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In addressing the optimal formation obstacle avoidance control problem for Autonomous Underwater Vehicles (AUVs) in environments with unknown and moving obstacles, this paper employs the Modified Fireworks Algorithm based on a Loser Elimination Mechanism (MLoTFWA) and constructs a Distributed Model Predictive Control (DMPC) framework to achieve obstacle avoidance for AUV formations. Initially, a prediction model is established, followed by feedback compensation to mitigate the effects of unknown perturbations. An appropriate fitness function is then formulated, and enhancements such as the loser elimination rule are introduced to optimize the fireworks algorithm. Additionally, the concept of an adaptive DMPC prediction window is proposed to conserve resources. The local and global stability of the DMPC formation control framework is theoretically proven. Simulations verify that the control system based on the DMPC framework ensures safe obstacle avoidance for the formation, maintains formation consistency, and achieves the shortest and smoothest path. The improved fireworks algorithm demonstrates superior performance compared with the original fireworks algorithm and other optimization algorithms. In testing, the improved fireworks algorithm exhibits better adaptability, higher average fitness, and best fitness, along with a significantly faster convergence speed. Compared with the ordinary fireworks algorithm, the convergence speed is reduced by 30%. [ABSTRACT FROM AUTHOR]

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Background and Objectives: This paper explores the realm of optimization by synergistically integrating two unique metaheuristic algorithms: The Wild Horse Optimizer (WHO) and the Fireworks Algorithm (FWA). WHO, inspired by the behaviors of wild horses, demonstrates proficiency in global exploration, while FWA emulates the dynamic behavior of fireworks, thereby enhancing local exploitation. The goal is to harness the complementary strengths of these algorithms, achieving a harmonious balance between exploration and exploitation to enhance overall optimization performance. Methods: The study introduces a novel hybrid metaheuristic algorithm, WHOFWA, detailing its design and implementation. Emphasis is placed on the algorithm's ability to balance exploration and exploitation. Extensive experiments, featuring a diverse set of benchmark optimization problems, including general test functions and those from CEC 2005, CEC 2019, and 2022, assess WHOFWA's effectiveness. Comparative analyses involve WHO, FWA, and other metaheuristic algorithms such as Reptile Search Algorithm (RSA), Prairie Dog Optimization (PDO), Fick’s Law Optimization (FLA), and Ladybug Beetle Optimization (LBO). Results: According to the Friedman and Wilcoxon signed-rank tests, for all selected test functions, WHOFWA outperforms WHO, FWA, RSA, PDO, FLA, and LBO by 42%, 55%, 74%, 71%, 48%, and 52%, respectively. Finally, the results derived from addressing real-world constrained optimization problems using the proposed algorithm demonstrate its superior performance when compared to several well-regarded algorithms documented in the literature. Conclusion: In conclusion, WHOFWA, the hybrid metaheuristic algorithm uniting WHO and FWA, emerges as a powerful optimization tool. Its unique ability to balance exploration and exploitation yields superior performance compared to WHO, FWA, and benchmark algorithms. The study underscores WHOFWA's potential in tackling complex optimization problems, making a valuable contribution to the realm of metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

Wind power has unpredictable, intermittent traits due to meteorological conditions and environmental factors. Large-scale grid integration of wind energy will undoubtedly challenge system stability. This study developed a fireworks algorithmbackpropagation (FWA-BP) neural network model to forecast wind power using wind speed, direction, and power as model inputs. Optimization of the BP network weights and thresholds occurred through the fireworks algorithm. Compared to a standard BP network, the FWA-BP model yielded improved prediction accuracy seen through a lower mean squared error. This implies that the approach introduced in this paper significantly enhances global search capabilities, prediction accuracy, and speed. It contributes to enhancing the reliability of the power system, optimizing resource allocation, and improving wind power scheduling, with substantial potential and economic significance. [ABSTRACT FROM AUTHOR]

The current cold chain logistics management and distribution routes generally face problems such as environmental pollution and high costs. Therefore, the study proposed an improved fireworks-artificial bee colony for optimizing delivery paths. Firstly, the artificial bee colony was improved by using neighborhood search. Secondly, for the optimal solution, the fireworks explosion operator was used for the final result search. The benchmark function validation showed that the proposed algorithm performed better than other algorithms in solving optimal value, average value, and standard deviation. In the simulation analysis of a fresh enterprise in China, the total delivery cost was reduced by an average of 3.30% and 4.93% compared to other algorithms, considering carbon emission and not considering it, respectively. This proposed algorithm had more advantages in reducing quality loss, pollutant emissions, and CE. Therefore, this improved fireworks-artificial bee colony can effectively reduce the economic costs and environmental pollution of cold chain logistics distribution routes. This ensures economic benefits while considering social benefits, achieving the optimal path planning for logistics distribution. [ABSTRACT FROM AUTHOR]

