Firefly Algorithm Based on Level-Based Attracting and Variable Step Size

In this paper, the Black–Scholes (B–S) model for the pricing of the European and the barrier call options are considered, which yields a partial differential problem. First, A numerical technique based on Crank–Nicolson (C–N) method is used to discretisize the time domain. Consequently, the partial differential equation will be converted to a system of an ordinary differential equation (ODE). Then, the multiple shooting method combined with Lagrange polynomials is utilized to solve the ODEs. Regarding the convergence order of the approximate solution which normally decreases due to the non-smooth properties of the option’s payoff (at the strike price), in this study, the equipped C–N scheme with variable step size strategy is applied for the time discretization. As a result, the variable step size strategy prevents the error propagation by controlling the error at each time step and increases the computational speed by raising the step size in the smooth points of the domain. In order to implement the variable step size, an algorithm is presented. In addition, the stability of the presented method is analyzed. The extracted numerical results represent the accuracy and efficiency of the proposed method.

The maximum power point tracking (MPPT) system ensures that the solar cell operates at its maximum power point, which is the point at which it produces the most power for a given set of conditions. This study uses an artificial bee colony (ABC) algorithm and particle swarm optimization (PSO) algorithms to optimize the boost converter. The ABC and PSO algorithms help to optimize the boost converter by finding the best possible duty cycle and other parameters that maximize efficiency. The resulting duty cycle of 20% produced the highest efficiency of 78.26% obtained from the boost converter. A system-wide test was conducted between 9:00 and 11:10 WIB. In MPPT systems using boost converters with the PSO algorithm, the average power is 16.80 W, while in MPPT systems using boost converters with the ABC algorithm, the average power is 14.53 W. The novelty of the study discusses a system designed to optimize power by using a boost converter in order to increase power output from solar panels. The algorithms PSO and ABC are used to analyze the data from the PV and adjust the converter parameters to optimize the output in order to increase the efficiency of the system.

This paper investigates the use of a Hybrid Energy Storage System (HESS) that contains a battery and fuel cell system with a microgrid (MG) to perform multiple functions such as supply-demand matching and energy arbitrage. The main objective of the proposed study is to obtain the optimal size of the MG system which minimizes the total costs and the total emissions. The problem is formulated as a nonlinear optimization problem with different constraints and solved using Hybrid Firefly and Particle Swarm Optimization (HFPSO) algorithm. To validate the effectiveness of the HFPSO, the HFPSO is compared with the Particle Swarm Optimization (PSO) algorithm and the Firefly algorithm (FA). The result of the comparison proves the effectiveness of the HFPSO, and this is considered the main reason for using the HFPSO to solve the proposed difficult optimization problem. The problem is implemented using MATLAB software. The policy of the MG system is illustrated, and the results and the curves are discussed to validate this policy.

The paper reviews and introduces the state-of-the-art nature-inspired metaheuristic algorithms in optimization, including Firefly algorithm, PSO algorithms and ABC algorithm. By implementing these algorithms in Matlab, we will use worked examples to show how each algorithm works. Firefly algorithm is one of the evolutionary optimization algorithms, and is inspired by the flashing behaviour of fireflies in nature. There are many noisy non-linear mathematical optimization problems that can be effectively solved by Metaheuristic Algorithms. Mathematical optimization or programming is the study of such planning and design problems using mathematical tools. Nowadays, computer simulations become an indispensable tool for solving such optimization problems with various efficient search algorithms. Nature-inspired algorithms are among the most powerful algorithms for optimization. Firefly algorithm is one of the new metaheuristic algorithms for optimization problems. The algorithm is inspired by the flashing behaviour of fireflies. A Firefly Algorithm (FA) is a recent nature inspired optimization algorithm, which simulates the flash pattern and characteristics of fireflies. It is a powerful swarm intelligence algorithm inspired by the flash phenomenon of the fireflies. In this context, three types of meta-heuristics called Artificial bee Colony algorithm, Particle Swarm Optimization (PSO) and Firefly algorithms were devised to find optimal solutions of noisy non-linear continuous mathematical models. A series of computational experiments using each algorithm were conducted. The stimulation result of this experiment were analyzed and compared to the best solutions found so The Firefly algorithm in each noisy non linear optimization function seems to perform better and efficient.

A variable step size total least squares affine-projection-like algorithm: Formula derivation and performance analysis

Aiming at the low computational efficiency of the fixed-step solution of the standard parabolic equation (SPE) in the study of complex environmental radio wave propagation, a variable step size technology for the standard parabolic equation is proposed. Based on the relationship between the factors such as step size and frequency with the calculation error in the SSFT solution, the basic criteria for the SPE variable step size solution are proposed; secondly, the complex environment of SPE application is graded, and the corresponding step size is selected for different complex environment levels under the condition of satisfying the error requirement. Finally, the method is used to simulate the radio wave characteristics of typical complex environment. The calculation results verify the reliability and efficiency of the proposed method. It shows that the proposed method can greatly improve the computational efficiency of parabolic equations under the condition of ensuring the accuracy of calculation.

