Fractional-order Particle Swarm Optimization Research Articles

Two Improved Multiobjective Fractional-Order Particle Swarm Optimization Algorithms for True Temperature Inversion of Multiwavelength Pyrometer

Two Improved Multiobjective Fractional-Order Particle Swarm Optimization Algorithms for True Temperature Inversion of Multiwavelength Pyrometer

Fraction order particle swarm optimization for parameter extraction of triple-diode photovoltaic models

This work proposes an application of Fractional Order Particle Swarm Optimization (FO-PSO), a meta-heuristic method for parameters estimation of photo-voltaic (PV) module as a non-linear, transcendental, multi-modal and implicit optimization problem. The uses single diode model (SDM), double diode model (DDM) and three-diode model (TDM) of PV modules with the constraint that only data-sheet information may be utilized. A fitness function based on the error amongst the computed values of current and voltage and the ones given in characteristic I-V curves of data-sheet, is minimized using the FO-PSO to get the required parameters. The comparative study between the estimated and data-sheet values provided by PV module manufacturers will determine the effectiveness of this research. The effectiveness of the FO-PSO is demonstrated by comparing the fitness values with that of other techniques. The FO-PSO technique makes a novel contribution to the PV power systems industry by making it possible to obtain a nearly realistic model of any commercial PV module. The effectiveness of the FO-PSO is determined by comparing the results for all the three models with the state of the art optimization techniques. The Root Mean Square error values calculated for the TDM is less than 10e–16, producing very consistent FO-PSO results. Therefore, FO-PSO is anticipated to be a competitive method for obtaining PV module specifications.

Fractional-Order Zener Model with Temperature-Order Equivalence for Viscoelastic Dampers

Viscoelastic (VE) dampers show good performance in dissipating energy, being widely used for reducing vibration in engineering structures caused by earthquakes and winds. Experimental studies have shown that ambient temperature has great influence on the mechanical behavior of VE dampers. Therefore, it is important to accurately model VE dampers considering the effect of temperature. In this paper, a new fractional-order Zener (AEF-Zener) model of VE dampers is proposed. Firstly, the important influence of fractional orders on the energy dissipation ability of materials is analyzed. Secondly, an equivalent AEF-Zener model is developed that incorporates the ambient temperature and fractional-order equivalence principle. Finally, the chaotic fractional-order particle swarm optimization (CFOPSO) algorithm is used to determine the model’s parameters. The accuracy of the AEF-Zener model is verified by comparing model simulations with experimental results. This study is helpful for designing and analyzing vibration reduction techniques for civil structures with VE dampers under the influence of temperature.

Multi-objective fractional-order particle swarm optimization algorithms for data processing of multi-wavelength pyrometer.

This paper focuses the algorithm of the true temperature inversion for high-temperature targets with unknown emissivity by transforming multi-spectral true temperature inversion into multi-objective minimum optimization. Two improved fractional-order particle swarm optimizations (IFOPSO), high-order nonlinear time-varying inertia weight (Hntiw) IFOPSO and global-local best values (Glbest) IFOPSO, are proposed to obtain the true temperature by solving the multi-objective minimum optimization. Combining the inherent advantages of fractional-order calculus to jump out of the local extreme value, the Hntiw IFOPSO algorithm is proposed by replacing the linear time-varying inertia weights with nonlinear functions related to the total number of iterations and the current number of iterations. The Glbest IFOPSO algorithm is designed by using the global local optimal inertia weight and acceleration constant to update the particle velocity and position values, which improves the multi-objective optimization ability and the accuracy of the true temperature inversion. The effectiveness of the proposed methods is verified by the simulation with typical spectral emissivity models and the measured data from rocket tail flame.

Pitch Control of Wind Turbine Blades Using Fractional Particle Swarm Optimization

To achieve the maximum power from wind in variable-speed regions of wind turbines (WTs), a suitable control signal should be applied to the pitch angle of the blades. However, the available uncertainty in the modeling of WTs complicates calculations of these signals. To cope with this problem, an optimal controller is suitable, such as particle swarm optimization (PSO). To improve the performance of the controller, fractional order PSO (FPSO) is proposed and implemented. In order to construct this approach for a two-mass WT, we propose a new state feedback, which was first applied to the turbine. The idea behind this state feedback was based on the Taylor series. Then, a linear model with uncertainty was obtained with a new input control signal. Thereafter, the conventional PSO (CPSO) and FPSO were used as optimal controllers for the resulting linear model. Finally, a comparison was performed between CPSO and FPSO and the fuzzy Takagi–Sugeno–Kang (TSK) inference system. The provided comparison demonstrates the advantages of the Taylor series with combination to these controllers. Notably, without the state feedback, CPSO, FPSO, and TSK fuzzy systems cannot stabilize WTs in tracking the desired trajectory.