The research on complex workshop scheduling methods has important academic significance and has wide applications in industrial manufacturing. Aiming at the job shop scheduling problem, a hybrid algorithm based on comprehensive search mechanisms (HACSM) is proposed to optimize the maximum completion time. HACSM combines three search methods with different optimization scales, including fireworks algorithm (FW), extended Akers graphical method (LS1+_AKERS_EXT), and tabu search algorithm (TS). FW realizes global search through information interaction and resource allocation, ensuring the diversity of the population. LS1+_AKERS_EXT realizes compound movement with Akers graphical method, so it has advanced global and local search capabilities. In LS1+_AKERS_EXT, the shortest path is the core of the algorithm, which directly affects the encoding and decoding of scheduling. In order to find the shortest path, an effective node expansion method is designed to improve the node expansion efficiency. In the part of centralized search, TS based on the neighborhood structure is used. Finally, the effectiveness and superiority of HACSM are verified by testing the relevant instances in the literature.

The relentless evolution of communication systems, driven by the demands of 5G and the impending 6G networks, necessitates heightened data rates and spectral efficiency. orthogonal frequency division multiplexing (OFDM), a form of multicarrier modulation employed in multi-input multioutput (MIMO) systems, stands as a pivotal technology. Yet, OFDM grapples with challenges, notably the peak-to-average power ratio (PAPR) issue. Selective mapping (SLM) has been a favored technique for mitigating PAPR in OFDM, albeit challenged by computational complexities in its pursuit of discovering optimal phase factors. This paper pioneers a transformative approach by integrating metaheuristic algorithms genetic algorithm (GA), particle swarm optimization (PSO), and the innovative fireworks algorithm (FWA) into SLM for PAPR reduction while minimizing computational complexity. Simulation results not only affirm the efficacy of SLM-based techniques but also spotlight the potential of metaheuristic algorithms in addressing PAPR challenges in modern communication systems. The study transcends single-antenna systems, extending to MIMOOFDM systems based on WiMAX standards, validating the efficacy of these techniques in multi-antenna configurations. Crucially, the FWA, proposed for the first time in this paper, emerges as a robust candidate, striking an enviable balance between computational efficiency and performance, achieving a notable PAPR reduction with a favorable search number. [ABSTRACT FROM AUTHOR]

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]

Internet of Things (IoT), cloud computing, and other significant advancements in communication have created new security challenges. Due to these advancements and the ineffectiveness of the current security measures, cyber‐attacks are also increasing quickly. Recently, several artificial intelligence (AI)–based solutions have been presented for various secure applications, such as intrusion detection. This article proposes an intrusion detection system using dynamic search fireworks optimization–based feature selection with optimal deep recurrent neural network (DFWAFS‐ODRNN) model in IoT environment. The presented DFWAFS‐ODRNN model follows a two‐stage process, namely, feature selection and intrusion classification. In the first phase, the DFWAFS‐ODRNN model elects an optimal subset of features using the dynamic search fireworks optimization algorithm (DFWAFS) technique. Next, in the second stage, the intrusions are identified and categorized using the DRNN model. At last, the hyperparameters of the DRNN are optimally chosen by the Nadam optimizer. A detailed simulation analysis of the DFWAFS‐ODRNN model is validated on benchmark intrusion detection system (IDS) dataset, and the outcomes show the efficacy of intrusion detection. The proposed model efficiently detects the intrusion detection with an accuracy of 96.11%. [ABSTRACT FROM AUTHOR]

Regarding the fault detection problem of the displacement sensor, an enhanced fireworks algorithm with information crossover and conversion factor (EFWA-IC) is proposed in this paper. In EFWA-IC, an information crossover strategy is proposed to maintain population diversity. This strategy is based on the predatory behavior of carnivores in nature. In addition, a conversion factor is set to control whether the explosion operator is executed or not to provide a more reasonable search. To fully evaluate the performance of EFWA-IC, a range of tests are carried out based on the CEC2017 and 23 classical test functions. The results show that the performance of EFWA-IC is better than other state-of-the-art optimization algorithms in terms of solution accuracy, convergence speed, and stability. Finally, EFWA-IC is utilized to optimize the particle filter (PF) to establish a fault detection model of displacement sensor in the continuous casting mold. The simulation experiment result of field data manifests that EFWA–IC–PF can accurately detect faults in the displacement sensor. For bias faults, the RMSE of the EFWA–IC–PF model is 0.14468, and the false alarm rate (FAR) and missed detection rate (MDR) are 1 % and 0.5 %, respectively. For stuck faults, the RMSE is 1.00148, and the FAR and MDR are 0.88 % and 1 %, respectively.

