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For cancer detection and tissue characterization, DCE-MRI segmentation and lesion detection is a critical image analysis task. To segment breast MR images for lesion detection, a hard-clustering technique with Grammatical Fireworks algorithm (GFWA) is proposed in this paper. GFWA is a Swarm Programming (SP) system for automatically generating computer programs in any language. GFWA is used to create the cluster core for clustering the breast MR images in this article. The presence of noise and intensity inhomogeneities in MR images complicates the segmentation process. As a result, the MR images are denoised at the start, and strength inhomogeneities are corrected in the preprocessing stage. The proposed GFWA-based clustering technique is used to segment the preprocessed MR images. Finally, from the segmented images, the lesions are removed. The proposed approach is tested on 5 patients’ 25 DCE-MRI slices. The proposed method’s experimental findings are compared to those of the Grammatical Swarm (GS)-based clustering technique and the K-means algorithm. The proposed method outperforms other approaches in terms of both quantitative and qualitative results.

In contemporary urban areas, the construction speed of urban roads lags far behind the growth rate of the number of vehicles. The traffic delay caused by excessive vehicles is a major challenge for modern transportation systems. In this paper, we design an adaptive coordination traffic signal control system based on a three-level framework. In the framework, we propose a hierarchical strategy, which is helpful in avoiding possible offset conflicts and configuring the offsets reasonably. In addition, we establish a multi-intersection traffic signal control model with the goal of minimizing traffic delays. To solve the proposed model, we propose a new algorithm, called the Immune-Fireworks algorithm (IM-FWA), on the basis of the artificial immune and fireworks algorithms. Inspired by the antibody maintenance mechanism, diversity mechanism and communication mechanism of the artificial immune algorithm, IM-FWA can effectively overcome the shortcomings of the fireworks algorithm, such as its limited search range and lack of interaction among fireworks. The experiments show that the proposed model and algorithm have good practicability and that our control system can obtain a better signal timing schedule to effectively reduce traffic delays.

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.

How to accurately estimate the probability integral parameters based on the measured data has always been a difficult point in the application of the probability integral method. This paper introdu...

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.

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 placemen...

As a comparatively new algorithm of swarm intelligence, the dynamic search fireworks algorithm (dynFWA) imitates the explosion procedure of fireworks. With the goal of achieving global optimization and further boosting performance of dynFWA, adaptive parameters are added in this present study, called dynamic search fireworks algorithm with adaptive parameters (dynFWAAP). In this novel dynFWAAP, a self-adaptive method is used to tune the amplification coefficient Ca and the reduction coefficient Cr for fast convergence. To balance exploration and exploitation, the coefficient of amplitude α and the coefficient of sparks β are also adapted, and a new selection operator is proposed. Evaluated on twelve benchmark functions, it is evident from the experimental results that the dynFWAAP significantly outperformed the three variants of fireworks algorithms (FWA) based on solution accuracy and performed best in other four algorithms of swarm intelligence in terms of time cost and solution accuracy.

In this chapter, a hybrid bare bones fireworks algorithm (HBBFWA) is proposed and its application in solving the load flow problem of islanded microgrid is demonstrated. The hybridization is carried out by updating the positions of generated sparks with the help of grasshopper optimization algorithm (GOA) mimicking the swarming behavior of grasshoppers. The purpose of incorporating GOA with bare bones fireworks algorithm (BBFWA) is to enhance the global searching capability of conventional BBFWA for complex optimization problems. The proposed HBBFWA is applied to perform the load flow analysis of a modified IEEE 37-Bus system. The performance of the proposed HBBFWA is compared against the performance of BBFWA in terms of computational time, convergence speed, and number of iterations required for convergence of the load flow problem. Moreover, standard statistical analysis test such as the independent sample t-test is conducted to identify statistically significant differences between the two algorithms.

This paper introduces a novel parallel way to combine different meta-heuristic algorithms by using the island model, which is called Hybrid Island Metaheuristic Algorithm (HIMA). This parallel hybridization structure can improve the diversity of the whole algorithm and combine the features of different algorithms together. In this paper, three traditional algorithms, Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Fireworks Algorithm (FWA) have been used to build three different HIMA algorithms, PSO-GAs (HIMA-PGA), FWA-GAs (HIMA-FGA) and FWA-PSO-GAs (HIMA-FPGA). The performance of the proposed algorithms is compared to that of the traditional Island GA and to that of the others as well. All three HIMA algorithms show a better result quality compared to the island GA. Moreover, the experiment results comfirm that the sub-PSO improves the convergence speed of the algorithm while the sub-FWA can improve the result quality on some proposed functions.