Stock Prediction Model Based on Mixed Fractional Brownian Motion and Improved Fractional-Order Particle Swarm Optimization Algorithm

As one of the main areas of value investing, the stock market attracts the attention of many investors. Among investors, market index movements are a focus of attention. In this paper, combining the efficient market hypothesis and the fractal market hypothesis, a stock prediction model based on mixed fractional Brownian motion (MFBM) and an improved fractional-order particle swarm optimization algorithm is proposed. First, the MFBM model is constructed by adjusting the parameters to mix geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM). After that, an improved fractional-order particle swarm optimization algorithm is proposed. The position and velocity formulas of the fractional-order particle swarm optimization algorithm are improved using new fractional-order update formulas. The inertia weight in the update formula is set to be linearly decreasing. The improved fractional-order particle swarm optimization algorithm is used to optimize the coefficients of the MFBM model. Through experiments, the accuracy and validity of the prediction model are proven by combining the error analysis. The model with the improved fractional-order particle swarm optimization algorithm and MFBM is superior to GBM, GFBM, and MFBM models in stock price prediction.

Novel Fractional Swarming with Key Term Separation for Input Nonlinear Control Autoregressive Systems

In recent decades, fractional order calculus has become an important mathematical tool for effectively solving complex problems through better modeling with the introduction of fractional differential/integral operators; fractional order swarming heuristics are also introduced and applied for better performance in different optimization tasks. This study investigates the nonlinear system identification problem of the input nonlinear control autoregressive (IN-CAR) model through the novel implementation of fractional order particle swarm optimization (FO-PSO) heuristics; further, the key term separation technique (KTST) is introduced in the FO-PSO to solve the over-parameterization issue involved in the parameter estimation of the IN-CAR model. The proposed KTST-based FO-PSO, i.e., KTST-FOPSO accurately estimates the parameters of an unknown IN-CAR system with robust performance in cases of different noise scenarios. The performance of the KTST-FOPSO is investigated exhaustively for different fractional orders as well as in comparison with the standard counterpart. The results of statistical indices through Monte Carlo simulations endorse the reliability and stability of the KTST-FOPSO for IN-CAR identification.

Knacks of Fractional Order Swarming Intelligence for Parameter Estimation of Harmonics in Electrical Systems

The efficient parameter estimation of harmonics is required to effectively design filters to mitigate their adverse effects on the power quality of electrical systems. In this study, a fractional order swarming optimization technique is proposed for the parameter estimation of harmonics normally present in industrial loads. The proposed fractional order particle swarm optimization (FOPSO) effectively estimates the amplitude and phase parameters corresponding to the first, third, fifth, seventh and eleventh harmonics. The performance of the FOPSO was evaluated for ten fractional orders with noiseless and noisy scenarios. The robustness efficiency of the proposed FOPSO was analyzed by considering different levels of additive white Gaussian noise in the harmonic signal. Monte Carlo simulations confirmed the reliability of the FOPSO for a lower fractional order (λ = 0.1) with a faster convergence rate and no divergent run compared to other fractional orders as well as to standard PSO (λ = 1).

Ship weather routing optimization based on improved fractional order particle swarm optimization

Based on the original FOPSO (fractional order particle swarm optimization) algorithm, this paper improves new coefficients of the fractional order velocity update formula to avoid falling into local optimization and premature problem. The coefficients change adaptively with the swarm evolution state to make the fractional order velocity occur some disturbances to jump out of the local optimal solution and the search space more comprehensively. In addition, by comparing with other PSO (particle swarm optimization) algorithms for solving typical benchmark functions, the superiority of the improved FOPSO algorithm in solving multi-dimensional nonlinear problems is confirmed. Then, taking a VLCC oil tanker as a research example, it is analyzed that under the objective function of minimum fuel oil consumption (FOC) and Estimated time of arrival (ETA), the maximum profit calculated by the proposed improved algorithm is 9.83 $/nm and 4.17 $/nm higher than that of the actual navigation, respectively. Meanwhile, when the weather forecast data is updated or the ship deviates from the voyage, the improved FOPSO algorithm will update the optimized route according to the current ship's position and sea conditions. Consequently, the improved FOPSO algorithm is quite suitable to solve the ship weather routing optimization problem with constraints.