This paper presents a comprehensive analysis of three predictive models, namely Multi-Layer Perceptron (MLP), LASSO, and Extreme Gradient Boosting (XGB) for estimating concentration (C) of a substance in a given dataset. Adsorption separation was considered for water treatment, and the models were employed for tracking the concentration variations of solute in the process. With x(m) and y(m) as input variables which are the location, and concentration (C) measured in mol/m³ as output, the dataset comprises more than 19,000 data points. The Fireworks Algorithm (FWA) was employed to perform hyper-parameter optimization for the models. Different metrics were utilized to gauge the proficiency of each model, such as the R2 (coefficient of determination) for both the training and testing datasets, RMSE, and MAE. Results indicate that the MLP model obtained the highest score in terms of R2, with values of 0.99751 for the training data and 0.99756 for the testing data, suggesting excellent predictive accuracy. The MLP model also demonstrated the lowest error rates, with an RMSE of 1.3937 E+00 and an MAE of 8.81875E-01. The results revealed that the employed machine learning models are well capable of predicting adsorption process when combined with mass transfer modeling and great accuracy can be obtained.

Since control instructions are the fundamental component of thermal power generation, the quality and effectiveness of implementation directly affect the efficiency of the energy system. In order to improve the efficiency of internal combustion engine control, an optimization method of internal combustion engine control based on enhanced clustering algorithm and swarm intelligence optimization algorithm is proposed. The process simplifies the main structure of the gas turbine, divides the combustion engine model into multi-input single-output systems, and introduces the artificial bee colony algorithm to optimize the parameters. A new nectar search formula is constructed by using the global optimal nectar, and the control parameters are calculated by fuzzy logic clustering. The experimental results showed that the modeling error of the load model of internal combustion engine was in the range of −0.47 MW $\sim ~0.51$ MW. When the training iteration speed was tested, the loss value of the research method dropped rapidly in the first 10 iterations. When analyzing the change of the control quantity during load change, if the exhaust flow rate was taken as the control quantity, the control results of the research method was always kept within 5lbm/s error. It demonstrates that this research method can effectively improve the running quality of the internal combustion engine and has a good running efficiency. The research can provide certain technical reference for gas turbine control in thermal power generation.

In addressing the optimal formation obstacle avoidance control problem for Autonomous Underwater Vehicles (AUVs) in environments with unknown and moving obstacles, this paper employs the Modified Fireworks Algorithm based on a Loser Elimination Mechanism (MLoTFWA) and constructs a Distributed Model Predictive Control (DMPC) framework to achieve obstacle avoidance for AUV formations. Initially, a prediction model is established, followed by feedback compensation to mitigate the effects of unknown perturbations. An appropriate fitness function is then formulated, and enhancements such as the loser elimination rule are introduced to optimize the fireworks algorithm. Additionally, the concept of an adaptive DMPC prediction window is proposed to conserve resources. The local and global stability of the DMPC formation control framework is theoretically proven. Simulations verify that the control system based on the DMPC framework ensures safe obstacle avoidance for the formation, maintains formation consistency, and achieves the shortest and smoothest path. The improved fireworks algorithm demonstrates superior performance compared with the original fireworks algorithm and other optimization algorithms. In testing, the improved fireworks algorithm exhibits better adaptability, higher average fitness, and best fitness, along with a significantly faster convergence speed. Compared with the ordinary fireworks algorithm, the convergence speed is reduced by 30%.

Developing a photovoltaic system that successfully harvests the sun's power is one of the most difficult aspects of boosting power generation. Consequently, our study focuses on the development of a hybrid intelligent maximum power point tracking (MPPT) regulator that combines an innovative optimization approach based on the fireworks algorithm (FWA) and an artificial neural network (ANN) model. The proposed approach is examined in the first part of this study for various ANN configuration scenarios to identify the appropriate hyperparameters values and training algorithm required to converge toward the ideal objective function. After the optimization and training processes are completed, the selected FWA–ANN model is simulated as an MPPT controller using MATLAB/Simulink software and compared to the most commonly used MPPT techniques to demonstrate its effectiveness under various partial shading conditions. The results show that our proposed FWA–ANN technique using the BR and four neurons in the hidden layer reaches an excellent mean-squared error value equal to 0.1159 in the optimization process and 2.74e - 13 in the training phase. In addition, our suggested model is compared to the most widely used MPPT techniques notably, perturb and observe, particle swarm optimization, grey wolf optimization, whale optimization algorithm, and fuzzy logic controller. The obtained outcomes prove that the FWA–ANN overpasses the applied techniques by tracking the maximum power point faster with a response time between 0.0048 and 0.0261 s, a power efficiency higher than 99.5749%, that can up to 99.9977%, and an extreme reduction of oscillations in the transient and steady states for all tested cases. [ABSTRACT FROM AUTHOR]

Livestock and poultry manure is usually recycled to the nearby cropland as it is rich in elements required for crop growth. It is necessary to measure the pollution risk caused by recycled manure. In this study, a risk assessment model based 2-tuple linguistic is constructed to evaluate the pollution risk. Firstly, based on pollution source factors and migration factors, the index system is established, which includes nominal indexes and quantitative indexes. The 2-tuple linguistic method converts two attribute indexes into one form. Meanwhile, the firework algorithm is adopted to make the weights of indicators objective. Then, livestock and poultry farms in Xinzhou District, Wuhan City, Hubei Province, are taken as the empirical objects to get the spatial distribution of farms' risk. Through the index ablation experiment and sensitivity analysis, it is found that the soil resistance factor, manure removal method and the river channel distance are the main influencing indexes. Targeted improvement of these three influencing indicators can reduce the pollution risk by manure. [ABSTRACT FROM AUTHOR]