The knowledge of the thermal boundary conditions helps to understand the heat transfer phenomena that takes place during heat treatment processes. Heat Transfer Coefficients (HTC) describe the heat exchange between the surface of an object and the surrounding medium. The Fireworks Algorithm (FWA) method was used on near-surface temperature-time cooling curve data obtained with the so-called Tensi multithermocouple 12.5 mm diameter x 45 mm Inconel 600 probe. The fitness function to be minimized by a Fireworks Algorithm (FWA) approach is defined by the deviation of the measured and calculated cooling curves. The FWA algorithm was parallelized and implemented on a Graphics Processing Unit architecture. This paper describes the FWA methodology used to compare and differentiate the potential quenching properties of a series of vegetable oils, including cottonseed, peanut, canola, coconut, palm, sunflower, corn, and soybean oil, versus a typical accelerated petroleum oil quenchant.

Aiming at the shortcomings of the fireworks algorithm (FWA) that it is easy to mature prematurely and has low accuracy and weak global search ability, a novel improved FWA whose solution space search strategy based on Elite Opposition-Based Learning (EOBLFWA) is proposed. The optimization results of 4 sets of standard functions show that EOBLFWA has higher convergence speed and convergence accuracy for numerical optimization. In this paper, the proposed algorithm is used to optimize the structural parameters of radiator. The result shows that the temperature of the heat source on the surface of the optimized radiator is lowered by 4.8 degree compared with the original model, and the calculation results are verified by the ICEPAK software.

This paper proposes a fireworks algorithm based path planning method for amphibious robots that operate in terraqueous environments. Firstly, the amphibious path planning is formulated into a constrained optimization problem by coordinate transformation and line segmentation. Distance, energy consumption, and robot mode switching costs regarding the unconventional characteristics of the amphibious environment are considered. Secondly, the fireworks algorithm (FWA) and the bare bones fireworks algorithm (BBFWA) are briefly introduced. Finally, both methods have been implemented for solving the amphibious path planning problem. Simulation experiments have been conducted to explore the effectiveness and performance of both methods. Results indicate that our proposed path planning method for terraqueous environments is effective, and the fireworks algorithm outperforms the bare bones fireworks algorithm despite the latter surpasses several enhanced variants of the former on certain benchmarks.

Power system fault diagnosis is an important means to ensure the safe andstable operation of power system. According to the specific situation ofChina’s current power grid automation level, a hierarchical fault diagnosismethod based on switch trip signal, protection information and fault record-ing information is proposed. This method can not only diagnose simple faultand complex fault, but also judge fault type and phase, and complete faultlocation, which provides reliable guarantee for operators to quickly removefault and resume operation. The diagnosis method based on this principle hasgood application effect in simulation test.

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.

Scheduling is critical part in most creation frameworks and information processing as sequencing of tasks or jobs framework executed on a grouping of processors. One of the NP-hard problem is “Job Shop Scheduling Problem”. In this work, a method of optimization proposed called “Fireworks Algorithm”. The solutions divided into fireworks and each one applied sparks to find the best solution. For some selected spark applied Gaussian mutation to find enhanced solution and find optimum solution. FWA tested on dataset to improve performance and it do well with respect to some other algorithm like Meerkat Clan Algorithm (MCA), Camel Herds Algorithm) CHA(, and Cukoo Search Algorithm (CSA).

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.

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 ineff...

A numerical method for coordinate and time-dependent Heat Transfer Coefficient estimation was developed. The main element of the developed estimation procedure is the Adaptive Fireworks Algorithm, which was used for solving the Inverse Heat Conduction Problem. A parallelized solution was implemented on graphic accelerator card to speed up the calculations and the Adaptive Fireworks Algorithm was compared with Genetic Algorithm based on their computation cost. In order to demonstrate the applicability of the method, Heat Transfer Coefficients, which appears during immersion quenching in an organic oil were estimated.