Analytical stability analysis of the fractional-order particle swarm optimization algorithm

Mathematical modeling plays an important role in biology for describing the dynamics of infectious diseases. A useful strategy for controlling infections and disorder conditions is to adopt computational algorithms for determining interactions among their processes. The use of fractional order (FO) calculus has been proposed as one relevant tool for improving heuristic models. The particles memory is captured by the FO derivative and that strategy opens the door for grasping the memory of the long-term particle past behavior. This papers studies the analytical convergence of FO particle swarm optimization algorithm (FOPSO) based on a weak stagnation assumption. This approach allows establishing systematic guidelines for the FOPSO parameters tuning. The FOPSO is formulated on the basis of a control block diagram and the particle dynamics are represented as a nonlinear feedback. To describe the historical evolution of the particles, a state-space representation of different types of the FOPSO is formulated as a delayed discrete-time system. The existence and uniqueness of the equilibrium point of the FOPSO are discussed, and the stability analysis is derived to determine its convergence boundaries. Several simulations confirm the stability region of the FOPSO equilibrium point. The algorithm is also applied to a practical application, namely the minimization of the blood glucose injection in Type I diabetes mellitus patients.

Quantum fractional order Darwinian particle swarm optimization for hyperspectral multi-level image thresholding

A Hyperspectral Image (HSI) is a data cube consisting of hundreds of spatial images. Each captured spatial band is an image at a particular wavelength. Thresholding of these images is itself a tedious task. Two procedures, viz., Qubit Fractional Order Particle Swarm Optimization and Qutrit Fractional Order Particle Swarm Optimization are proposed in this paper for HSI thresholding. The Improved Subspace Decomposition Algorithm, Principal Component Analysis, and a Band Selection Convolutional Neural Network are used in the preprocessing stage for band reduction or informative band selection. For optimal segmentation of the HSI, modified Otsu’s criterion, Masi entropy and Tsallis entropy are used. A new method for quantum disaster operation is implemented to prevent the algorithm from getting stuck into local optima. The implementations are carried out on three well known datasets viz., the Indian Pines, the Pavia University and the Xuzhou HYSPEX. The proposed methods are compared with state-of-the-art methods viz., Particle Swarm Optimization (PSO), Ant Colony Optimization, Darwinian Particle Swarm Optimization, Fractional Order Particle Swarm Optimization, Exponential Decay Weight PSO and Heterogeneous Comprehensive Learning PSO concerning the optimal thresholds, best fitness value, computational time, mean and standard deviation of fitness values. Furthermore, the performance of each method is validated with Peak signal-to-noise ratio and Sørensen–Dice Similarity Index. The Kruskal–Wallis test, a statistical significance test, is conducted to establish the superiority in favor of the proposed methods. The proposed algorithms are also implemented on some benchmark functions and real life images to establish their universality.

MULTI-AUV DYNAMIC MANEUVER DECISION-MAKING BASED ON INTUITIONISTIC FUZZY COUNTER-GAME AND FRACTIONAL-ORDER PARTICLE SWARM OPTIMIZATION

In this paper, a multi-AUV dynamic maneuver decision-making algorithm is studied based on intuitionistic fuzzy game and fractional-order Particle Swarm Optimization (PSO). Because of the weak communication condition and complex marine environment, a maneuver decision-making algorithm is usually hard to realize in real-time multi-AUV couter-game process. First, the weak communication condition is analyzed according to sonar and other equipment characteristics. Then, the multi-AUV maneuver attributes evaluation and maneuver decision-making modeling are investigated under the obtained weak communication constraints. Subsequently, a fractional-order PSO optimization method is proposed to solve the strategy optimization problem of multi-AUV maneuver decision-making process. At last, an example is presented to verify the effectiveness and superiority of the obtained algorithm.

