Search results for: robust optimization

Authors: Pulak Swain, A. K. Ojha

Abstract:

Portfolio optimization is based on dealing with the problems of efficient asset allocation. Risk and Expected return are two conflicting criteria in such problems, where the investor prefers the return to be high and the risk to be low. Using multi-objective approach we can solve those type of problems. However the information which we have for the input parameters are generally ambiguous and the input values can fluctuate around some nominal values. We can not ignore the uncertainty in input values, as they can affect the asset allocation drastically. So we use Robust Optimization approach to the problems where the input parameters comes under box uncertainty. In this paper, we solve the multi criteria robust problem with the help of  E- constraint method.

Keywords: Portfolio optimization, multi-objective optimization, E-constraint method, box uncertainty, robust optimization.

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Authors: S.F. Faisal, A.H.M.A. Rahim, J.M. Bakhashwain

Abstract:

Design of a fixed parameter robust STATCOM controller for a multi-machine power system through an H-? based loop-shaping procedure is presented. The trial and error part of the graphical loop-shaping procedure has been eliminated by embedding a particle swarm optimization (PSO) technique in the design loop. Robust controllers were designed considering the detailed dynamics of the multi-machine system and results were compared with reduced order models. The robust strategy employing loop-shaping and PSO algorithms was observed to provide very good damping profile for a wide range of operation and for various disturbance conditions. 

Keywords: STATCOM, Robust control, Power system damping, Particle Swarm Optimization, Loop-shaping.

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Authors: J.Dinesh Peter

Abstract:

This paper describes a new method for affine parameter estimation between image sequences. Usually, the parameter estimation techniques can be done by least squares in a quadratic way. However, this technique can be sensitive to the presence of outliers. Therefore, parameter estimation techniques for various image processing applications are robust enough to withstand the influence of outliers. Progressively, some robust estimation functions demanding non-quadratic and perhaps non-convex potentials adopted from statistics literature have been used for solving these. Addressing the optimization of the error function in a factual framework for finding a global optimal solution, the minimization can begin with the convex estimator at the coarser level and gradually introduce nonconvexity i.e., from soft to hard redescending non-convex estimators when the iteration reaches finer level of multiresolution pyramid. Comparison has been made to find the performance of the results of proposed method with the results found individually using two different estimators.

Keywords: Image Processing, Affine parameter estimation, Outliers, Robust Statistics, Robust M-estimators

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Authors: S. Swain, P. S. Khuntia

Abstract:

In this paper an optimal convex controller is designed to control the angle of attack of a FOXTROT aircraft. Then the order of the system model is reduced to a low-dimensional state space by using Balanced Truncation Model Reduction Technique and finally the robust stability of the reduced model of the system is tested graphically by using Kharitonov rectangle and Zero Exclusion Principle for a particular range of perturbation value. The same robust stability is tested theoretically by using Frequency Sweeping Function for robust stability.

Keywords: Convex Optimization, Kharitonov Stability Criterion, Model Reduction, Robust Stability.

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Authors: Abdolsalam Ghaderi

Abstract:

In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. This problem has many applications, especially in the area of supply chain management and distribution systems. To get closer to real-world situations, travel time of vehicles, the fixed cost of vehicles usage and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a heuristic algorithm based on Variable Neighborhood Search(VNS) is presented to solve the model. Finally, the computational results are presented and future research directions are discussed.

Keywords: Location-routing problem, robust optimization, Stochastic Programming, variable neighborhood search.

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Authors: Sidhartha Panda, N. P. Padhy

Abstract:

Power system stabilizers (PSS) are now routinely used in the industry to damp out power system oscillations. In this paper, particle swarm optimization (PSO) technique is applied to design a robust power system stabilizer (PSS). The design problem of the proposed controller is formulated as an optimization problem and PSO is employed to search for optimal controller parameters. By minimizing the time-domain based objective function, in which the deviation in the oscillatory rotor speed of the generator is involved; stability performance of the system is improved. The non-linear simulation results are presented under wide range of operating conditions; disturbances at different locations as well as for various fault clearing sequences to show the effectiveness and robustness of the proposed controller and their ability to provide efficient damping of low frequency oscillations. Further, all the simulations results are compared with a conventionally designed power system stabilizer to show the superiority of the proposed design approach.

