Search results for: partial swarm optimisation

Authors: Y. Harold Robinson, M. Rajaram, Honey Raju

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Image segmentation and color identification is an important process used in various emerging fields like intelligent robotics. A method is proposed for the manipulator to grasp and place the color object into correct location. The existing methods such as PSO, has problems like accelerating the convergence speed and converging to a local minimum leading to sub optimal performance. To improve the performance, we are using watershed algorithm and for color identification, we are using EPSO. EPSO method is used to reduce the probability of being stuck in the local minimum. The proposed method offers the particles a more powerful global exploration capability. EPSO methods can determine the particles stuck in the local minimum and can also enhance learning speed as the particle movement will be faster.

Keywords: Color information, EPSO, hue, saturation, value (HSV), image segmentation, particle swarm optimization (PSO). Active Contour, GMM.

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Authors: Pham Van Nha, Le Cam Binh

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Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: Analysis of optimization, artificial intelligence-based optimization, optimization for learning and data analysis, global optimization.

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Authors: S. N. Deepa, G. Sugumaran

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This paper proposes a new algebraic scheme to design a PID controller for higher order linear time invariant continuous systems. Modified PSO (MPSO) based model order formulation techniques have applied to obtain the effective formulated second order system. A controller is tuned to meet the desired performance specification by using pole-zero cancellation method. Proposed PID controller is attached with both higher order system and formulated second order system. The closed loop response is observed for stabilization process and compared with general PSO based formulated second order system. The proposed method is illustrated through numerical example from literature.

Keywords: Higher order systems, model order formulation, modified particle swarm optimization, PID controller, pole-zero cancellation.

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

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In this work, we obtain some analytic solutions for the (3+1)-dimensional breaking soliton after obtaining its Hirota-s bilinear form. Our calculations show that, three-wave method is very easy and straightforward to solve nonlinear partial differential equations.

Keywords: (3+1)-dimensional breaking soliton equation, Hirota'sbilinear form.

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Authors: Vishwesh Kulkarni, Nikhil Bellarykar

Abstract:

Cellular complexity stems from the interactions among thousands of different molecular species. Thanks to the emerging fields of systems and synthetic biology, scientists are beginning to unravel these regulatory, signaling, and metabolic interactions and to understand their coordinated action. Reverse engineering of biological networks has has several benefits but a poor quality of data combined with the difficulty in reproducing it limits the applicability of these methods. A few years back, many of the commonly used predictive algorithms were tested on a network constructed in the yeast Saccharomyces cerevisiae (S. cerevisiae) to resolve this issue. The network was a synthetic network of five genes regulating each other for the so-called in vivo reverse-engineering and modeling assessment (IRMA). The network was constructed in S. cereviase since it is a simple and well characterized organism. The synthetic network included a variety of regulatory interactions, thus capturing the behaviour of larger eukaryotic gene networks on a smaller scale. We derive a new set of algorithms by solving a nonlinear optimization problem and show how these algorithms outperform other algorithms on these datasets.

Keywords: Synthetic gene network, network identification, nonlinear modeling, optimization.

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Authors: S. Dehghan, B. Kiani, A. Kazemi, A. Parizad

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The utilization of renewable energy sources in electric power systems is increasing quickly because of public apprehensions for unpleasant environmental impacts and increase in the energy costs involved with the use of conventional energy sources. Despite the application of these energy sources can considerably diminish the system fuel costs, they can also have significant influence on the system reliability. Therefore an appropriate combination of the system reliability indices level and capital investment costs of system is vital. This paper presents a hybrid wind/photovoltaic plant, with the aim of supplying IEEE reliability test system load pattern while the plant capital investment costs is minimized by applying a hybrid particle swarm optimization (PSO) / harmony search (HS) approach, and the system fulfills the appropriate level of reliability.

Keywords: Distributed Generation, Fuel Cell, HS, Hybrid Power Plant, PSO, Photovoltaic, Reliability.

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Talal H. Alzanki

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This paper presents a hybrid fuzzy logic control strategy for a unicycle trajectory following robot on irregular terrains. In literature, researchers have presented the design of path tracking controllers of mobile robots on non-frictional surface. In this work, the robot is simulated to drive on irregular terrains with contrasting frictional profiles of peat and rough gravel. A hybrid fuzzy logic controller is utilised to stabilise and drive the robot precisely with the predefined trajectory and overcome the frictional impact. The controller gains and scaling factors were optimised using spiral dynamics optimisation algorithm to minimise the mean square error of the linear and angular velocities of the unicycle robot. The robot was simulated on various frictional surfaces and terrains and the controller was able to stabilise the robot with a superior performance that is shown via simulation results.

Keywords: Fuzzy logic control, mobile robot, trajectory tracking, spiral dynamic algorithm.

