Search results for: Discrete stochastic optimization

Authors: Omid Sojodishijani, Saeed Ebrahimijam, Vahid Rostami

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This paper presents an optimized algorithm for robot localization which increases the correctness and accuracy of the estimating position of mobile robot to more than 150% of the past methods [1] in the uncertain and noisy environment. In this method the odometry and vision sensors are combined by an adapted well-known discrete kalman filter [2]. This technique also decreased the computation process of the algorithm by DKF simple implementation. The experimental trial of the algorithm is performed on the robocup middle size soccer robot; the system can be used in more general environments.

Keywords: Discrete Kalman filter, odometry sensor, omnidirectional vision sensor, Robot Localization.

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Authors: A. A. Khan, M. Naeem, S. Bashir, S. I. Shah

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In this paper we propose a Particle Swarm heuristic optimized Multi-Antenna (MA) system. Efficient MA systems detection is performed using a robust stochastic evolutionary computation algorithm based on movement and intelligence of swarms. This iterative particle swarm optimized (PSO) detector significantly reduces the computational complexity of conventional Maximum Likelihood (ML) detection technique. The simulation results achieved with this proposed MA-PSO detection algorithm show near optimal performance when compared with ML-MA receiver. The performance of proposed detector is convincingly better for higher order modulation schemes and large number of antennas where conventional ML detector becomes non-practical.

Keywords: Multi Antenna (MA), Multi-input Multi-output(MIMO), Particle Swarm Optimization (PSO), ML detection.

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Authors: Sebastian Kusch, Markus Kaiser

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In this paper we analyze the application of a formal proof system to the discrete logarithm problem used in publickey cryptography. That means, we explore a computer verification of the ElGamal encryption scheme with the formal proof system Isabelle/HOL. More precisely, the functional correctness of this algorithm is formally verified with computer support. Besides, we present a formalization of the DSA signature scheme in the Isabelle/HOL system. We show that this scheme is correct what is a necessary condition for the usefulness of any cryptographic signature scheme.

Keywords: Formal proof system, higher-order logic, formal verification, cryptographic signature scheme.

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Authors: Pooja, Megha Kulshrestha, V. K. Banga, Parvinder S. Sandhu

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To support mobility in ATM networks, a number of technical challenges need to be resolved. The impact of handoff schemes in terms of service disruption, handoff latency, cost implications and excess resources required during handoffs needs to be addressed. In this paper, a one phase handoff and route optimization solution using reserved PVCs between adjacent ATM switches to reroute connections during inter-switch handoff is studied. In the second phase, a distributed optimization process is initiated to optimally reroute handoff connections. The main objective is to find the optimal operating point at which to perform optimization subject to cost constraint with the purpose of reducing blocking probability of inter-switch handoff calls for delay tolerant traffic. We examine the relation between the required bandwidth resources and optimization rate. Also we calculate and study the handoff blocking probability due to lack of bandwidth for resources reserved to facilitate the rapid rerouting.

Keywords: Wireless ATM, Mobility, Latency, Optimization rateand Blocking Probability.

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Authors: Sidhartha Panda, N. P. Padhy

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Recently, genetic algorithms (GA) and particle swarm optimization (PSO) 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 PSO and GA optimization techniques, for Thyristor Controlled Series Compensator (TCSC)-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 in terms of computational time and convergence rate is compared. Further, the optimized controllers are tested on a weakly 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 TCSC-based controller, to enhance power system stability.

Keywords: Thyristor Controlled Series Compensator, geneticalgorithm; particle swarm optimization; Phillips-Heffron model;power system stability.

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Authors: Nidal F. Shilbayeh, Belal AbuHaija, Zainab N. Al-Qudsy

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In this paper, a hybrid blind digital watermarking system using Discrete Wavelet Transform (DWT) and Contourlet Transform (CT) has been implemented and tested. The implemented combined digital watermarking system has been tested against five common types of image attacks. The performance evaluation shows improved results in terms of imperceptibility, robustness, and high tolerance against these attacks; accordingly, the system is very effective and applicable.