Summary form only given. This paper presents a Variable Step Size (VSS) technique that is integrated with a Stop-And-Go (SAG) approach for blind adaptive equalization of Quadrature Amplitude Modulation (QAM) signals. The proposed technique is applied to the Constant-Modulus Algorithm (CMA) and the Multi-Modulus Algorithm (MMA). The SAG approach allows the VSS technique to either vary the step size or to hold the previous one depending on a specific error criterion. This leads to the reduction of the amount of computations involved Simulation results show that algorithms with the VSS technique result in less steady-state Mean-Squared Errors (MSEs) than those obtained for algorithms without the VSS technique for the same speed of convergence.

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

Hippopotamus algorithm for optimal sizing of hybrid renewable energy system

Delta Sigma Analog to Digital Converters (ADCs) are superior to their counterparts in achieving high resolution for low to medium bandwidth applications. This paper discusses an improved digital calibration technique for enhancing Signal to Noise ratio (SNR) of Delta Sigma ADC which is directly related to Effective Number of Bits (ENOB). The proposed method uses the Adaptive Line Enhancer (ALE) for improving the SNR of the modulator. Adaptive Line Enhancer filters out the estimate of signal of interest from noisy input signal by updating filter coefficients using Least Mean Square (LMS) Algorithm. Variable step size (VSS) LMS is used for updating filter coefficients in Adaptive Line Enhancer instead of Fixed step size (FSS) LMS to reduce the required number of iterations. The simulation results for second order single loop Delta Sigma modulator show approximately 20dB improvement in SNR after calibration and substitution of VSS LMS with FSS LMS has reduced approximately 4000 iterations.

An adaptive system is a well-known method for removing noise from noise-corrupted speech. The problem arises in many situations such as airplane cockpits and automobiles. The variable step size normalized least mean squares (VSS-NLMS) algorithm incorporating a variable step size parameter whose values are based on the ratio of signal-to-noise power has very good convergence speed and low steady-state misadjustment. This paper investigates the rate of convergence by the wavelet based LMS (WLMS) algorithm to the noise speech problem. Simulation results are presented to compare the performance of the variable step size NLMS algorithm, the wavelet based LMS Algorithm, and other commonly used fixed step size LMS algorithms.

A novel performance criterion approach to optimum design of PID controller using cuckoo search algorithm for AVR system

Swarm intelligence (SI) optimization algorithms are fast and robust global optimization methods, and have attracted significant attention due to their ability to solve complex optimization problems. The underlying idea behind all SI algorithms is similar, and various SI algorithms differ only in their details. In this paper we discuss the algorithmic equivalence of particle swarm optimization (PSO) and various other newer SI algorithms, including the shuffled frog leaping algorithm (SFLA), the group search optimizer (GSO), the firefly algorithm (FA), artificial bee colony algorithm (ABC) and the gravitational search algorithm (GSA). We find that the original versions of SFLA, GSO, FA, ABC, and GSA, are all algorithmically identical to PSO under certain conditions. We discuss their diverse biological motivations and algorithmic details as typically implemented, and show how their differences enhance the diversity of SI research and application. Then we numerically compare SFLA, GSO, FA, ABC, and GSA, with basic and advanced versions on some continuous benchmark functions and combinatorial knapsack problems. Empirical results show that an advanced version of ABC performs best on the continuous benchmark functions, and advanced versions of SFLA and GSA perform best on the combinatorial knapsack problems. We conclude that although these SI algorithms are conceptually equivalent, their implementation details result in notably different performance levels.

The step size of least mean square (LMS) algorithm is significant for its performance. To be specific, small step size can get small excess mean square error but results in slow convergence. However, large step size may cause instability. Many variable step size least mean square (VSSLMS) algorithms have been developed to enhance the control performance. In this paper, a new VSSLMS was proposed based on Kwong’s algorithm to evaluate the robustness. The approximate analysis of dynamic and steady-state performance of this developed VSSLMS algorithm was given. An active vibration control system of piezoelectric cantilever beam was established to verify the performance of the VSSLMS algorithms. By comparing with the current VSSLMS algorithms, the proposed method has better performance in active vibration control applications.

Myosin VI dimer walks toward the minus end of the actinfilamentwith a large and variable step size of 25–36 nm. Two competingmodels have been put forward to explain this large step size. TheSpudich model assumes that the myosin VI dimer associates at a distaltail near the cargo-binding domain, which makes two full-length singleα-helix (SAH) domains serve as long legs. In contrast, the Houdusse–Sweeneymodel assumes that the association occurs in the middle (between residues913 and 940) of the SAH domain and that the three-helix bundles unfoldto ensure the large step size. Their consistency with the observationof stepping motion with a large and variable step size has not beenexamined in detail. To compare the two proposed models of myosin VI,we computationally characterized the free energy landscape experiencedby the leading head during the stepping movement along the actin filamentusing the elastic network model of two heads and an implicit modelof the SAH domains. Our results showed that the Spudich model is moreconsistent with the 25–36 nm step size than the Houdusse–Sweeneymodel. The unfolding of the three-helix bundles gives rise to thefree energy bias toward a shorter distance between two heads. Besides,the stiffness of the SAH domain is a key factor for giving strongenergetic bias toward the longer distance of stepping. Free energyanalysis of the stepping motion complements the visual inspectionof static structures and enables a deeper understanding of underlyingmechanisms of molecular motors.