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The purpose of this paper is to present a modified firefly algorithm (FA) considering the population diversity to avoid local optimum and improve the algorithm’s precision.

When the population diversity is below the given threshold value, the fireflies’ positions update according to the modified equation which can dynamically adjust the fireflies’ exploring and exploiting ability.

A novel metaheuristic algorithm called FA has emerged. It is inspired by the flashing behavior of fireflies. In basic FA, randomly generated solutions will be considered as fireflies, and brightness is associated with the objective function to be optimized. However, during the optimization process, the fireflies become more and more similar and gather into the neighborhood of the best firefly in the population, which may make the algorithm prematurely converged around the local solution.

Due to different dimensions and different ranges, the population diversity is different undoubtedly. And how to determine the diversity threshold value is still required to be further researched.

This paper presents a modified FA which uses a diversity threshold value to guide the algorithm to alternate between exploring and exploiting behavior. Experiments on 17 benchmark functions show that the proposed algorithm can improve the performance of the basic FA.

This paper aims to propose an optimized overview of firefly algorithm (FA) over physical-natural impression of fireflies and its application in mobile robot navigation under the natural intelligence mechanism.

The brightness and luminosity are the decision variables in proposed study. The paper achieves the two major goals of robot navigation; first, the optimum path generation and, second, as an obstacle avoidance by co-in-centric sphere-based geometrical technique. This technique comprises the optimum path decision to objective function and constraints to paths and obstacles as the function of algebraic-geometry co-relation. Co-in-centric sphere is the proposed technique to correlate the constraints.

It is found that the present FA based on concentric sphere is suitable for efficient navigation of mobile robots at the level of optimum significance when compared with other approaches.

The paper introduces a novel approach to implement the FA for unknown and uncertain environment.

For delivering high-quality software applications, proper testing is required. A software test will function successfully if it can find more software faults. The traditional method of assessing the quality and effectiveness of a test suite is mutation testing. One of the main drawbacks of mutation testing is its computational cost. The research problem of this study is the high computational cost of the mutation test. Reducing the time and cost of the mutation test is the main goal of this study.

With regard to the 80–20 rule, 80% of the faults are found in 20% of the fault-prone code of a program. The proposed method statically analyzes the source code of the program to identify the fault-prone locations of the program. Identifying the fault-prone (complex) paths of a program is an NP-hard problem. In the proposed method, a firefly optimization algorithm is used for identifying the most fault-prone paths of a program; then, the mutation operators are injected only on the identified fault-prone instructions.

The source codes of five traditional benchmark programs were used for evaluating the effectiveness of the proposed method to reduce the mutant number. The proposed method was implemented in Matlab. The mutation injection operations were carried out by MuJava, and the output was investigated. The results confirm that the proposed method considerably reduces the number of mutants, and consequently, the cost of software mutation-test.

The proposed method avoids the mutation of nonfault-prone (simple) codes of the program, and consequently, the number of mutants considerably is reduced. In a program with n branch instructions (if instruction), there are 2n execution paths (test paths) that the data and codes into each of these paths can be considered as a target of mutation. Identifying the error-prone (complex) paths of a program is an NP-hard problem. In the proposed method, a firefly optimization algorithm as a heuristic algorithm is used for identifying the most error-prone paths of a program; then, the mutation operators (faults) are injected only on the identified fault-prone instructions.

The purpose of this paper is to minimize the mean flow time in open shop scheduling problem (OSSP). The scheduling problems consist of n jobs and m machines, in which each job has O operations. The processing time for 50 OSSP was generated using a linear congruential random number.

Different evolutionary algorithms are used to minimize the mean flow time of OSSP. This research study used simulated annealing (SA), Discrete Firefly Algorithm and a Hybrid Firefly Algorithm with SA. These methods are referred as A1, A2 and A3, respectively.

A comparison of the results obtained from the three methods shows that the Hybrid Firefly Algorithm with SA (A3) gives the best mean flow time for 76 percent instances. Also, it has been observed that as the number of jobs increases, the chances of getting better results also increased. Among the first 25 problems (i.e. job ranging from 3 to 7), A3 gave the best results for 13 instances, i.e., for 52 percent of the first 25 instances. While for the last 25 problems (i.e. Job ranging from 8 to 12), A3 gave the best results for all 25 instances, i.e. for 100 percent of the problems.

From the literature it has been observed that no researchers have attempted to solve OOSPs using Firefly Algorithm (FA). In this research work an attempt has been made to apply the FA and its hybridization to solve OSSP. Also the research work carried out in this paper can also be applied for a real-time Industrial problem.

The purpose of this paper is to develop, extend and propose an improved proportional integral derivative (PID) rate control of a quadrotor unmanned aerial vehicle based on a convexity-based surrogated firefly algorithm.

An improved PID controller structure is proposed for the rate dynamics of the quadrotor. Optimality of the controller is ensured by a recent, simple yet efficient firefly optimization method. The hybrid structure is further enhanced with a convexity-based surrogated model function.

Monte Carlo, transient response, error metrics and histogram distribution analyzes are conducted to show the performance of the proposed controller. The performance of the proposed method is evaluated under various convex combination values to further investigate the effect of the proposed surrogated model. According to the results, the proposed method is capable of controlling the rate quadrotor dynamics with the steady-state error of 0.0023 (rad/s) for P, −0.0024 (rad/s) for Q and 0 (rad/s) for the R state, respectively. Also, the least mean objective value is achieved at = 0 value of convexity in Monte Carlo trials.

The originality of this paper is to propose an improved PID rate controller with a convexity-based surrogated firefly algorithm.