Keywords: DWT, contourlet transform, digital image watermarking, copyright protection, geometric attack.

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Authors: Bao Thach Nguyen, Abbas Mohajerani

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A typical flexible pavement structure consists of the surface, base, sub-base and subgrade soil. The loading traffic is transferred from the top layer with higher stiffness to the layer below with less stiffness. Under normal traffic loading, the behaviour of flexible pavement is very complex and can be predicted by using the repeated load triaxial test equipment in the laboratory. However, the nature of the repeated load triaxial testing procedure is considered time-consuming, complicated and expensive, and it is a challenge to carry out as a routine test in the laboratory. Therefore, the current paper proposes a numerical approach to simulate the repeated load triaxial test by employing the discrete element method. A sample with particle size ranging from 2.36mm to 19.0mm was constructed. Material properties, which included normal stiffness, shear stiffness, coefficient of friction, maximum dry density and particle density, were used as the input for the simulation. The sample was then subjected to a combination of deviator and confining stress and it was found that the discrete element method is able to simulate the repeated load triaxial test in the laboratory.

Keywords: Discrete element method, repeated load triaxial, pavement materials.

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Authors: Hussain Syed Asad, Richard Kwok Kit Yuen, Gongsheng Huang

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Real-time optimization has been considered an effective approach for improving energy efficient operation of heating, ventilation, and air-conditioning (HVAC) systems. In model-based real-time optimization, model mismatches cannot be avoided. When model mismatches are significant, the performance of the real-time optimization will be impaired and hence the expected energy saving will be reduced. In this paper, the model mismatches for chiller plant on real-time optimization are considered. In the real-time optimization of the chiller plant, simplified semi-physical or grey box model of chiller is always used, which should be identified using available operation data. To overcome the model mismatches associated with the chiller model, hybrid Genetic Algorithms (HGAs) method is used for online real-time training of the chiller model. HGAs combines Genetic Algorithms (GAs) method (for global search) and traditional optimization method (i.e. faster and more efficient for local search) to avoid conventional hit and trial process of GAs. The identification of model parameters is synthesized as an optimization problem; and the objective function is the Least Square Error between the output from the model and the actual output from the chiller plant. A case study is used to illustrate the implementation of the proposed method. It has been shown that the proposed approach is able to provide reliability in decision making, enhance the robustness of the real-time optimization strategy and improve on energy performance.

Keywords: Energy performance, hybrid adaptive modeling, hybrid genetic algorithms, real-time optimization, heating, ventilation, and air-conditioning.

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Authors: Badr M. Alshammari, T. Guesmi

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In this paper, the concept of a non-dominated sorting multi-objective particle swarm optimization with local search (NSPSO-LS) is presented for the optimal design of multimachine power system stabilizers (PSSs). The controller design is formulated as an optimization problem in order to shift the system electromechanical modes in a pre-specified region in the s-plan. A composite set of objective functions comprising the damping factor and the damping ratio of the undamped and lightly damped electromechanical modes is considered. The performance of the proposed optimization algorithm is verified for the 3-machine 9-bus system. Simulation results based on eigenvalue analysis and nonlinear time-domain simulation show the potential and superiority of the NSPSO-LS algorithm in tuning PSSs over a wide range of loading conditions and large disturbance compared to the classic PSO technique and genetic algorithms.

Keywords: Multi-objective optimization, particle swarm optimization, power system stabilizer, low frequency oscillations.

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Authors: Romisaa Ali

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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: Pulak Swain, A. K. Ojha

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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: Basant Kumar, Animesh Anand, S.P. Singh, Anand Mohan

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This paper presents a new spread-spectrum watermarking algorithm for digital images in discrete wavelet transform (DWT) domain. The algorithm is applied for embedding watermarks like patient identification /source identification or doctors signature in binary image format into host digital radiological image for potential telemedicine applications. Performance of the algorithm is analysed by varying the gain factor, subband decomposition levels, and size of watermark. Simulation results show that the proposed method achieves higher watermarking capacity.