Keywords: Particle swarm optimization, power system stabilizer, low frequency oscillations, power system stability.

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Authors: T. Niknam, M. Nayeripour, B.Bahmani Firouzi

Abstract:

Clustering techniques have received attention in many areas including engineering, medicine, biology and data mining. The purpose of clustering is to group together data points, which are close to one another. The K-means algorithm is one of the most widely used techniques for clustering. However, K-means has two shortcomings: dependency on the initial state and convergence to local optima and global solutions of large problems cannot found with reasonable amount of computation effort. In order to overcome local optima problem lots of studies done in clustering. This paper is presented an efficient hybrid evolutionary optimization algorithm based on combining Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO), called PSO-ACO, for optimally clustering N object into K clusters. The new PSO-ACO algorithm is tested on several data sets, and its performance is compared with those of ACO, PSO and K-means clustering. The simulation results show that the proposed evolutionary optimization algorithm is robust and suitable for handing data clustering.

Keywords: Ant Colony Optimization (ACO), Data clustering, Hybrid evolutionary optimization algorithm, K-means clustering, Particle Swarm Optimization (PSO).

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Authors: Christopher C. Ihueze, Charles C. Okpala, Christian E. Okafor, Peter O. Ogbobe

Abstract:

This paper focuses on robust design and optimization of industrial production wastes. Past literatures were reviewed to case study Clamason Industries Limited (CIL) - a leading ladder-tops manufacturer. A painstaking study of the firm-s practices at the shop floor revealed that Over-production, Waiting time, Excess inventory, and Defects are the major wastes that are impeding their progress and profitability. Design expert8 software was used to apply Taguchi robust design and response surface methodology in order to model, analyse and optimise the wastes cost in CIL. Waiting time and overproduction rank first and second in contributing to the costs of wastes in CIL. For minimal wastes cost the control factors of overproduction, waiting-time, defects and excess-inventory must be set at 0.30, 390.70, 4 and 55.70 respectively for CIL. The optimal value of cost of wastes for the months studied was 22.3679. Finally, a recommendation was made that for the company to enhance their profitability and customer satisfaction, they must adopt the Shingeo Shingo-s Single Minute Exchange of Dies (SMED), which will immediately tackle the waste of waiting by drastically reducing their setup time.

Keywords: Excess-inventory, setup time, single minute exchange of dies, optimal value, over-production, robust design.

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Authors: Sidhartha Panda, C. Ardil

Abstract:

Power system stabilizers (PSS) are now routinely used in the industry to damp out power system oscillations. In this paper, real-coded genetic algorithm (RCGA) optimization technique is applied to design robust power system stabilizer for both singlemachine infinite-bus (SMIB) and multi-machine power system. The design problem of the proposed controller is formulated as an optimization problem and RCGA is employed to search for optimal controller parameters. By minimizing the time-domain based objective function, in which the deviation in the oscillatory rotor speed of the generator is involved; stability performance of the system is improved. The non-linear simulation results are presented under wide range of operating conditions; disturbances at different locations as well as for various fault clearing sequences to show the effectiveness and robustness of the proposed controller and their ability to provide efficient damping of low frequency oscillations.

Keywords: Particle swarm optimization, power system stabilizer, low frequency oscillations, power system stability.

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Authors: S. A. Gayvoronsky, T. A. Ezangina

Abstract:

The robust control system objects with interval- undermined parameters is considers in this paper. Initial information about the system is its characteristic polynomial with interval coefficients. On the basis of coefficient estimations of quality indices and criterion of the maximum stability degree, the methods of synthesis of a robust regulator parametric is developed. The example of the robust stabilization system synthesis of the rope tension is given in this article.