Because of the shortcomings of traditional infrared-polarization image fusion algorithm, such as low intelligence and single optimization index, this paper proposes an intelligent infrared-polarization image fusion optimization algorithm based on fireworks algorithm. Firstly, an improved differential image correction method based on single pixel nonuniformity is proposed to remove the cold reflection. The two-dimensional discrete cosine transform (DCT) is used to reduce the image sensitivity and improve the robustness, and the Stokes vector formula is used to obtain the polarization characteristic image. Secondly, based on the strong complementarity between infrared-intensity image and degree of linear-polarization (DOLP) image and the explosive optimization of fireworks algorithm, the problem model of weighted fusion algorithm is established, and the fitness function based on root mean square error (RMSE) is constructed to calculate the optimal weight of source image. In the fusion experiment of long-wave infrared-intensity image and DOLP image, this method is compared with the common fusion algorithms. The results show that this method can effectively fuse the infrared-intensity and degree of polarization information, and the evaluation indexes of standard deviation, spatial frequency, mutual information, structural similarity, peak signal-to-noise ratio and information entropy of the fusion image are better than the comparison algorithm. In the future, cooperated with the long-wave infrared-polarization imaging system, this method can be applied to improve the infrared detection ability in complex environment.

With the growing demand for public security and intelligent life as well as the expansion of the Internet of Things (IoT), it is indispensable to make a plan how to place the minimum number of cameras or guards to achieve secure surveillance. The optimal cameras placement is a hard combinatorial problem, and it can be formulated as seeking the smallest number of guards to cover every point in a complex setting. In this article, we propose an adjusted version of the bare bone fireworks algorithm and one deterministic technique for tackling cameras placement problem. Both versions of novel algorithms have been implemented and tested over two hundreds of randomly generated orthogonal polygons. According to the outcomes presented in the experimental analysis, it can be noticed that the first approach based on metaheuristics beats the deterministic method for practically all instances.

In this paper a new approach based on the fireworks algorithm (FWA) is proposed to solve the frequency assignment problem (FAP), the FAP is well known NP-complete optimization problem, the objective of the FAP is to minimize the number of interference generated by a solution, fireworks algorithm has been performed on several instances of the FAP. The obtained results show that this algorithm can be very useful to solve more complex benchmark problems studied in the literature.

Swarm programming is the swarm-based automatic programming in which swarm intelligence algorithms are used to evolve computer programs automatically. Automatic programming is a division of machine learning where machines learn how to write the program for themselves. Grammar-based swarm programming is an interesting research topic in recent times. In grammar-based swarm programming, context-free grammar (CFG) is utilized in the generation of computer programs automatically in any arbitrary target computer language. In this paper, grammatical multi-verse optimizer (GMVO) is proposed to generate computer programs automatically. The proposed method is applied to three benchmark problems such as Santa Fe Ant Trail (SFAT), 3-multiplexer, and symbolic regression. The experimental results of the proposed GMVO are compared with that of grammatical fireworks algorithm (GFWA), grammatical bee colony (GBC), and grammatical swarm (GS). The empirical results with analysis demonstrate that the GMVO can be used in automatic generation of computer programs in any arbitrary target computer language.

In the last decades, swarm intelligence algorithms have become a powerful tool for solving hard optimization problems. Nowadays numerous algorithms are proved to be good for different problems. With the overwhelming number of algorithms, it became hard for a common user to choose an appropriate method for solving a certain problem. To provide guidelines, it is necessary to classify optimization metaheuristics according to their capabilities. Deep statistical comparison represents a novel method for comparing and analyzing optimization algorithms. In this paper, the deep statistical comparison method was used for comparing different versions of the widely used fireworks algorithm. The fireworks algorithm was developed and improved in the last ten year, and this paper provides a theoretical analysis of five different versions, a cooperative framework for FWA, bare bones FWA, guided FWA, loser-out tournament based FWA, and dynamic search FWA. Based on the obtained results, the loser-out tournament based FWA has the best performance in the term of the solution quality, while the dynamic search FWA is the best in term of the solutions distribution in the search space.

A new report on childhood obesity is published every so often. The bad habits of food and the increasingly sedentary life of children in a border society has caused an alarming increase in the cases of children who are overweight or obese. Formerly, it seemed to be a problem of countries with unhealthy eating habits, such as the United States or Mexico in Latin America, where junk food is part of the diet in childhood. However, obesity is a problem that we already have around the corner and that is not so difficult to fight in children. In the present research the development of an application that reduces the problem of the lack of movement in the childhood of a smart city is considered a future problem which it is the main contribution, coupled with achieving an innovative way of looking for an Olympic sport without the complexity of physically moving to a space with high maintenance costs and considering the adverse weather conditions.