Keywords: Watermarking, spread-spectrum, discrete wavelettransform, telemedicine

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Authors: Sh. Derakhshan, A. Mostafavi

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Nowadays, the challenge in hydraulic turbine design is the multi-objective design of turbine runner to reach higher efficiency. The hydraulic performance of a turbine is strictly depends on runner blades shape. The present paper focuses on the application of the multi-objective optimization algorithm to the design of a small Francis turbine runner. The optimization exercise focuses on the efficiency improvement at the best efficiency operating point (BEP) of the GAMM Francis turbine. A global optimization method based on artificial neural networks (ANN) and genetic algorithms (GA) coupled by 3D Navier-Stokes flow solver has been used to improve the performance of an initial geometry of a Francis runner. The results show the good ability of optimization algorithm and the final geometry has better efficiency with initial geometry. The goal was to optimize the geometry of the blades of GAMM turbine runner which leads to maximum total efficiency by changing the design parameters of camber line in at least 5 sections of a blade. The efficiency of the optimized geometry is improved from 90.7% to 92.5%. Finally, design parameters and the way of selection have been considered and discussed.

Keywords: Francis Turbine, Runner, Optimization, CFD

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Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai

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Elliptic curve discrete logarithm problem(ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard’s rho method to evaluate the security of ECDLP on Barreto-Naehrig(BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.

Keywords: Pollard’s rho method, BN curve, Montgomery multiplication.

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Authors: I. Brandys, M. Levy, K. Harush, Y. Haim, M. Korngold

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Theoretical optimization of a copper-water negative inclination heat pipe with internal composite wick structure had been performed, regarding a new introduced parameter: the ratio between the coarse mesh wraps and the fine mesh wraps of the composite wick. Since in many cases, the design of a heat pipe matches specific thermal requirements and physical limitations, this work demonstrates the optimization of a 1m length, 8mm internal diameter heat pipe without an adiabatic section, at a negative inclination angle of -10º. The optimization is based on a new introduced parameter, LR: the ratio between the coarse mesh wraps and the fine mesh wraps.

Keywords: Heat pipe, inclination, optimization, ratio.

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Authors: Lukumba Phiri, Simon Tembo, Kumbuso Joshua Nyoni

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In Zambia, recent initiatives by various power operators like ZESCO, CEC, and consumers like the mines, to upgrade power systems into smart grids, target an even tighter integration with information technologies to enable the integration of renewable energy sources, local and bulk generation, and demand response. Thus, for the reliable operation of smart grids, its information infrastructure must be secure and reliable in the face of both failures and cyberattacks. Due to the nature of the systems, ICS/SCADA cybersecurity and governance face additional challenges compared to the corporate networks, and critical systems may be left exposed. There exist control frameworks internationally such as the NIST framework, however, they are generic and do not meet the domain-specific needs of the SCADA systems. Zambia is also lagging in cybersecurity awareness and adoption, and therefore there is a concern about securing ICS controlling key infrastructure critical to the Zambian economy as there are few known facts about the true posture. In this paper, we present a stochastic Edged-based Anomaly Detection for SCADA systems (SEADS) framework for threat modeling and risk assessment. SEADS enables the calculation of steady-steady probabilities that are further applied to establish metrics like system availability, maintainability, and reliability.

Keywords: Anomaly detection, SmartGrid, edge, maintainability, reliability, stochastic process.