Regarding the spatial profile extraction method of a multi-field co-simulation dataset, different extraction directions, locations, and numbers of profiles will greatly affect the representativeness and integrity of data. In this study, a multi-field co-simulation data extraction method based on adaptive infinitesimal elements is proposed. The multifield co-simulation dataset based on related infinitesimal elements is constructed, and the candidate directions of data profile extraction undergo dimension reduction by principal component analysis to determine the direction of data extraction. Based on the fireworks algorithm, the data profile with optimal representativeness is searched adaptively in different data extraction intervals to realize the adaptive calculation of data extraction micro-step length. The multi-field co-simulation data extraction process based on adaptive microelement is established and applied to the data extraction process of the multi-field co-simulation dataset of the sintering furnace. Compared with traditional data extraction methods for multi-field co-simulation, the approximate model constructed by the data extracted from the proposed method has higher construction efficiency. Meanwhile, the relative maximum absolute error, root mean square error, and coefficient of determination of the approximation model are better than those of the approximation model constructed by the data extracted from traditional methods, indicating higher accuracy, it is verified that the proposed method demonstrates sound adaptability and extraction efficiency. [ABSTRACT FROM AUTHOR]

Based on cloud computing technology, this paper constructs a benefit-optimal enterprise resource scheduling model and an enterprise cost management prediction model to maximize the economic benefits of enterprise resources and optimize the management costs, respectively. Combining the improved greedy algorithm and the benefit function, a cloud resource scheduling algorithm based on benefit optimization is proposed, defining the benefit function about time and cost, and taking the highest user satisfaction as the optimal resource scheduling objective. A mathematical model for management cost prediction is constructed by using the fireworks algorithm to optimize the number of trees and the number of leaf nodes in the random forest, and the Informatica software is used to manage and integrate the enterprise source data. The performance of the company’s operating conditions after optimizing resource management and cost savings is explored as a case study of Company S. In 2023, the total asset turnover ratio of Company S increased to 21.45 from 0.48 in 2022, and the overall asset operating efficiency improved. Working capital rose to 262,852,200 yuan. The current ratio, quick ratio, and cash ratio improved, while the gearing ratio, equity ratio, and equity multiplier showed a downward trend. The net operating margin achieved the maximum profitability in the last three years, net total assets margin, and net equity margin, with an increase of 25.42%, 20.65%, and 31.49%, respectively.

The dynamic landscape of public health occurrences presents a formidable challenge to the emotional well-being of college students, necessitating a precise appraisal of their mental health (MH) status. A pivotal metric in this realm is the Mental Health Assessment Index, a prevalent gauge utilized to ascertain an individual's psychological well-being. However, prevailing indices predominantly stem from a physical vantage point, neglecting the intricate psychological dimensions. In pursuit of a judicious evaluation of college students' mental health within the crucible of public health vicissitudes, we have pioneered an innovative metric, underscored by temporal perception, in concert with a hybrid clustering algorithm. This augmentation stands poised to enrich the extant psychological assessment index framework. Our approach hinges on the transmutation of temporal perception into a quantifiable measure, harmoniously interwoven with established evaluative metrics, thereby forging a novel composite evaluation metric. This composite metric serves as the fulcrum upon which we have conceived a pioneering clustering algorithm, seamlessly fusing the fireworks algorithm with K-means clustering. The strategic integration of the fireworks algorithm addresses a noteworthy vulnerability inherent to K-means-its susceptibility to converging onto local optima. Empirical validation of our paradigm attests to its efficacy. The proposed hybrid clustering algorithm aptly captures the dynamic nuances characterizing college students' mental health trajectories. Across diverse assessment stages, our model consistently attains an accuracy threshold surpassing 90%, thus outshining existing evaluation techniques in both precision and simplicity. In summation, this innovative amalgamation presents a formidable stride toward an augmented understanding of college students' mental well-being during times of fluctuating public health dynamics. [ABSTRACT FROM AUTHOR]

The single-row facility layout problem (SRFLP) decides upon the arrangement of facilities in a straight row so as to minimise the material handling cost. Generally, this problem allows the placement of the facilities in any location in any order without any restriction, but some practical SRFLP cases are required to meet various types of constraints imposed on the placement of its facilities in the engineering of the placement of factory machinery and equipment. According to this new perspective, we studied the constrained SRFLP (cSRFLP) in this paper. In this problem, a few facilities need to be placed in certain positions or specified orders with or without the requirement to be located next to each other. To address this novel layout problem, related constraints are defined and classified, and novel mixed-integer programming models for the problem are formulated. Subsequently, the CPLEX software is employed to solve this problem. Then a constrained improved fireworks algorithm is presented, which is discretised to solve the considered cSRFLP. Our computational experiments demonstrate that the proposed algorithm performs better than the existing algorithms in solving the problem. [ABSTRACT FROM AUTHOR]