The fireworks algorithm (FWA) is a newly proposed swarm intelligence algorithm inspired by the phenomena of fireworks explosion and has solved many real-world optimization problems successfully. A loser-out tournament-based fireworks algorithm (LoTFWA) is a new baseline in the development of FWA due to its outstanding independent framework and competition mechanism for multimodal optimization. Under this framework, each firework calculates its expected fitness improvement compared with the best fitness to determine whether to be reinitialized. Although LoTFWA achieves the best performance among the variants of FWA, it lacks of comprehensive consideration of the fireworks’ cooperation and hence weakens the algorithm’s power. This paper improves the cooperation of fireworks in LoTFWA based on the idea of population migration and mutation in biogeography-based optimization (BBO). The proposed mechanism not only promotes fireworks’ exploration ability but also enhances their exploitation ability greatly. Experimental results show that the proposed algorithm attains superior performance than the state-of-the-art fireworks algorithm in both unimodal and multimodal functions.

Breast cancer causes the highest number of deaths among all types of cancers in women. Therefore, it is necessary to properly diagnose the breast cancer for treatment of the patients. At present, dynamic contrast-enhanced (DCE)-MRI is widely used biomedical imaging technique to diagnose the breast cancer. In this paper, a breast DCE-MRI segmentation method using modified hard-clustering with Fireworks Algorithm (FWA) is developed for lesion detection. The segmentation of DCE-MRI suffers from noise and intensity inhomogeneities present in the images. On the outset, MR images are denoised using anisotropic diffusion filter and intensity inhomogeneities are corrected using max filter-based method in the preprocessing step. After that, images are segmented using hard-clustering technique with FWA algorithm. Finally, the lesions are extracted from the segmented images in the postprocessing step. The results of the proposed segmentation method are compared with segmentation methods based on Particle Swarm Optimizer (PSO), and K-means algorithms. The experimental results demonstrate that the proposed method outperforms other methods in the segmentation of breast DCE-MRI.

Aiming at the problems of the firework algorithm (FWA) that is easy to fall into the local optimum and the search efficiency and accuracy are low, a firework algorithm with local search optimization (LSFWA) is proposed. In this paper, we present two performance enhancing strategies. The first strategy is that the iterative local search is performed to find the current optimal location. The second strategy is the perturbation strategy, which increases the diversity of sparks to a certain extent by introducing a probability perturbation, then, search for sparks with better fitness near the local extremum to improve the ability to search for the global optimal location. The simulation experiment on 9 test functions shows that LSFWA displays better optimization speed and optimization accuracy compared to the typical algorithm FWA, FAGSO, PSO and GSA.

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.

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.

For the dynamic reconfiguration problem of distribution networks, the handling of switching cost constraint and the division of time period are the two key aspects that affect the performance of the reconfiguration algorithm. In this paper, an improved temporal constrained hierarchical clustering algorithm for dynamic reconfiguration of distribution networks is proposed. Firstly, the improved hierarchical clustering approach considering the temporal constraint is used to divide the operating status of the distribution network into multiple time intervals according to the similarity of loads and the output power of distributed generations (DGs). The dynamic reconfiguration of distribution networks is then transformed into multiple single-stage static reconfiguration problems, and the cluster center is used to approximately represent the load state and DG output state of the period. In order to reduce the number of infeasible solutions and poor solutions, a coding method based on heuristic rules to reduce the solution space of distribution network reconfiguration is proposed. An improved fireworks algorithm based on heuristic rules is proposed to solve the reconfiguration problem. Finally, a modified IEEE-33 test system is used to verify the validity of the proposed method.

Aiming at the problem of low operating efficiency of traditional fireworks algorithm in distribution network optimization and reconstruction, some improved strategies are proposed. The algorithm takes the minimum loss of distribution network as the fitness function, the mapping rules of the traditional fireworks algorithm are improved and optimized, and the sparks are double mapped, which improves the optimization speed of the algorithm. By improving the operation, the population diversity of the evolutionary algorithm is improved, so the accuracy and speed of the algorithm are improved. Through the simulation analysis of the IEEE33 node system, it is proved that the improved fireworks algorithm can get the optimal result of distribution network structure, and can adapt to the optimal reconfiguration of the distribution network. Through the example simulation of Zhengzhou distribution network, the practical application of the algorithm is verified.

With the rapid development of network technology, network intrusion has become increasingly frequent. In network intrusion detection technology, how to reduce feature dimensions and reduce redundant information is the key to improve the detection accuracy. To solve this problem, this paper proposes a new feature selection method SIFWA for intrusion detection based on improved fireworks algorithm. SIFWA optimized and improved the selection strategy of fireworks algorithm, which adopted the selection strategy based on fitness value to screen the next generation of fireworks, which could greatly improve the ability of fireworks algorithm to find the optimal solution and search efficiency to select more effective features for intrusion detection. Simulation experiments were conducted using UCI data. Simulation results show that SIFWA has higher detection accuracy than the benchmark algorithm.