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Authors: Yahya H. Zweiri

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The back-propagation algorithm calculates the weight changes of an artificial neural network, and a two-term algorithm with a dynamically optimal learning rate and a momentum factor is commonly used. Recently the addition of an extra term, called a proportional factor (PF), to the two-term BP algorithm was proposed. The third term increases the speed of the BP algorithm. However, the PF term also reduces the convergence of the BP algorithm, and optimization approaches for evaluating the learning parameters are required to facilitate the application of the three terms BP algorithm. This paper considers the optimization of the new back-propagation algorithm by using derivative information. A family of approaches exploiting the derivatives with respect to the learning rate, momentum factor and proportional factor is presented. These autonomously compute the derivatives in the weight space, by using information gathered from the forward and backward procedures. The three-term BP algorithm and the optimization approaches are evaluated using the benchmark XOR problem.

Keywords: Neural Networks, Backpropagation, Optimization.

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Authors: Anatoli Torokhti, Phil Howlett

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A theory for optimal filtering of infinite sets of random signals is presented. There are several new distinctive features of the proposed approach. First, a single optimal filter for processing any signal from a given infinite signal set is provided. Second, the filter is presented in the special form of a sum with p terms where each term is represented as a combination of three operations. Each operation is a special stage of the filtering aimed at facilitating the associated numerical work. Third, an iterative scheme is implemented into the filter structure to provide an improvement in the filter performance at each step of the scheme. The final step of the scheme concerns signal compression and decompression. This step is based on the solution of a new rank-constrained matrix approximation problem. The solution to the matrix problem is described in this paper. A rigorous error analysis is given for the new filter.

Keywords: Optimal filtering, data compression, stochastic signals.

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Authors: Vahid Mohammadi Saffarzadeh, Pourya Jafarzadeh, Masoud Mazloom

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This paper presents a hybrid approach for solving nqueen problem by combination of PSO and SA. PSO is a population based heuristic method that sometimes traps in local maximum. To solve this problem we can use SA. Although SA suffer from many iterations and long time convergence for solving some problems, By good adjusting initial parameters such as temperature and the length of temperature stages SA guarantees convergence. In this article we use discrete PSO (due to nature of n-queen problem) to achieve a good local maximum. Then we use SA to escape from local maximum. The experimental results show that our hybrid method in comparison of SA method converges to result faster, especially for high dimensions n-queen problems.

Keywords: PSO, SA, N-queen, CSP

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Authors: Jagannath Aryal, Don Kulasiri, Dishi Liu

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This paper describes the optimization of a complex dairy farm simulation model using two quite different methods of optimization, the Genetic algorithm (GA) and the Lipschitz Branch-and-Bound (LBB) algorithm. These techniques have been used to improve an agricultural system model developed by Dexcel Limited, New Zealand, which describes a detailed representation of pastoral dairying scenarios and contains an 8-dimensional parameter space. The model incorporates the sub-models of pasture growth and animal metabolism, which are themselves complex in many cases. Each evaluation of the objective function, a composite 'Farm Performance Index (FPI)', requires simulation of at least a one-year period of farm operation with a daily time-step, and is therefore computationally expensive. The problem of visualization of the objective function (response surface) in high-dimensional spaces is also considered in the context of the farm optimization problem. Adaptations of the sammon mapping and parallel coordinates visualization are described which help visualize some important properties of the model-s output topography. From this study, it is found that GA requires fewer function evaluations in optimization than the LBB algorithm.

Keywords: Genetic Algorithm, Linux Cluster, LipschitzBranch-and-Bound, Optimization

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Authors: Meysam Mohamad pour, Fardad Farokhi

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In this paper in consideration of each available techniques deficiencies for speech recognition, an advanced method is presented that-s able to classify speech signals with the high accuracy (98%) at the minimum time. In the presented method, first, the recorded signal is preprocessed that this section includes denoising with Mels Frequency Cepstral Analysis and feature extraction using discrete wavelet transform (DWT) coefficients; Then these features are fed to Multilayer Perceptron (MLP) network for classification. Finally, after training of neural network effective features are selected with UTA algorithm.