As road traffic develops, energy-saving and efficient street lights have become a key research field for relevant professionals. To reduce street lights energy consumption, a fireworks algorithm is used to optimize the membership function parameters of fuzzy control and the initial parameters of PI control. A fireworks algorithm improved adaptive fuzzy PI solar LED street light control system is designed. The results showed that in the calculation of Root-mean-square deviation and Mean absolute error, the Root-mean-square deviation of the adaptive fuzzy PI control system improved by the fireworks algorithm was 0.213, 0.258, 0.243, 0.220, and the Mean absolute error was 0.143, 0.152, 0.154, 0.139, respectively, which proved that the prediction accuracy was high and the stability was good. In the calculation of the 1-day power consumption of the solar LED intelligent control system, the average power consumption of the designed solar LED intelligent control system was about 2000W, which was 25.9%, 47.4%, and 42.9% lower than the other three control methods, respectively. This proves that its energy consumption is low, and its heat generation is low, and the battery service life is long. The research and design of an adaptive fuzzy PI control solar LED street light intelligent control system has good performance, which can effectively achieve intelligent management and energy conservation and emission reduction in smart cities.

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]

Loser-out tournament-based fireworks algorithm (LoTFWA) is a new baseline of fireworks algorithm (FWA). However, its ability to search deeply in local areas and communicate among fireworks is not satisfying enough. Therefore, this paper proposes a new triple-spark guiding strategy for LoTFWA to deal with the mentioned problems. Among the three sparks generated for guiding, one is exactly the same as the original one in LoTFWA, the second one uses the centroid of good sparks to enhance the local exploitation, and the last one is based on Differential evolution (DE) mutation and used to enhance cooperation and exploration. Experimental results show that with low computational cost, the proposed guiding strategy attains significantly better results than LoTFWA and is competitive with state-of-the-art FWA variants. Furthermore, comprehensive experiments show that the proposed strategy has the potential to combine with other FWA variants to achieve better results.

In order to address the problems of redundancy and waste of resources in the deployment of monitoring points in mesoscale chemical hazard areas, we propose a method for the deployment of monitoring points in mesoscale chemical hazard areas by combining weight and fireworks algorithms. Taking the mesoscale chemical hazard monitoring area as the research background, we take the probabilistic sensing model of telemetry sensor nodes as the research object, make a reasonable grid division of the mesoscale monitoring area, calculate the importance of each grid and perform clustering, utilize the diversity of the fireworks algorithm and the rapidity of the solution to solve the monitoring point deployment model and discuss the relevant factors affecting the deployment scheme. The simulation results show that the proposed algorithm can achieve the optimal coverage monitoring for monitoring areas with different importance and reduce the number of monitoring nodes and redundancy; meanwhile, the relevant factors such as the grid edge length, the number of clusters, and the average importance of monitoring areas have different degrees of influence on the complexity of the algorithm and the deployment scheme. [ABSTRACT FROM AUTHOR]

The Capacitated Vehicle Routing Problem (CVRP) is a classical combinatorial optimization problem, which objective is to minimize the vehicle travel distance. In this paper a hybrid ant colony optimization based on Fireworks Algorithm (FWA) is proposed to solve the CVRP. The main work of hybrid algorithm is reflected in three aspects: firstly, FWA is introduced on the basis of Ant Colony Optimization (ACO) algorithm to increase the diversity of algorithms and avoid falling into local optimum too early in the search process; secondly, the elite ant strategy is added to increase the attractiveness of the local optimal path to the ants; thirdly, the Max-Min Ant System (MMAS) is added to limit the pheromone value within a range to prevent the pheromone from increasing too fast on the path. In this paper, the proposed hybrid algorithm is tested in 71 instances and compared with other intelligent algorithms. Experimental results show that the proposed hybrid algorithm finds new best solutions and is competitive with other algorithms. [ABSTRACT FROM AUTHOR]

A constrained multi-objective optimization model for the low-carbon vehicle routing problem (VRP) is established. A carbon emission measurement method considering various practical factors is introduced. It minimizes both the total carbon emissions and the longest time consumed by the sub-tours, subject to the limited number of available vehicles. According to the characteristics of the model, a region enhanced discrete multi-objective fireworks algorithm is proposed. A partial mapping explosion operator, a hybrid mutation for adjusting the sub-tours, and an objective-driven extending search are designed, which aim to improve the convergence, diversity, and spread of the non-dominated solutions produced by the algorithm, respectively. Nine low-carbon VRP instances with different scales are used to verify the effectiveness of the new strategies. Furthermore, comparison results with four state-of-the-art algorithms indicate that the proposed algorithm has better performance of convergence and distribution on the low-carbon VRP. It provides a promising scalability to the problem size.