In this paper, a new approach to resolve the problem of frequency assignment problem is proposed. (FAP) is well known in the NP-complete problems and can be modeled as an optimization problem, which the objective is to minimize the costs due to interference generated by a solution. The fireworks algorithm (FWA) is proposed for solving FAP. FWA is a recently developed swarm intelligence algorithm. FWA is a meta-heuristic method and has a good convergence property and can always find the global optimal solutions.

Backpropagation is the most common method of training artificial neural networks in use. However, backpropagation has a tendency to get trapped in locally optimum solutions. This paper compares the ability of Barebones Fireworks Algorithm, Particle Swarm Optimization, and Cooperative Particle Swarm Optimization to improve upon an artificial neural network trained with backpropagation. The learning ability of the search algorithms and the simulations are hindered by the high dimensionality of the artificial neural network. An analysis of the simulation results shows that the Barebones Fireworks Algorithm outperforms the other two algorithms.

This chapter presents Interval Type 2 Fuzzy Fireworks Algorithm for clustering (IT2FWAC). It is an optimization method for finding the optimal number of clusters based on the centroid features which uses the Fireworks Algorithm (FWA), but with a dynamic adjustment of parameters using an Interval Type 2 Fuzzy Inference System (IT2FIS). Three variations of the IT2FWAC are proposed to find the optimal number of clusters for different datasets: IT2FWAC -I, IT2FWAC -II, and IT2FWAC –III. They are explained in detail.

The Dynamic Search Fireworks Algorithm (dynFWA) is an effective algorithm for solving optimization problems. However, dynFWA is easy to fall into local optimal solutions prematurely and it also provides a slow convergence rate. To address these problems, an improved dynFWA (IdynFWA) is proposed in this chapter. In IdynFWA, the population is first initialized based on opposition-based learning. The adaptive mutation is proposed for the core firework (CF) which chooses whether to use Gaussian mutation or Levy mutation for the CF according to the mutation probability. A new selection strategy, namely disruptive selection, is proposed to maintain the diversity of the algorithm. The results show that the proposed algorithm achieves better overall performance on the standard test functions. Meanwhile, IdynFWA is used to optimize the Extreme Learning Machine (ELM), and a virtual machine fault warning model is proposed based on ELM optimized by IdynFWA. The results show that this model can achieve higher accuracy and better stability to some extent.

Fireworks algorithm (FWA) is an emerging swarm intelligence inspired by the phenomenon of fireworks explosion. The numbers of sparks generated by fireworks have a great impact on the algorithm performance. It is widely accepted that promising fireworks should generate more sparks. However, in many researches, the quality of a firework is judged only on its current fitness value. This work proposes a Learning Automata-based Fireworks Algorithm (LA-FWA) introduced Learning automata (LA) to assign sparks for a better algorithm performance. Sparks are assigned to fireworks according to a state probability vector, which is updated constantly based on feedbacks from an environment so that it accumulates historical information. The probability vector converges as the search proceeds so that the local search ability of the LAFWA turns strong in the late search stage. Experimental results performed on CEC2013 benchmark functions show that the LAFWA outperforms several pioneering FWA variants.

In recent years, computer technology and artificial intelligence have developed rapidly, and research in the field of mobile robots has continued to deepen with development of artificial intelligence. Path planning is an essential content of mobile robot navigation of computing a collision-free path between a starting point and a goal. It is necessary for mobile robots to move and maneuver in different kinds of environment with objects and obstacles. The main goal of path planning is to find the optimal path between the starting point and the target position in the minimal possible time. A new firework algorithm (FWA) integrated with a graph theory, Dijkstra's algorithm developed for autonomous robot navigation, is proposed in this chapter. The firework algorithm is improved by a local search procedure that a LIDAR-based local navigator algorithm is implemented for local navigation and obstacle avoidance. The grid map is utilized for real-time intelligent robot mapping and navigation. In this chapter, both simulation and comparison studies of an autonomous robot navigation demonstrate that the proposed model is capable of planning more reasonable and shorter, collision-free paths in non-stationary and unstructured environments compared with other approaches.