Keywords: Multilayer perceptron (MLP) neural network, Discrete Wavelet Transform (DWT) , Mels Scale Frequency Filter , UTA algorithm.

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Authors: A. Charlangsut, N. Rugthaicharoencheep, S. Auchariyamet

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Network reconfiguration is an operation to modify the network topology. The implementation of network reconfiguration has many advantages such as loss minimization, increasing system security and others. In this paper, two topics about the network reconfiguration in distribution system are briefly described. The first topic summarizes its impacts while the second explains some heuristic optimization techniques for solving the network reconfiguration problem.

Keywords: Network Reconfiguration, Optimization Techniques, Distribution System

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Authors: H. Nikzad, S. Yoshitomi

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In this paper, an optimization procedure is applied for 3D Reinforced concrete building structure with shear wall.  In the optimization problem, cross sections of beams, columns and shear wall dimensions are considered as design variables and the optimal cross sections can be derived to minimize the total cost of the structure. As for final design application, the most suitable sections are selected to satisfy ACI 318-14 code provision based on static linear analysis. The validity of the method is examined through numerical example of 15 storied 3D RC building with shear wall.  This optimization method is expected to assist in providing a useful reference in design early stage, and to be an effective and powerful tool for structural design of RC shear wall structures.

Keywords: Structural optimization, linear static analysis, ETABS, MATLAB, RC moment frame, RC shear wall structures.

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Authors: A.Sankara Subramanian, G.Gurusamy, G.Selvakumar, P.Gnanasekar, A.Nagappan

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This paper presents an algorithm based on the wavelet decomposition, for feature extraction from the ECG signal and recognition of three types of Ventricular Arrhythmias using neural networks. A set of Discrete Wavelet Transform (DWT) coefficients, which contain the maximum information about the arrhythmias, is selected from the wavelet decomposition. After that a novel clustering algorithm based on nature inspired algorithm (Ant Colony Optimization) is developed for classifying arrhythmia types. The algorithm is applied on the ECG registrations from the MIT-BIH arrhythmia and malignant ventricular arrhythmia databases. We applied Daubechies 4 wavelet in our algorithm. The wavelet decomposition enabled us to perform the task efficiently and produced reliable results.

Keywords: Daubechies 4 Wavelet, ECG, Nature inspired algorithm, Ventricular Arrhythmias, Wavelet Decomposition.

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Authors: E. Diryak, P. Lefley, L. Petkovska, G. Cvetkovski

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This paper presents the optimum design for a double stator, cup rotor machine; a novel type of BLDC PM Machine. The optimization approach is divided into two stages: the first stage is calculating the machine configuration using Matlab, and the second stage is the optimization of the machine using Finite Element Modeling (FEM). Under the design specifications, the machine model will be selected from three pole numbers, namely, 8, 10 and 12 with an appropriate slot number. A double stator brushless DC permanent magnet machine is designed to achieve low cogging torque; high electromagnetic torque and low ripple torque.

Keywords: Permanent magnet machine, low- cogging torque, low- ripple torque, high- electromagnetic torque, design optimization.

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Authors: Xi Pei, Ruifen Cao, Hui Liu, Chufeng Jin, Mengyun Cheng, Huaqing Zheng, Yican Wu, FDS Team

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In intensity modulated radiation therapy (IMRT) treatment planning, beam angles are usually preselected on the basis of experience and intuition. Therefore, getting an appropriate beam configuration needs a very long time. Based on the present situation, the paper puts forward beam orientation optimization using ant colony optimization (ACO). We use ant colony optimization to select the beam configurations, after getting the beam configuration using Conjugate Gradient (CG) algorithm to optimize the intensity profiles. Combining with the information of the effect of pencil beam, we can get the global optimal solution accelerating. In order to verify the feasibility of the presented method, a simulated and clinical case was tested, compared with dose-volume histogram and isodose line between target area and organ at risk. The results showed that the effect was improved after optimizing beam configurations. The optimization approach could make treatment planning meet clinical requirements more efficiently, so it had extensive application perspective.