Improved Fractional-Order PSO for PID Tuning

The traditional fractional-order particle swarm optimization (FOPSO) algorithm depends on the fractional order [Formula: see text], and it is easy to fall into local optimum. To overcome these disadvantages, a novel perspective with PID gains tuning procedure is proposed by combining the time factor with FOPSO, i.e. a new fractional-order particle swarm optimization called TFFV-PSO, which reduces the dependence on the fractional order to enhance the ability of particles to escape from local optimums. According to its influence on the performance of the algorithm, the time factor is varied with population diversity parameters to balance the exploration and exploitation capabilities of the particle swarm, so as to adjust the convergence speed of the algorithm, then it follows that a better convergence performance will be obtained. The improved method is tested on several benchmark functions and applied to tune the PID controller parameters. The experimental results and the comparison with previous other methods show that our proposed TFFV-PSO provides an adequate velocity of convergence and a satisfying accuracy, as well as even better robustness.

Hypersonic reentry trajectory planning by using hybrid fractional-order particle swarm optimization and gravitational search algorithm

This paper proposes a novel hybrid algorithm called Fractional-order Particle Swarm optimization Gravitational Search Algorithm (FPSOGSA) and applies it to the trajectory planning of the hypersonic lifting reentry flight vehicles. The proposed method is used to calculate the control profiles to achieve the two objectives, namely a smoother trajectory and enforcement of the path constraints with terminal accuracy. The smoothness of the trajectory is achieved by scheduling the bank angle with the aid of a modified scheme known as a Quasi-Equilibrium Glide (QEG) scheme. The aerodynamic load factor and the dynamic pressure path constraints are enforced by further planning of the bank angle with the help of a constraint enforcement scheme. The maximum heating rate path constraint is enforced through the angle of attack parameterization. The Common Aero Vehicle (CAV) flight vehicle is used for the simulation purpose to test and compare the proposed method with that of the standard Particle Swarm Optimization (PSO) method and the standard Gravitational Search Algorithm (GSA). The simulation results confirm the efficiency of the proposed FPSOGSA method over the standard PSO and the GSA methods by showing its better convergence and computation efficiency.

Complex-order particle swarm optimization

In this paper, the generalization of the Particle Swarm Optimization (PSO) algorithm is proposed. The new algorithm involves the adoption of complex-order derivatives (CD). Since the CD produce complex-valued results, conjugate pairs of CD are considered for designing the Complex-Order PSO (CoPSO). First, an extensive sensitivity analysis is carried out for studying the influence of the control parameters on the performance of CoPSO. Then, a set of classical benchmark functions are tested to verify the performance of CoPSO. Both valued- and ranked-based methods are conducted to compare the performance of the algorithm on the whole test suite. The Friedman test is applied to determine the average ranking of the algorithms based on their performances. Additionally, the mean and the standard deviation of the best results are examined in each experiment. The results indicate that the CoPSO has outstanding performance in comparison with previous algorithms, including the standard PSO, the fractional order PSO and the linear and nonlinear decreasing inertia weight PSO. The experimental results indicate the feasibility and efficiency of the CoPSO.

Reentry guidance by accelerated fractional-order particle swarm optimization method

PurposeThe aim of this study is to design a guidance method to generate a smoother and feasible gliding reentry trajectory, a highly constrained problem by formalizing the control variables profile.Design/methodology/approachA novel accelerated fractional-order particle swarm optimization (FAPSO) method is proposed for velocity updates to design the guidance method for gliding reentry flight vehicles with fixed final energy.FindingsBy using the common aero vehicle as a test case for the simulation purpose, it is found that during the initial phase of the longitudinal guidance, there are oscillations in the state parameters which cause to violate the path constraints. For the glide phase of the longitudinal guidance, the path constraints have higher values because of the increase in the atmosphere density.Research limitations/implicationsThe violation in the path constraints may compromise the flight vehicle safety, whereas the enforcement assures the flight safety by flying it within the reentry corridor.Originality/valueAn oscillation suppression scheme is proposed by using the FAPSO method during the initial phase of the reentry flight, which smooths the trajectory and enforces the path constraints partially. To enforce the path constraints strictly in the glide phase, ultimately, another scheme by using the FAPSO method is proposed. The simulation results show that the proposed algorithm is efficient to achieve better convergence and accuracy for nominal as well as dispersed conditions.