Keywords: An interval polynomial, controller synthesis, analysis of quality factors, maximum degree of stability, robust degree of stability, robust oscillation, system accuracy.

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Authors: Jing-ran Lin, Qi-cong Peng, Huai-zong Shao

Abstract:

The performance of adaptive beamforming degrades substantially in the presence of steering vector mismatches. This degradation is especially severe in the near-field, for the 3-dimensional source location is more difficult to estimate than the 2-dimensional direction of arrival in far-field cases. As a solution, a novel approach of near-field robust adaptive beamforming (RABF) is proposed in this paper. It is a natural extension of the traditional far-field RABF and belongs to the class of diagonal loading approaches, with the loading level determined based on worst-case performance optimization. However, different from the methods solving the optimal loading by iteration, it suggests here a simple closed-form solution after some approximations, and consequently, the optimal weight vector can be expressed in a closed form. Besides simplicity and low computational cost, the proposed approach reveals how different factors affect the optimal loading as well as the weight vector. Its excellent performance in the near-field is confirmed via a number of numerical examples.

Keywords: Robust adaptive beamforming (RABF), near-field, steering vector mismatches, diagonal loading, worst-case performanceoptimization.

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Authors: Sarah Odofin, Zhiwei Gao, Sun Kai

Abstract:

Operations, maintenance and reliability of wind turbines have received much attention over the years due to the rapid expansion of wind farms. This paper explores early fault diagnosis technique for a 5MW wind turbine system subjected to multiple faults, where genetic optimization algorithm is employed to make the residual sensitive to the faults, but robust against disturbances. The proposed technique has a potential to reduce the downtime mostly caused by the breakdown of components and exploit the productivity consistency by providing timely fault alarms. Simulation results show the effectiveness of the robust fault detection methods used under Matlab/Simulink/Gatool environment.

Keywords: Disturbance robustness, fault monitoring and detection, genetic algorithm and observer technique.

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Authors: S. Raissi, R- Eslami Farsani

Abstract:

In recent years, response surface methodology (RSM) has brought many attentions of many quality engineers in different industries. Most of the published literature on robust design methodology is basically concerned with optimization of a single response or quality characteristic which is often most critical to consumers. For most products, however, quality is multidimensional, so it is common to observe multiple responses in an experimental situation. Through this paper interested person will be familiarize with this methodology via surveying of the most cited technical papers. It is believed that the proposed procedure in this study can resolve a complex parameter design problem with more than two responses. It can be applied to those areas where there are large data sets and a number of responses are to be optimized simultaneously. In addition, the proposed procedure is relatively simple and can be implemented easily by using ready-made standard statistical packages.

Keywords: Multi-Response Surface Methodology (MRSM), Design of Experiments (DOE), Process modeling, Quality improvement; Robust Design.

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Authors: Romisaa Ali

Abstract:

The Policy Gradient approach is a subset of the Deep Reinforcement Learning (DRL) combines Deep Neural Networks (DNN) with Reinforcement Learning (RL). This approach finds the optimal policy of robot movement, based on the experience it gains from interaction with its environment. Unlike previous policy gradient algorithms, which were unable to handle the two types of error variance and bias introduced by the DNN model due to over- or underestimation, this algorithm is capable of handling both types of error variance and bias. This article will discuss the state-of-the-art SOTA policy gradient technique, trust region policy optimization (TRPO), by applying this method in various environments compared to another policy gradient method, the Proximal Policy Optimization (PPO), to explain their robust optimization, using this SOTA to gather experience data during various training phases after observing the impact of hyper-parameters on neural network performance.

Keywords: Deep neural networks, deep reinforcement learning, Proximal Policy Optimization, state-of-the-art, trust region policy optimization.

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Authors: Ginalber L. O. Serra

Abstract:

This work proposes a recursive weighted ELS algorithm for system identification by applying numerically robust orthogonal Householder transformations. The properties of the proposed algorithm show it obtains acceptable results in a noisy environment: fast convergence and asymptotically unbiased estimates. Comparative analysis with others robust methods well known from literature are also presented.

