployment method has high node redundancy rate and low network coverage. This paper proposed distributed firework algorithm for wireless sensor network coverage optimization. Combined the good results search ability of firework algorithm and the efficient speed of distributed computing, solved the model efficiently. Experimental results show that the algorithm is better than the general algorithm and the convergence rate is faster. [ABSTRACT FROM AUTHOR]

The wide use of renewable energy sources stimulates the implementation of microgrid (MG) systems. MG is an independent power system that consists of various distributed generations (DGs), storage devices, and loads. The optimization problems of MG have gained wide spread interest considering the economic and environmental operation management of the system. To address the multi-variable non-linear programming problem with multiple hybrid constraints, this paper proposes a novel hybrid multi-objective fireworks algorithm with gravitational search operator (MFAGSO). In the algorithm, the operator, as a new search mechanism, directs the sparks in the clustered region to exchange positional information with Pareto-optimal solutions at each iteration process for obtaining accurate results. The operation management of typical grid-connected MG, which comprises various DGs and storage battery, was optimized within 24 hours to evaluate the performance of the proposed algorithm. Considering operation cost and pollutant emission individually or simultaneously, 3 scenarios were involved in operation management for power market planning and practical considerations. The simulation results of the proposed algorithm were compared with those from other methods employed in previous literature and original fireworks algorithm. The results demonstrated the superior performance of the proposed method to solve operation management for optimizing problems of MG. [ABSTRACT FROM AUTHOR]

In the process of shock wave testing, the test signal is distorted by the limited bandwidth and low resonant frequency of pressure sensor. In order to solve this problem, a pressure sensor dynamic compensation method which is based on fireworks algorithm is presented. And the fitness function for the dynamic compensation is improved to increase the dynamic performance. The transfer function of dynamic compensation of pressure sensor is obtained from the test data of shock tube. The rise time of step pressure signal can be improved to 15.0 μs, and the overshoot is reduced to 8.27% after dynamic compensation by the proposed method. In the actual muzzle shock wave test, the dynamic compensation method can suppress the resonant frequency effectively, and make the pressure sensor test system achieve a better dynamic performance. [ABSTRACT FROM AUTHOR]

Purpose Parameter identification is an important issue in structural health monitoring and damage identification for concrete dams. The purpose of this paper is to introduce a novel adaptive fireworks algorithm (AFWA) into inverse analysis of parameter identification.Design/methodology/approach Swarm intelligence algorithms and finite element analysis are integrated to identify parameters of hydraulic structures. Three swarm intelligence algorithms: AFWA, standard particle swarm optimization (SPSO) and artificial bee colony algorithm (ABC) are adopted to make a comparative study. These algorithms are introduced briefly and then tested by four standard benchmark functions. Inverse analysis methods based on AFWA, SPSO and ABC are adopted to identify Young’s modulus of a concrete gravity dam and a concrete arch dam.Findings Numerical results show that swarm intelligence algorithms are powerful tools for parameter identification of concrete structures. The proposed AFWA-based inverse analysis algorithm for concrete dams is promising in terms of accuracy and efficiency.Originality/value Fireworks algorithm is applied for inverse analysis of hydraulic structures for the first time, and the problem of parameter selection in AFWA is studied. [ABSTRACT FROM AUTHOR]