The main goal of this paper is to improve the performance of the Fuzzy Fireworks Algorithm (FFWA), which is a variation of conventional Fireworks Algorithm (FWA). In previous work the FFWA was proposed on Type-1 Fuzzy Logic to adjust parameters dynamically and the difference now in this work is that we use the Interval Type-2 Fuzzy Logic for and adjust the parameter of the explosion amplitude of each firework, and this variation, we called as Interval Type-2 Fuzzy Fireworks Algorithm and we denoted as IT2FFWA. To evaluate the performance of FFWA and IT2FFWA we tested both algorithms with 12 mathematical Benchmark functions.

Financial time series are highly nonlinear and their movement is quite unpredictable. Artificial neural networks (ANN) have ample applications in financial forecasting. Performance of ANN models mainly depends upon its training. Though gradient descent-based methods are common for ANN training, they have several limitations. Fireworks algorithm (FWA) is a recently developed metaheuristic inspired from the phenomenon of fireworks explosion at night, which poses characteristics such as faster convergence, parallelism, and finding the global optima. This chapter intends to develop a hybrid model comprising FWA and ANN (FWANN) used to forecast closing prices series, exchange series, and crude oil prices time series. The appropriateness of FWANN is compared with models such as PSO-based ANN, GA-based ANN, DE-based ANN, and MLP model trained similarly. Four performance metrics, MAPE, NMSE, ARV, and R2, are considered as the barometer for evaluation. Performance analysis is carried out to show the suitability and superiority of FWANN.

This chapter proposes the application of a discrete version of the Fireworks Algorithm (FWA) and a novel PSO-FWA hybrid algorithm to optimize the energy efficiency of a metro railway line. This optimization consists in determining the optimal configuration of the Energy Storage Systems (ESSs) to install in a railway line, including their number, location, and power (kW). The installation of the ESSs will improve the energy efficiency of the system by incrementing the use of the regenerated energy produced by the trains in the braking phases, as the ESSs will store the excess of regenerated energy and return it to the system when necessary. The results for this complex optimization problem produced by the two algorithms are excellent and authors prove that the novel PSO-FWA algorithm proposed in this chapter outperforms the standard FWA.

The crow is one of the most intelligent bird and infamous for observing other birds so that they can steal their food. The crow search algorithm (CSA), a nature-based optimizer, is inspired by the social behavior of crows. Scholars have applied the CSA to obtain efficient solutions to certain function and combinatorial optimization problems. Another popular and powerful method with several real-world applications (e.g., energy, finance, marketing, and medical imaging) is fuzzy clustering. The fuzzy c-means (FCM) algorithm is a critical fuzzy clustering approach given its efficiency and implementation easily. However, the FCM algorithm can be easily trapped in the local optima. To solve this data clustering problem, this study proposes a hybrid fuzzy clustering algorithm combines the CSA and a fireworks algorithm. The algorithm performance is evaluated using eight well-known UCI benchmarks. The experimental analysis concludes that adding the fireworks algorithm improved the CSA’s performance and offered better solutions than those by other meta-heuristic algorithms.

As a recently developed swarm intelligence algorithm, fireworks algorithm (FWA) is an optimization algorithm with good convergence and extensible properties. Moreover, it is usually able to find the global solutions. The advantages of FWA are both optimization accuracy and convergence speed which endue the FWA with a promising prospect of application and extension. This chapter mainly focuses on the application of FWA in classification problems and the improvement of FWA. Many prior studies around FWA have been produced. The author here probes improvement of FWA and its application in classification. The chapter studies FWA around: (1) Application of FWA in classification problems; (2) Improvement of FWA's candidate solution generation strategy (CSGS), including the employment of self-adaptive mechanisms; (3) Improved SaFWA and classification model. For each part, the author conducts research through theory, experimentation, and results analysis.

This chapter briefly reviews the basic explosion mechanism used in the fireworks algorithm (FWA) and comprehensively investigates relevant research on explosion operations. Since the explosion mechanism is one of the most core operations directly affecting the performance of FWA, the authors focus on analyzing the FWA explosion operation and highlighting two novel explosion strategies: a multi-layer explosion strategy and a scouting explosion strategy. The multi-layer explosion strategy allows an individual firework to perform multiple explosions instead of the single explosion used in the original FWA, where each round of explosion can be regarded as a layer; the scouting explosion strategy controls an individual firework to generate spark individuals one by one instead of generating all spark individuals within the explosion amplitude at once. The authors then introduce several other effective strategies to further improve the performance of FWA by full using the information generated by the explosion operation. Finally, the authors list some open topics for discussion.