Keywords: Stochastic Systems, Robust Identification, Parameter Estimation, Systems Identification.

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Authors: M. Polanský

Abstract:

This paper introduces a new method called ARPDC (Advanced Robust Parallel Distributed Compensation) for automatic control of nonlinear systems. This method improves a quality of robust control by interpolating of robust and optimal controller. The weight of each controller is determined by an original criteria function for model validity and disturbance appreciation. ARPDC method is based on nonlinear Takagi-Sugeno (T-S) fuzzy systems and Parallel Distributed Compensation (PDC) control scheme. The relaxed stability conditions of ARPDC control of nominal system have been derived. The advantages of presented method are demonstrated on the inverse pendulum benchmark problem. From comparison between three different controllers (robust, optimal and ARPDC) follows, that ARPDC control is almost optimal with the robustness close to the robust controller. The results indicate that ARPDC algorithm can be a good alternative not only for a robust control, but in some cases also to an adaptive control of nonlinear systems.

Keywords: Robust control, optimal control, Takagi–Sugeno (TS) fuzzy models, linear matrix inequality (LMI), observer, Advanced Robust Parallel Distributed Compensation (ARPDC).

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Authors: Dinesh Inamadar, R. Venugopalan, K. Padmini

Abstract:

An attempt has been made in the present communication to elucidate the efficacy of robust ANOVA methods to analyse horticultural field experimental data in the presence of outliers. Results obtained fortify the use of robust ANOVA methods as there was substantiate reduction in error mean square, and hence the probability of committing Type I error, as compared to the regular approach.

Keywords: Outliers, robust ANOVA, horticulture, Cook distance, Type I error.

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Authors: M. G. C. A. Cimino, G. Frosini, B. Lazzerini, F. Marcelloni

Abstract:

In the last decades, a number of robust fuzzy clustering algorithms have been proposed to partition data sets affected by noise and outliers. Robust fuzzy C-means (robust-FCM) is certainly one of the most known among these algorithms. In robust-FCM, noise is modeled as a separate cluster and is characterized by a prototype that has a constant distance δ from all data points. Distance δ determines the boundary of the noise cluster and therefore is a critical parameter of the algorithm. Though some approaches have been proposed to automatically determine the most suitable δ for the specific application, up to today an efficient and fully satisfactory solution does not exist. The aim of this paper is to propose a novel method to compute the optimal δ based on the analysis of the distribution of the percentage of objects assigned to the noise cluster in repeated executions of the robust-FCM with decreasing values of δ . The extremely encouraging results obtained on some data sets found in the literature are shown and discussed.

Keywords: noise prototype, robust fuzzy clustering, robustfuzzy C-means

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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3ⁿ enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3ⁿ integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

Keywords: Constrained integer problems, enumerative search algorithm, Heuristic algorithm, tunneling algorithm.

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Authors: H. Shayeghi, A. Safari, H. A. Shayanfar

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In this paper, multiobjective design of multi-machine Power System Stabilizers (PSSs) using Particle Swarm Optimization (PSO) is presented. The stabilizers are tuned to simultaneously shift the lightly damped and undamped electro-mechanical modes of all machines to a prescribed zone in the s-plane. A multiobjective problem is formulated to optimize a composite set of objective functions comprising the damping factor, and the damping ratio of the lightly damped electromechanical modes. The PSSs parameters tuning problem is converted to an optimization problem which is solved by PSO with the eigenvalue-based multiobjective function. The proposed PSO based PSSs is tested on a multimachine power system under different operating conditions and disturbances through eigenvalue analysis and some performance indices to illustrate its robust performance.

Keywords: PSS Design, Particle Swarm Optimization, Dynamic Stability, Multiobjective Optimization.