Harris Hawks optimization (HHO) is a swarm optimization approach capable of handling a broad range of optimization problems. HHO, on the other hand, is commonly plagued by inadequate exploitation and a sluggish rate of convergence for certain numerical optimization. This study combines the fireworks algorithm’s explosion search mechanism into HHO and proposes a framework for fireworks explosion-based HHo to address this issue (FWHHO). More specifically, the proposed FWHHO structure is comprised of two search phases: harris hawk search and fireworks explosion search. A search for fireworks explosion is done to identify locations where superior hawk solutions may be developed. On the CEC2014 benchmark functions, the FWHHO approach outperforms the most advanced algorithms currently available. Moreover, the new FWHHO framework is compared to four existing HHO and fireworks algorithms, and the experimental results suggest that FWHHO significantly outperforms existing HHO and fireworks algorithms. Finally, the proposed FWHHO is employed to evolve a kernel extreme learning machine for diagnosing COVID-19 utilizing biochemical indices. The statistical results suggest that the proposed FWHHO can discriminate and classify the severity of COVID-19, implying that it may be a computer-aided approach capable of providing adequate early warning for COVID-19 therapy and diagnosis. [ABSTRACT FROM AUTHOR]

Fireworks algorithm is a novel swarm intelligence optimization framework which focuses on the potential of collaboration among multiple subpopulations with independent search ability. Although it has been proved to perform excellently in many tasks, the collaborative mechanism of fireworks is still quite undeveloped. In this paper, a theoretical model of fireworks algorithm based on search space partition is proposed, analyzed and implemented. The local search of each firework is replaced by covariance matrix adaptation evolution strategy for efficient exploitation. A coordination strategy inspired from Voronoi diagram is proposed to approximate the theoretical model for stable global exploration. Experimental results show that the proposed algorithm not only outperforms previous variants of fireworks algorithm significantly, but also achieves competitive results compared with state‐of‐the‐art evolutionary algorithms, which are intensively fine‐tuned on the objective functions. [ABSTRACT FROM AUTHOR]

This study introduces a novel Parallel Hybrid Island architecture which shows a parallel way to combine different meta-heuristic algorithms by using the island model as the base. The corresponding hybrid algorithm is called Parallel Hybrid Island Metaheuristic Algorithms (PHIMA). The hybrid parallel structure exploits the characteristics of the individual metaheuristic algorithms to boost robustness and diversity. Island Genetic Algorithm has been combined with Particle Swarm Optimization and Fireworks Algorithm to build three different PHIMA algorithms: PSO-GA (PHIMA-PGA), FWA-GA (PHIMA-FGA) and FWA-PSO-GA (PHIMA-FPGA). Further, another implementational variation known as “co-evolution” is applied to the sub-GA islands of PHIMA-FPGA to improve the performance on multi-modal high-dimensional problems. This variation is referred to as PHIMA-FPGA-Co. Each PHIMA Algorithm exhibits different advantages and characteristics, and the parallel hybridization using the island model is found to improve robustness and population diversity. The performances of the four new algorithms are compared with each other and that of the traditional Island GAs and all four proposed PHIMA algorithms show better result quality.

The artificial fish swarm algorithm can achieve good convergence effects in the early stage, but in the late stage, the algorithm has the problems of slow convergence speed and low optimization accuracy, and it is easy to fall into local extremes, making the algorithm's convergence effect poor. Therefore, the characteristics of fireworks algorithm are used to improve the deficiency of fish swarm algorithm that is easy to fall into local extreme value in the late stage, and FWA-artificial fish swarm algorithm is put forward. When the effect of artificial fish swarm algorithm is poor, the explosion, mutation, mapping, and selection operations of fireworks algorithm are introduced to increase the variability of artificial fish, so as to enhance the optimization speed and ability of the algorithm. Finally, the improved algorithm is tested by four typical complex functions which are difficult to find the optimal solution by traditional method. Simulation results prove that the algorithm has the advantages of faster optimization speed, higher precision, and stronger stability. [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]

The fireworks algorithm (FWA) has achieved significant global optimization ability by organizing multiple simultaneous local searches. By dynamically decomposing the target problem and handling each one with a sub-population, it has presented distinct property and applicability compared with traditional evolutionary algorithms. In this paper, we extend the theoretical model of fireworks algorithm based on search space partition to obtain a hierarchical collaboration model. It maintains both multiple local fireworks for local exploitation and one global firework for overall population distribution control. The implemented hierarchical collaborated fireworks algorithm is able to combine the advantages of both classic evolutionary algorithms and fireworks algorithms. Several experiments are provided for in-depth analysis and discussion on the proposed algorithm. The effectiveness of proposed strategy is demonstrated on the benchmark test suite from CEC 2020. Experimental results validate that the hierarchical collaborated fireworks algorithm outperforms former fireworks algorithms significantly and achieves similar results compared with state-of-the-art evolutionary algorithms. [ABSTRACT FROM AUTHOR]

This paper proposes an optimal over-frequency generator tripping strategy aiming at implementing the least amount of generator tripping for the regional power grid with high penetration level of wind/photovoltaic (PV), to handle the over-frequency problem in the sending-end power grid under large disturbances. A steady-state frequency abnormal index is defined to measure the degrees of generator over-tripping and under-tripping, and a transient frequency abnormal index is presented to assess the system abnormal frequency effect during the transient process, which reflects the frequency security margin during the generator tripping process. The scenario-based analysis method combined with the non-parametric kernel density estimation method is applied to model the uncertainty of the outgoing power caused by the stochastic fluctuations of wind/PV power and loads. Furthermore, an improved fireworks algorithm is utilized for the solution of the proposed optimization model. Finally, the simulations are performed on a real-sized regional power grid in Southern China to verify the effectiveness and adaptability of the proposed model and method.