Assembly lines are one of the places where energy consumption is intensive in manufacturing enterprises. The use of robots in assembly lines not only increases productivity but also increases energy consumption and carbon emissions. The purpose of this paper is to minimize the cycle time and total energy consumption simultaneously in parallel robotic assembly lines (PRAL).

Due to the NP-hardness of the problem, A Pareto hybrid discrete firefly algorithm based on probability attraction (PHDFA-PA) is developed. The algorithm parameters are optimized using the Taguchi method. To evaluate the results of the algorithm, a multi-objective programming model and a restarted simulated annealing (RSA) algorithm are used.

According to the comparative study, the PHDFA-PA has a competitive performance with the RSA. Thus, it is possible to achieve a sustainable PRAL through the proposed method by addressing the cycle time and total energy consumption simultaneously.

To the best knowledge of the authors, this is the first study addressing energy consumption in PRAL. The proposed method for PRAL is efficient in solving the multi-objective balancing problem.

Accurate foreign tourist arrivals forecasting can help public and private sectors to formulate scientific tourism planning and improve the allocation efficiency of tourism resources. This paper aims to address the problem of low prediction accuracy of Chinese inbound tourism demand caused by the lack of valid historical data.

A novel hybrid Chinese inbound tourism demand forecasting model combining fractional non-homogenous discrete grey model and firefly algorithm is constructed. In the proposed model, all adjustable parameters of the fractional non-homogenous discrete grey model are optimized simultaneously by the firefly algorithm.

The data sets of annual foreign tourist arrivals to China are used to verify the validity of the proposed model. Experimental results show that the proposed method is effective and can be used as a useful predictor for the prediction of Chinese inbound tourism demand.

The method proposed in this paper is effective and can be used as a feasible approach for forecasting the development trend of Chinese inbound tourism.

Phishing is one of the major challenges faced by the world of e-commerce today. Thanks to phishing attacks, billions of dollars has been lost by many companies and individuals. The global impact of phishing attacks will continue to be on the increase and thus a more efficient phishing detection technique is required. The purpose of this paper is to investigate and report the use of a nature inspired based-machine learning (ML) approach in classification of phishing e-mails.

ML-based techniques have been shown to be efficient in detecting phishing attacks. In this paper, firefly algorithm (FFA) was integrated with support vector machine (SVM) with the primary aim of developing an improved phishing e-mail classifier (known as FFA_SVM), capable of accurately detecting new phishing patterns as they occur. From a data set consisting of 4,000 phishing and ham e-mails, a set of features, suitable for phishing e-mail detection, was extracted and used to construct the hybrid classifier.

The FFA_SVM was applied to a data set consisting of up to 4,000 phishing and ham e-mails. Simulation experiments were performed to evaluate and compared the performance of the classifier. The tests yielded a classification accuracy of 99.94 percent, false positive rate of 0.06 percent and false negative rate of 0.04 percent.

The hybrid algorithm has not been earlier apply, as in this work, to the classification and detection of phishing e-mail, to the best of the authors’ knowledge.

This study aims to present a unique hybrid metaheuristic approach to solving the nonlinear analysis of hall currents and electric double layer (EDL) effects in multiphase wavy flow by merging the firefly algorithm (FA) and the water cycle algorithm (WCA).

Nonlinear Hall currents and EDL effects in multiphase wavy flow are originally described by partial differential equations, which are then translated into an ordinary differential equation model. The hybrid FA-WCA technique is used to take on the optimization challenge and find the best possible design weights for artificial neural networks. The fitness function is efficiently optimized by this hybrid approach, allowing the optimal design weights to be determined.

The proposed strategy is shown to be effective by taking into account multiple variables to arrive at a single answer. The numerical results obtained from the proposed method exhibit good agreement with the reference solution within finite intervals, showcasing the accuracy of the approach used in this study. Furthermore, a comparison is made between the presented results and the reference numerical solutions of the Hall Currents and electroosmotic effects in multiphase wavy flow problem.

This comparative analysis includes various performance indices, providing a statistical assessment of the precision, efficiency and reliability of the proposed approach. Moreover, to the best of the authors’ knowledge, this is a new work which has not been explored in existing literature and will add new directions to the field of fluid flows to predict most accurate results.

Cloud eases information processing, but it holds numerous risks, including hacking and confidentiality problems. It puts businesses at risk in terms of data security and compliance. This paper aims to maximize the covered human resource (HR) vulnerabilities and minimize the security costs in the enterprise cloud using a fuzzy-based method and firefly optimization algorithm.

Cloud computing provides a platform to improve the quality and availability of IT resources. It changes the way people communicate and conduct their businesses. However, some security concerns continue to derail the expansion of cloud-based systems into all parts of human life. Enterprise cloud security is a vital component in ensuring the long-term stability of cloud technology by instilling trust. In this paper, a fuzzy-based method and firefly optimization algorithm are suggested for optimizing HR vulnerabilities while mitigating security expenses in organizational cloud environments. MATLAB is employed as a simulation tool to assess the efficiency of the suggested recommendation algorithm. The suggested approach is based on the firefly algorithm (FA) since it is swift and reduces randomization throughout the lookup for an optimal solution, resulting in improved performance.

The fuzzy-based method and FA unveil better performance than existing met heuristic algorithms. Using a simulation, all the results are verified. The study findings showed that this method could simulate complex and dynamic security problems in cloud services.

The findings may be utilized to assist the cloud provider or tenant of the cloud infrastructure system in taking appropriate risk mitigation steps.

Using a fuzzy-based method and FA to maximize the covered HR vulnerabilities and minimize the security costs in the enterprise cloud is the main novelty of this paper.