Keywords: intensity modulated radiation therapy, ant colonyoptimization, Conjugate Gradient algorithm

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Authors: Vassilios Moussas, Dimos N. Pantazis, Panagiotis Stratakis

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The aim of this paper is to present the optimization methodology developed in the frame of a Coastal Transport Information System. The system will be used for the effective design of coastal transportation lines and incorporates subsystems that implement models, tools and techniques that may support the design of improved networks. The role of the optimization and decision subsystem is to provide the user with better and optimal scenarios that will best fulfill any constrains, goals or requirements posed. The complexity of the problem and the large number of parameters and objectives involved led to the adoption of an evolutionary method (Genetic Algorithms). The problem model and the subsystem structure are presented in detail, and, its support for simulation is also discussed.

Keywords: Coastal transport, modeling, optimization.

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Authors: M.H.Aziz, Erik L.J.Bohez, Manukid Parnichkun, Chanchal Saha

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Petri Net (PN) has proven to be effective graphical, mathematical, simulation, and control tool for Discrete Event Systems (DES). But, with the growth in the complexity of modern industrial, and communication systems, PN found themselves inadequate to address the problems of uncertainty, and imprecision in data. This gave rise to amalgamation of Fuzzy logic with Petri nets and a new tool emerged with the name of Fuzzy Petri Nets (FPN). Although there had been a lot of research done on FPN and a number of their applications have been anticipated, but their basic types and structure are still ambiguous. Therefore, in this research, an effort is made to categorize FPN according to their structure and algorithms Further, literature review of the applications of FPN in the light of their classifications has been done.

Keywords: Discrete event systems, Fuzzy logic, Fuzzy Petri nets, and Petri nets.

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Authors: Ali Ben Abbes, ImedRiadh Farah, Vincent Barra

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Remotely sensed data are a significant source for monitoring and updating databases for land use/cover. Nowadays, changes detection of urban area has been a subject of intensive researches. Timely and accurate data on spatio-temporal changes of urban areas are therefore required. The data extracted from multi-temporal satellite images are usually non-stationary. In fact, the changes evolve in time and space. This paper is an attempt to propose a methodology for changes detection in urban area by combining a non-stationary decomposition method and stochastic modeling. We consider as input of our methodology a sequence of satellite images I₁, I₂, … I_n at different periods (t = 1, 2, ..., n). Firstly, a preprocessing of multi-temporal satellite images is applied. (e.g. radiometric, atmospheric and geometric). The systematic study of global urban expansion in our methodology can be approached in two ways: The first considers the urban area as one same object as opposed to non-urban areas (e.g. vegetation, bare soil and water). The objective is to extract the urban mask. The second one aims to obtain a more knowledge of urban area, distinguishing different types of tissue within the urban area. In order to validate our approach, we used a database of Tres Cantos-Madrid in Spain, which is derived from Landsat for a period (from January 2004 to July 2013) by collecting two frames per year at a spatial resolution of 25 meters. The obtained results show the effectiveness of our method.

Keywords: Multi-temporal satellite image, urban growth, Non-stationarity, stochastic modeling.

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Authors: S. Khamsawang, S. Jiriwibhakorn

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This paper proposes an improved approach based on conventional particle swarm optimization (PSO) for solving an economic dispatch(ED) problem with considering the generator constraints. The mutation operators of the differential evolution (DE) are used for improving diversity exploration of PSO, which called particle swarm optimization with mutation operators (PSOM). The mutation operators are activated if velocity values of PSO nearly to zero or violated from the boundaries. Four scenarios of mutation operators are implemented for PSOM. The simulation results of all scenarios of the PSOM outperform over the PSO and other existing approaches which appeared in literatures.

Keywords: Novel particle swarm optimization, Economic dispatch problem, Mutation operator, Prohibited operating zones, Differential Evolution.

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