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]

Accurate and stable load forecasting has great significance to ensure the safe operation of distributed energy system. For the purpose of improving the accuracy and stability of distributed energy system load forecasting, a forecasting model in view of kernel principal component analysis (KPCA), kernel extreme learning machine (KELM) and fireworks algorithm (FWA) is proposed. First, KPCA modal is used to reduce the dimension of the feature, thus redundant input samples are merged. Next, FWA is employed to optimize the parameters C and σ of KELM. Lastly, the load forecasting modal of KPCA-FWA-KELM is established. The relevant data of a distributed energy system in Beijing, China, is selected for training test to verify the effectiveness of the proposed method. The results show that the new hybrid KPCA-FWA-KELM method has superior performance, robustness and versatility in load prediction of distributed energy systems. [ABSTRACT FROM AUTHOR]

Abstract In densely populated urban centers, planning optimized capacity for the fifth-generation (5G) and beyond wireless networks is a challenging task. In this paper, we propose a mathematical framework for the planning capacity of a 5G and beyond wireless networks. We considered a single-hop wireless network consists of base stations (BSs), relay stations (RSs), and user equipment (UEs). Wireless network planning (WNP) should decide the placement of BSs and RSs to the candidate sites and decide the possible connections among them and their further connections to UEs. The objective of the planning is to minimize the hardware and operational cost while planning capacity of a 5G and beyond wireless networks. The formulated WNP is an integer programming problem. Finding an optimal solution by using exhaustive search is not practical due to the demand for high computing resources. As a practical approach, a new population-based meta-heuristic algorithm is proposed to find a high-quality solution. The proposed discrete fireworks algorithm (DFWA) uses an ensemble of local search methods: insert, swap, and interchange. The performance of the proposed DFWA is compared against the low-complexity biogeography-based optimization (LC-BBO), the discrete artificial bee colony (DABC), and the genetic algorithm (GA). Simulation results and statistical tests demonstrate that the proposed algorithm can comparatively find good-quality solutions with moderate computing resources.

Wireless Sensor Network (WSN) as one of the representatives of the Internet of Things technology has also received much attention. To accurately diagnose fault sensor nodes, a fault diagnosis method based on fireworks algorithm optimization convolutional neural network algorithm is proposed. The weights and biases of the convolutional neural networks are optimized by using the self-regulating mechanism of global and local searching ability of fireworks algorithm. So the problem of convolution neural network in extreme judgment and limited convergence speed is solved, to effectively realize the fault diagnosis of the WSN. Simulation experiments show that this algorithm has higher fault diagnosis accuracy than other classic WSN fault diagnosis algorithms.

Aiming at the typical problems of deploying sonar buoys in appointed sea area, this paper summarizes two problems existing in previous studies and puts forward a quick deployment method for sonar buoys detection under the overview situation of underwater cluster targets. Firstly, considering the influence of an underwater target course on target strength, the overlapping coefficient ”buoy group” mode is introduced to deploy the array. And combining with the random distribution law of underwater targets in the exploration area, the mathematical optimization model for sonar buoys detection under the overview situation of underwater cluster targets is established. Then, the fitness function corresponding to the buoy deployment optimization model is defined, and the adaptive fireworks algorithm is used to solve the optimization problem for obtaining the sonar buoys deployment scheme. Finally, through the comparison and analysis of results for the seven group simulation experiments, the conclusions that are beneficial to improve the detection efficiency of the sonar buoy deployment are obtained. The proposed method can provide useful support for underwater cluster multi-target detection and the problem of counterattack underwater cluster multi-platform.

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]

The traditional fireworks algorithm (FWA) is easy to fall into the local extremum and the accuracy of the solution is not high as that the explosion amplitudes and the selection mechanism are inefficient. A FWA based on dynamic search and tournament selection is proposed. The algorithm redefines the original explosion amplitudes, introducing the concept of minimum explosion amplitudes. In order to make the explosion amplitudes calculated dynamically, the number of iterations and the maximum number of iterations are introduced into the updating formula. Meanwhile, without changing the physical meaning of the original algorithm, the formula preserves the fitness value. Updating the new explosion amplitudes by non-linear method, thereby, it achieves the goal of the global search in the early phases and the local search in the late part phases. At the same time, the tournament selection mechanism is used to select some excellent individuals from the population. And then it selects the best one to enter the offspring population until the new population size reaches the population size. It makes the result closer to the desired results and improves the accuracy of the solution. The proposed algorithm balances the global and local search abilities, making the calculation results more accurate. [ABSTRACT FROM AUTHOR]

