This study adopted a metaheuristic approach based on the firefly algorithm (FA) optimization to generate an appropriate configuration for an 8 × 8 Substitution boxes (S-boxes). The FA can construct a ...strong S-box that satisfies the stipulated criteria by rapidly searching for the optimal or near-optimal feature subsets that minimize a given fitness function. The FA is a newly developed computation technique inspired by fireflies and their flash lighting process. However, FA may suffer from premature convergence when solving optimization problems. This study proposes a new FA modification, namely, globalized firefly algorithm (GFA), which employs random movement based on the best firefly using chaotic maps. The best firefly does not conduct any search in the standard firefly algorithm (SFA). The proposed algorithm utilizes a new design for retrieving strong S-boxes based on SFA and GFA.
Bijectivity, strict avalanche criteria, nonlinearity, input/output XOR distribution, bit independence criteria, and linear probability were also analyzed. The result was compared with a few previous S-box generation methods. Overall, the experimental outcome revealed that the design of the proposed S-boxes has satisfactory cryptographic characteristics.
•A hybrid FA and PS technique is proposed for AGC of multi-area power system.•A two area two unit non-reheat thermal systems is initially considered.•Proposed approach exhibits better performance ...than ZN, GA, BFOA and FA approaches.•Sensitivity analysis is performed to show the robustness of the proposed controllers.•The study is extended to four unit hydro thermal system with/without physical constraints.
In this paper, a novel hybrid Firefly Algorithm and Pattern Search (hFA–PS) technique is proposed for Automatic Generation Control (AGC) of multi-area power systems with the consideration of Generation Rate Constraint (GRC). Initially a two area non-reheat thermal system with Proportional Integral Derivative (PID) controller is considered and the parameters of PID controllers are optimized by Firefly Algorithm (FA) employing an Integral Time multiply Absolute Error (ITAE) objective function. Pattern Search (PS) is then employed to fine tune the best solution provided by FA. The superiority of the proposed hFA–PS based PID controller has been demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA) and conventional Ziegler Nichols (ZN) based PI/PID controllers for the same interconnected power system. Furthermore, sensitivity analysis is performed to show the robustness of the optimized controller parameters by varying the system parameters and operating load conditions from their nominal values. Finally, the proposed approach is extended to multi area multi source hydro thermal power system with/without considering the effect of physical constraints such as time delay, reheat turbine, GRC, and Governor Dead Band (GDB) nonlinearity. The controller parameters of each area are optimized under normal and varied conditions using proposed hFA–PS technique. It is observed that the proposed technique is able to handle nonlinearity and physical constraints in the system model.
In this paper, a Firefly Algorithm (FA) based Fractional Order PID (FOPID) Controller is proposed for Brushless DC (BLDC) motor to achieve an effective control of torque and speed. In a conventional ...control of BLDC motors, the torque references are converted into current references and phase currents are controlled using current controllers. This indirect way of controlling torque is not effective and results in a ripple in the torque. This paper proposes a direct instantaneous scheme in which reference torques are compared with estimated torques directly and the error is given to FOPID controller. The FOPID torque controller controls the motor torque effectively with a very low ripple. Here, FA technique is used to tune the FOPID parameters. Simulation results are verified in Matlab/Simulink environment and also the effectiveness of proposed FOPID controller is compared with GA based FOPID controller.
Wireless Sensor Networks (WSN) are operated on battery source, and the sensor nodes are used for collecting the information from the environment and transmitting the same to the base station. The ...sensor nodes consume more energy for the process of data communication and also affect the network lifetime. Energy efficiency is one of the important features for designing the sensor networks. Clustering technique is mainly used to perform the energy-efficient data transmission that consumes the minimum energy and also prolongs the lifetime of the network. In this paper, a Hybrid approach of Firefly Algorithm with Particle Swarm Optimization (HFAPSO) is proposed for finding the optimal cluster head selection in the LEACH-C algorithm. The hybrid algorithm improves the global search behavior of fireflies by using PSO and achieves optimal positioning of the cluster heads. The performance of the proposed methodology is evaluated by using the number of alive nodes, residual energy and throughput. The results show the improvement in network lifetime, thus increasing the alive nodes and reducing the energy utilization. While making a comparison with the firefly algorithm, it has been found that the proposed methodology has achieved better throughput and residual energy.
•A new discrete constrained Electromagnetism-like Firefly Algorithm (EFA) for solving discrete optimization problems.•Modified interactive forces among individuals for improving bi-directional local ...search ability of EFA and handling constrained violations.•A novel “current-to-best” electromagnetic movement for enhancing the convergence speed of EFA.•A harmonized selection mechanism combined with the traditional and elitist selections is proposed and applied.•A rounding technique is applied to the proposed EFA, FA and EM for solving discrete optimization problems.
