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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.

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.

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.

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.

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.

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.

Supply chains (SCs) have been growingly virtualized in response to the market challenges and opportunities that are presented by new and cost-effective internet-based technologies today. This paper designed a virtual closed-loop supply chain (VCLSC) network based on multiperiod, multiproduct and by using the Internet of Things (IoT). The purpose of the paper is the optimization of the VCLSC network.

The proposed model considers the maximization of profit. For this purpose, costs related to virtualization such as security, energy consumption, recall and IoT facilities along with the usual costs of the SC are considered in the model. Due to real-world demand fluctuations, in this model, demand is considered fuzzy. Finally, the problem is solved using the Grey Wolf algorithm and Firefly algorithm. A numerical example and sensitivity analysis on the main parameters of the model are used to describe the importance and applicability of the developed model.

The findings showed that the Firefly algorithm performed better and identified more profit for the SC in each period. Also, the results of the sensitivity analysis using the IoT in a VCLSC showed that the profit of the virtual supply chain (VSC) is higher compared to not using IoT due to tracking defective parts and identifying reversible products. In proposed model, chain members can help improve chain operations by tracking raw materials and products, delivering products faster and with higher quality to customers, bringing a new level of SC efficiency to industries. As a result, VSCs can be controlled, programmed and optimized remotely over the Internet based on virtual objects rather than direct observation.

There are limited researches on designing and optimizing the VCLSC network. This study is one of the first studies that optimize the VSC networks considering minimization of virtual costs and maximization of profits. In most researches, the theory of VSC and its advantages have been described, while in this research, mathematical optimization and modeling of the VSC have been done, and it has been tried to apply SC virtualization using the IoT. Considering virtual costs in VSC optimization is another originality of this research. Also, considering the uncertainty in the SC brings the issue closer to the real world. In this study, virtualization costs including security, recall and energy consumption in SC optimization are considered.

1. Investigates the role of IoT for virtual supply chain profit optimization and mathematical optimization of virtual closed-loop supply chain (VCLSC) based on multiperiod, multiproduct with emphasis on using the IoT under uncertainty.

2. Considering the most important costs of virtualization of supply chain include: cost of IoT information security, cost of IoT energy consumption, cost of recall the production department, cost of IoT facilities.

3. Selection of the optimal suppliers in each period and determination of the price of each returned product in virtual supply chain.

4. Solving and validating the proposed model with two meta-heuristic algorithms (the Grey Wolf algorithm and Firefly algorithm).

Investigates the role of IoT for virtual supply chain profit optimization and mathematical optimization of virtual closed-loop supply chain (VCLSC) based on multiperiod, multiproduct with emphasis on using the IoT under uncertainty.

Considering the most important costs of virtualization of supply chain include: cost of IoT information security, cost of IoT energy consumption, cost of recall the production department, cost of IoT facilities.

Selection of the optimal suppliers in each period and determination of the price of each returned product in virtual supply chain.

Solving and validating the proposed model with two meta-heuristic algorithms (the Grey Wolf algorithm and Firefly algorithm).

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.

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.

Optimization involves changing the input parameters of a process that is experimented with different conditions to obtain the maximum or minimum result. Increasing interest is shown by antenna researchers in finding the optimum solution for designing complex antenna arrays which are possible by optimization techniques.

Design of antenna array is a significant electro-magnetic problem of optimization in the current era. The philosophy of optimization is to find the best solution among several available alternatives. In an antenna array, energy is wasted due to side lobe levels which can be reduced by various optimization techniques. Currently, developing optimization techniques applicable for various types of antenna arrays is focused on by researchers.

In the paper, different optimization algorithms for reducing the side lobe level of the antenna array are presented. Specifically, genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO), cuckoo search algorithm (CSA), invasive weed optimization (IWO), whale optimization algorithm (WOA), fruitfly optimization algorithm (FOA), firefly algorithm (FA), cat swarm optimization (CSO), dragonfly algorithm (DA), enhanced firefly algorithm (EFA) and bat flower pollinator (BFP) are the most popular optimization techniques. Various metrics such as gain enhancement, reduction of side lobe, speed of convergence and the directivity of these algorithms are discussed. Faster convergence is provided by the GA which is used for genetic operator randomization. GA provides improved efficiency of computation with the extreme optimal result as well as outperforming other algorithms of optimization in finding the best solution.

The originality of the paper includes a study that reveals the usage of the different antennas and their importance in various applications.