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Authors: H. Alkhatib, J. Duveau

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Genetic algorithms (GAs) have been widely used for global optimization problems. The GA performance depends highly on the choice of the search space for each parameter to be optimized. Often, this choice is a problem-based experience. The search space being a set of potential solutions may contain the global optimum and/or other local optimums. A bad choice of this search space results in poor solutions. In this paper, our approach consists in extending the search space boundaries during the GA optimization, only when it is required. This leads to more diversification of GA population by new solutions that were not available with fixed search space boundaries. So, these dynamic search spaces can improve the GA optimization performances. The proposed approach is applied to power system stabilizer optimization for multimachine power system (16-generator and 68-bus). The obtained results are evaluated and compared with those obtained by ordinary GAs. Eigenvalue analysis and nonlinear system simulation results show the effectiveness of the proposed approach to damp out the electromechanical oscillation and enhance the global system stability.

Keywords: Genetic Algorithms, Multiobjective Optimization, Power System Stabilizer, Small Signal Stability.

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Authors: Randeep Kaur, Jyoti Ohri

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This paper proposes a new technique to design a fixed-structure robust loop shaping controller for the pneumatic servosystem. In this paper, a new method based on a particle swarm optimization (PSO) algorithm for tuning the weighting function parameters to design an H∞ controller is presented. The PSO algorithm is used to minimize the infinity norm of the transfer function of the nominal closed loop system to obtain the optimal parameters of the weighting functions. The optimal stability margin is used as an objective in PSO for selecting the optimal weighting parameters; it is shown that the proposed method can simplify the design procedure of H∞ control to obtain optimal robust controller for pneumatic servosystem. In addition, the order of the proposed controller is much lower than that of the conventional robust loop shaping controller, making it easy to implement in practical works. Also two-degree-of-freedom (2DOF) control design procedure is proposed to improve tracking performance in the face of noise and disturbance. Result of simulations demonstrates the advantages of the proposed controller in terms of simple structure and robustness against plant perturbations and disturbances.

Keywords: Robust control, Pneumatic Servosystem, PSO, H∞ control, 2DOF.

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Authors: Florin Leon, Silvia Curteanu

Abstract:

The Bacterial Foraging Optimization (BFO) algorithm is inspired by the behavior of bacteria such as Escherichia coli or Myxococcus xanthus when searching for food, more precisely the chemotaxis behavior. Bacteria perceive chemical gradients in the environment, such as nutrients, and also other individual bacteria, and move toward or in the opposite direction to those signals. The application example considered as a case study consists in establishing the dependency between the reaction yield of hydrogels based on polyacrylamide and the working conditions such as time, temperature, monomer, initiator, crosslinking agent and inclusion polymer concentrations, as well as type of the polymer added. This process is modeled with a neural network which is included in an optimization procedure based on BFO. An experimental study of BFO parameters is performed. The results show that the algorithm is quite robust and can obtain good results for diverse combinations of parameter values.

Keywords: Bacterial foraging optimization, hydrogels, neural networks, modeling.

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Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

Abstract:

This paper studies a robust stabilization problem of a single agent in a multi-agent consensus system composed of identical agents, when the network topology of the system is completely unknown. It is shown that the transfer function of an agent in a consensus system can be described as a multiplicative perturbation of the isolated agent transfer function in frequency domain. From an existing robust stabilization result, we present sufficient conditions for a robust stabilization of an agent against unknown network topology.

Keywords: Multi-agent System, Robust Stabilization, Transfer Function.

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Authors: Zixin Liu

Abstract:

The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method.

Keywords: Robust stabilization, robust stability, discrete-time system, time delay.

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Authors: Kuo-Lung Wu

Abstract:

The weighting exponent m is called the fuzzifier that can have influence on the clustering performance of fuzzy c-means (FCM) and mÎ[1.5,2.5] is suggested by Pal and Bezdek [13]. In this paper, we will discuss the robust properties of FCM and show that the parameter m will have influence on the robustness of FCM. According to our analysis, we find that a large m value will make FCM more robust to noise and outliers. However, if m is larger than the theoretical upper bound proposed by Yu et al. [14], the sample mean will become the unique optimizer. Here, we suggest to implement the FCM algorithm with mÎ[1.5,4] under the restriction when m is smaller than the theoretical upper bound.