The accurate and reliable prediction of future runoff is important to guarantee for strengthening water resource optimization and management. The novel contribution of this article is the development of a hybrid model (FWA-ANFIS), which is based on the improvement of the adaptive neuro-fuzzy inference system (ANFIS) with the fireworks algorithm (FWA). The dominant driving factors of runoff are selected from several hydro-meteorological indices (precipitation, soil moisture content, and evaporation) as predictors by correlation coefficient (CC) analysis, mutual information (MI) analysis, correlation analysis and principal component analysis (CC-PCA), mutual information and kernel principal component analysis (MI-KPCA), MI-PCA, and CC-KPCA. The FWA-ANFIS model is applied to the Beiru River, China, with data from 1985–2016 (1985–2012 for model training and 2013–2016 for model prediction). The standard ANFIS, the GA-ANFIS, the PSO-ANFIS, the FWA-ELM, the GA-ELM, and the PSO-ELM are utilized as compared prediction models on the identical dataset. The results indicate that CC-PCA outperforms the other methods regarding the selection of predictors, and FWA-ANFIS has the best performance in terms of the root mean square error, correlation coefficient, and coefficient of determination, followed by the GA-ANFIS, PSO-ANFIS, ANFIS, FWA-ELM, GA-ELM, and PSO-ELM models. Furthermore, the degrees of uncertainty of the models increase in the following order: FWA-ANFIS, GA-ANFIS, PSO-ANFIS, ANFIS, PSO-ELM, GA-ELM, and FWA-ELM. [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]

Many real-world problems can be abstracted as multimodal global optimization, which is one of the main challenges for optimization algorithms due to its complexity. The fireworks algorithm (FWA) is a swarm intelligence optimization algorithm that has been widely studied and applied by virtue of the synergistic property among fireworks. Current FWA variants have poor exploitation capability to handle some locally complex multimodal functions, which greatly limits the application of the FWA to practical problems. To solve the above problems, in this paper, we propose the multi-guiding spark fireworks algorithm (MGFWA) to solve multimodal functions by enhancing FWA exploitation capabilities. Three different strategies which are boosted guiding vector, multi-guiding sparks, and population-based random mapping are designed to boost the guiding vector, enrich the guiding spark diversity, and fix the mapping function, separately. The validity and parameter setting of MGFWA are theoretically analyzed. Experimentally, the results on the CEC2013 and CEC2017 single objective optimization benchmarks illustrate the remarkable performance of the MGFWA compared to other typical optimization algorithms and FWA variants. Moreover, the ablation study shows each of the three parts plays an important role in the algorithm and the efficiency experiment shows the MGFWA can improve the efficiency of guiding sparks by 10%. We believe that the MGFWA can be considered the SOTA variant of the FWA. • Utilizing boosted guiding vector, multi-guiding sparks, and population-based random mapping to enhance the exploitation capability of the fireworks algorithm. • State-of-the-art performance among fireworks algorithm variants. • Superior performance on multimodal global optimization among several typical swarm intelligence optimization algorithms and evolutionary algorithms. • Extensive experiments (about 60 test functions) and theoretical analyses to demonstrate the effectiveness. [ABSTRACT FROM AUTHOR]

Wireless energy replenishment using mobile wireless charging equipment (WCE) has been a hot topic recently in areas of wireless rechargeable sensor networks (WRSNs) and mobile computing. Previous studies of multi-node charging planning usually assumed that the WCE was equipped with sufficient energy to accomplish the charging task. However, the energy of the WCE is limited in practice. Therefore, a multi-node charging planning algorithm with energy-limited WCE in WRSNs is proposed in this paper. Moreover, three charging planning models and their corresponding charging planning algorithms are proposed based on the different real conditions of the WCE: sufficient moving energy and limited charging energy, limited moving energy and sufficient charging energy, as well as both limited moving energy and charging energy. Furthermore, a hybrid simulated annealing discrete fireworks algorithm (HSA-DFWA) is proposed due to the NP-Hard complexity of the charging planning problem. The experiments show that compared to DFWA, MM-ANT, E-greedy, and P-greedy algorithms, the HSA-DFWA outperforms these algorithms empirically.

Aiming at the characteristics of MM* model fault diagnosis, a fireworks algorithm based on a dual population strategy is designed. The dual population of the algorithm is operated independently in parallel, and cooperative operator and optimal operator are cross-executed in the iterative process. The cooperative operator enables two populations to exchange effective information, avoiding the premature maturity of the algorithm. The optimal operator helps to strengthen the global search power of the algorithm and improve the convergence rate of the algorithm. At the same time, the constraint equation is designed, a new fitness function is proposed, and the mutation operator and selection strategy are optimized. The experimental comparison shows that the algorithm improves the efficiency and accuracy of system-level fault diagnosis and has good practicability. Finally, the correctness of the algorithm is proved by theory, and the time complexity of the algorithm is analyzed.