Investigation of singular ordinary differential equations by a neuroevolutionary approach.

In this research, we have investigated doubly singular ordinary differential equations and a real application problem of studying the temperature profile in a porous fin model. We have suggested a novel soft computing strategy for the training of unknown weights involved in the feed-forward artificial neural networks (ANNs). Our neuroevolutionary approach is used to suggest approximate solutions to a highly nonlinear doubly singular type of differential equations. We have considered a real application from thermodynamics, which analyses the temperature profile in porous fins. For this purpose, we have used the optimizer, namely, the fractional-order particle swarm optimization technique (FO-DPSO), to minimize errors in solutions through fitness functions. ANNs are used to design the approximate series of solutions to problems considered in this paper. We find the values of unknown weights such that the approximate solutions to these problems have a minimum residual error. For global search in the domain, we have initialized FO-DPSO with random solutions, and it collects best so far solutions in each generation/ iteration. In the second phase, we have fine-tuned our algorithm by initializing FO-DPSO with the collection of best so far solutions. It is graphically illustrated that this strategy is very efficient in terms of convergence and minimum mean squared error in its best solutions. We can use this strategy for the higher-order system of differential equations modeling different important real applications.

Design and optimization of a CMOS power amplifier using innovative fractional-order particle swarm optimization

In this paper, a new optimization algorithm is proposed to design and optimize a CMOS power amplifier at the frequency of 2.4 GHz for wireless applications in TSMC 0.18μm with respect to stability. In this new algorithm which is denoted as Hunter-Attack Fractional-order Particle Swarm Optimization (HAFPSO) algorithm, two main weaknesses of the classic Particle Swarm Optimization (PSO), i.e. trapping in local optima (stagnation) and the slow convergence rate are resolved. In the proposed algorithm, using the fractional-order derivatives, the particle convergence rates accelerate to the optimal solution. In addition, Hunter-attack strategy is used to avoid stagnation in classic PSO. In order to investigate the performance of the HAFPSO optimization algorithm, fifteen computationally expensive benchmark optimization problems are utilized. The results of experiments show the significant performance of the proposed algorithm in comparison with seven other well known optimization algorithms i.e GA, PSO, HFPSO, CLPSO, PSOGSA, GAPSO and FPSO. A statistical test procedure is also exploited to show significant difference performance of proposed algorithm from other optimization algorithms. The power amplifier is designed using HAFPSO, GA and two PSO-based optimization algorithms, i.e. classic PSO and Fractional-order PSO (FPSO). The results show the improvement of 50% of in PAE of the power amplifier.

Fractional-order particle swarm based multi-objective PWR core loading pattern optimization

In this study the multi-objective core reload pattern optimization has been performed using the Fractional Order Particle Swarm Optimization (FOPSO) algorithm. The multi-objective goals aimed at maximization of the cycle multiplication factor while maintaining the core radial power peaking factor flat within the prescribed safety limits. These calculations have been performed for the first core loading of CHASNUPP-1 using PSU-LEOPARD and MCRAC codes for burnup dependent group constant generation and the subsequent diffusion theory-based criticality and cycle burnup calculations, respectively. Using the proposed FOPSO scheme, enhancement in the cycle length have been observed while maintaining power peaking factor within the prescribed constraints throughout the cycle. The FOPSO methodology has been found robust and efficient.

A fractional-order genetic algorithm for parameter optimization of the moisture movement in a bio-retention system

A bio-retention system is an important measure for non-point source pollution control. In order to improve the calculation precision for parameter optimization of the moisture movement in a bio-retention system, a real-encoded genetic algorithm based on the fractional-order operation is proposed, in which initial populations are generated by random mapping, and the searching range is automatically renewed with the excellent individuals by fractional-order particle swarm optimization operation. Its efficiency is verified experimentally. The results indicate that the absolute error by the fractional-order operation decreases by 67.73%, 62.23%, and 4.16%, and the relative error decreases by 42.88%, 35.76%, and 6.77%, respectively, compared to those by the standard binary-encoded genetic algorithm, random algorithm, and the particle swarm optimization algorithm. The fractional-order operation has higher precision and it is good for the practical parameter optimization in ecological environment systems.