Keywords: Fuzzy c-means, robust, fuzzifier.

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Authors: R. Rama Kishore, Sunesh

Abstract:

Nowadays, robust and secure watermarking algorithm and its optimization have been need of the hour. A watermarking algorithm is presented to achieve the copy right protection of the owner based on visual cryptography, histogram shape property and entropy. In this, both host image and watermark are preprocessed. Host image is preprocessed by using Butterworth filter, and watermark is with visual cryptography. Applying visual cryptography on water mark generates two shares. One share is used for embedding the watermark, and the other one is used for solving any dispute with the aid of trusted authority. Usage of histogram shape makes the process more robust against geometric and signal processing attacks. The combination of visual cryptography, Butterworth filter, histogram, and entropy can make the algorithm more robust, imperceptible, and copy right protection of the owner.

Keywords: Butterworth filter, digital watermarking, histogram, visual cryptography.

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Authors: A.K.Balirsingh, S.C.Swain, S. Panda

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Recently, Genetic Algorithms (GA) and Differential Evolution (DE) algorithm technique have attracted considerable attention among various modern heuristic optimization techniques. Since the two approaches are supposed to find a solution to a given objective function but employ different strategies and computational effort, it is appropriate to compare their performance. This paper presents the application and performance comparison of DE and GA optimization techniques, for flexible ac transmission system (FACTS)-based controller design. The design objective is to enhance the power system stability. The design problem of the FACTS-based controller is formulated as an optimization problem and both the PSO and GA optimization techniques are employed to search for optimal controller parameters. The performance of both optimization techniques has been compared. Further, the optimized controllers are tested on a weekly connected power system subjected to different disturbances, and their performance is compared with the conventional power system stabilizer (CPSS). The eigenvalue analysis and non-linear simulation results are presented and compared to show the effectiveness of both the techniques in designing a FACTS-based controller, to enhance power system stability.

Keywords: Differential Evolution, Flexible AC TransmissionSystems (FACTS), Genetic Algorithm, Low Frequency Oscillations, Single-machine Infinite Bus Power System.

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Authors: H. Ashrafi, S. Ebrahimi, H. Kamalzadeh

Abstract:

With the development of business competition, it is important for healthcare providers to improve their service qualities. In order to improve service quality of a clinic, four important dimensions are defined: tangibles, responsiveness, empathy, and reliability. Moreover, there are several service stages in hospitals such as financial screening and examination. One of the most challenging limitations for improving service quality is budget which impressively affects the service quality. In this paper, we present an approach to address budget uncertainty and provide guidelines for service resource allocation. In this paper, a service quality improvement approach is proposed which can be adopted to multistage service processes to improve service quality, while controlling the costs. A multi-objective function based on the importance of each area and dimension is defined to link operational variables to service quality dimensions. The results demonstrate that our approach is not ultra-conservative and it shows the actual condition very well. Moreover, it is shown that different strategies can affect the number of employees in different stages.

Keywords: Service quality assessment, healthcare resource allocation, robust optimization, budget uncertainty.

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Authors: Sidhartha Panda, C. Ardil

Abstract:

Power system stabilizers (PSS) are now routinely used in the industry to damp out power system oscillations. In this paper, particle swarm optimization (PSO) technique is applied to coordinately design multiple power system stabilizers (PSS) in a multi-machine power system. The design problem of the proposed controllers is formulated as an optimization problem and PSO is employed to search for optimal controller parameters. By minimizing the time-domain based objective function, in which the deviation in the oscillatory rotor speed of the generator is involved; stability performance of the system is improved. The non-linear simulation results are presented for various severe disturbances and small disturbance at different locations as well as for various fault clearing sequences to show the effectiveness and robustness of the proposed controller and their ability to provide efficient damping of low frequency oscillations.

Keywords: Low frequency oscillations, Particle swarm optimization, power system stability, power system stabilizer, multimachine power system.

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