A new optimization method called Electromagnetism-like Firefly Algorithm (EFA), which is a novel hybrid between the Electromagnetism-like Algorithm (EM) and the Firefly Algorithm (FA) for discrete structural optimization is proposed. The EFA inherits the advantages of both the FA and the EM. This proposed optimization algorithm is then presented to improve both solution accuracy and convergence speed, as well as to treat constrained optimization problems with discrete design variables. In EFA, modified formulas of interactive forces are used to increase the diversification of the population, and the constraint violations are embedded into the charges of all electromagnetic fireflies to avoid becoming trapped in unfeasible domains. A mechanism called “current-to-best” electromagnetic movement is incorporated with traditional interactive movements to balance the exploration and the exploitation abilities of the EFA. In the local search phase, a newly bi-directional searching procedure is performed on the best firefly to intensify effectively its local optimum. In order to guarantee the convergence capability of the EFA, a harmonized selection mechanism combined with the traditional and elitist selections is proposed and applied if the algorithm cannot find a better optimal solution during a number of predetermined optimization loops. In addition, in this study, the FA and EM with some improvements in several phases are also proposed to solve the constrained optimization problems. Finally, a rounding technique is applied to the proposed EFA, FA and EM for solving discrete optimization problems. The improved performance of the EFA in comparison with the FA, EM as well as other optimization algorithms in the literature is demonstrated by six popular truss optimization problems with discrete variables.
Photovoltaic modules subjected to partial shading conditions (PSC) can drastically decrease their power output. Hence, there have been various maximum power point tracking (MPPT) control algorithms ...developed to reduce or counteract the shading effects. Recently, a new metaheuristic algorithm known as firefly algorithm (FA) was developed, which, under PSC, has been shown to successfully track the global maximum point (GMP). Nevertheless, the FA still has some inherent problems that may hinder the performance of the MPPT. This paper modifies the existing FA to counteract these problems. As will be demonstrated in this paper, the proposed modified FA method can reduce the number of computation operations and the time for converging to the GMP that the existing FA requires. Experimental results show that the proposed method can track the global point under various PSC, has a faster convergence time compared with the FA, and can effectively suppress power and voltage fluctuations.
•A hybrid FA and PS optimized fuzzy PID controller is proposed for LFC of multi-area power system.•Proposed approach exhibits better performance than DE and CPSO approaches.•Sensitivity analysis is ...performed to show the robustness of the proposed controllers.•The study is extended to a three unequal area by considering the physical constraints.•Parameters of the proposed controllers need not be reset with system parameter variation.
A hybrid Firefly Algorithm (FA) and Pattern Search (PS) optimized fuzzy PID controller is proposed for Load Frequency Control (LFC) of multi area power systems. Initially a two area thermal system with Governor Dead Band (GDB) nonlinearity is considered and the gains of the fuzzy PID controller are optimized employing a hybrid FA and PS (hFA–PS) optimization technique. The supremacy of proposed hFA–PS over FA is also demonstrated. The advantage of the proposed fuzzy PID controller has been shown by comparing the results with some recently published techniques, such as Differential Evolution (DE) and Craziness based Particle Swarm Optimization (CPSO). Further, sensitivity analysis is performed by varying the system parameters and operating load conditions from their nominal values. It is observed that the optimum gains of the proposed controller need not be reset even if the system is subjected to wide variation in loading condition and system parameters. Additionally, the proposed approach is further extended to three unequal area thermal systems with physical constraints such as time delay, reheat turbine, Generation Rate Constraint (GRC) and GDB nonlinearity. It is observed that the proposed technique is able to handle nonlinearity and physical constraints in the system model.
A firefly algorithm (FA) inspired band selection and optimized extreme learning machine (ELM) for hyperspectral image classification is proposed. In this framework, FA is to select a subset of ...original bands to reduce the complexity of the ELM network. It is also adapted to optimize the parameters in ELM (i.e., regularization coefficient C, Gaussian kernel σ, and hidden number of neurons L). Due to very low complexity of ELM, its classification accuracy can be used as the objective function of FA during band selection and parameter optimization. In the experiments, two hyperspectral image datasets acquired by HYDICE and HYMAP are used, and the experiment results indicate that the proposed method can offer better performance, compared with particle swarm optimization and other related band selection algorithms.
The Maximal Covering Location Problem (MCLP) is concerned with the optimal placement of a fixed number of facilities to cover the maximum number of customers. This article considers a new variant of ...MCLP where both the coverage radii of facilities and the distance between customer and facility are fuzzy. Moreover, the finite capacity of each facility is considered. We call this problem the capacitated MCLP with fuzzy coverage area (FCMCLP), and it is formulated as a 0–1 linear programming problem. In this article, two classical metaheuristics: particle swarm optimization, differential evolution, and two new-generation metaheuristics: artificial bee colony algorithm, firefly algorithm, are proposed for solving FCMCLP. Each of the customized metaheuristics utilizes a greedy deterministic heuristic to generate their initial populations. They also incorporate a local neighborhood search to improve their convergence rates. New instances of FCMCLP are generated from the traditional MCLP instances available in the literature, and IBM’s CPLEX solver is used to generate benchmark solutions. An experimental comparative study among the four customized metaheuristics is described in this article. The performances of the proposed metaheuristics are also compared with the benchmark solutions obtained from CPLEX.
•A new variant of the maximal covering location problem is considered•Capacitated facilities with fuzzy coverage areas are considered.•Benchmark solutions are generated using CPLEX solver for newly generated instances.•A comparative study among four metaheuristic algorithms is presented.
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