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Authors: Zineddine Bouyahiaoui, Rabah Haoui

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The aim of this work is to analyze a flow around the axisymmetric blunt body taken into account the chemical and vibrational nonequilibrium flow. This work concerns the entry of spacecraft in the atmosphere of the planet Mars. Since the equations involved are non-linear partial derivatives, the volume method is the only way to solve this problem. The choice of the mesh and the CFL is a condition for the convergence to have the stationary solution.

Keywords: Hypersonic flow, nonequilibrium flow, shock wave, blunt body.

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Authors: Adel Sabry Eesa, Adnan Mohsin Abdulazeez Brifcani, Zeynep Orman

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This paper presents a new meta-heuristic bio-inspired optimization algorithm which is called Cuttlefish Algorithm (CFA). The algorithm mimics the mechanism of color changing behavior of the cuttlefish to solve numerical global optimization problems. The colors and patterns of the cuttlefish are produced by reflected light from three different layers of cells. The proposed algorithm considers mainly two processes: reflection and visibility. Reflection process simulates light reflection mechanism used by these layers, while visibility process simulates visibility of matching patterns of the cuttlefish. To show the effectiveness of the algorithm, it is tested with some other popular bio-inspired optimization algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Bees Algorithm (BA) that have been previously proposed in the literature. Simulations and obtained results indicate that the proposed CFA is superior when compared with these algorithms.

Keywords: Cuttlefish Algorithm, bio-inspired algorithms, optimization.

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Authors: Tarek Aboueldahab

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In this paper, we propose a new hybrid learning model for stock market indices prediction by adding a passive congregation term to the standard hybrid model comprising Particle Swarm Optimization (PSO) with Genetic Algorithm (GA) operators in training Neural Networks (NN). This new passive congregation term is based on the cooperation between different particles in determining new positions rather than depending on the particles selfish thinking without considering other particles positions, thus it enables PSO to perform both the local and global search instead of only doing the local search. Experiment study carried out on the most famous European stock market indices in both long term and short term prediction shows significantly the influence of the passive congregation term in improving the prediction accuracy compared to standard hybrid model.

Keywords: Global Search, Hybrid Model, Passive Congregation, Stock Market Prediction.

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Authors: Manirath Wongsim, Pawornprat Hongsakon

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Information Quality (IQ) has become a critical, strategic issue in Accounting Information Systems (AIS) adoption. In order to implement AIS adoption successfully, it is important to consider the quality of information use throughout the adoption process, which seriously impacts the effectiveness of AIS adoption practice and the optimisation of AIS adoption decisions. There is a growing need for research to provide insights into issues and solutions related to IQ in AIS adoption. The need for an integrated approach to improve IQ in AIS adoption, as well as the unique characteristics of accounting data, demands an AIS adoption specific IQ framework. This research aims to explore ways of managing information quality and AIS adoption to investigate the relationship between the IQ issues and AIS adoption process. This study has led to the development of a framework for understanding IQ management in AIS adoption. This research was done on 44 respondents as ten organisations from manufacturing firms in Thailand. The findings of the research’s empirical evidence suggest that IQ dimensions in AIS adoption to provide assistance in all process of decision making. This research provides empirical evidence that information quality of AIS adoption affect decision making and suggests that these variables should be considered in adopting AIS in order to improve the effectiveness of AIS.

Keywords: Information quality, information quality dimensions, accounting information systems, accounting Information system adoption.

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Authors: Tebogo Phetla, Edison Muzenda, M Belaid

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This study investigated possible ways to improve the efficiency of the platinum precipitation process using ammonium chloride by reducing the platinum content reporting to the effluent. The ore treated consist of five platinum group metals namely, ruthenium, rhodium, iridium, platinum, palladium and a precious metal gold. Gold, ruthenium, rhodium and iridium were extracted prior the platinum precipitation process. Temperature, reducing agent, flow rate and potential difference were the variables controlled to determine the operation conditions for optimum platinum precipitation efficiency. Hydrogen peroxide was added as the oxidizing agent at the temperature of 85-90oC and potential difference of 700-850mV was the variable used to check the oxidizing state of platinum. The platinum was further purified at temperature between 60-65oC, potential difference above 700 mV, ammonium chloride of 200 l, and at these conditions the platinum content reporting to the effluent was reduced to less than 300ppm, resulting in optimum platinum precipitation efficiency and purity of 99.9%.

Keywords: Platinum Group Metals (PGM), Potential difference, Precipitation, Redox reactions.

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Authors: Xiaoli Shen, Yuehui Chen

Abstract:

Interactions among proteins are the basis of various life events. So, it is important to recognize and research protein interaction sites. A control set that contains 149 protein molecules were used here. Then 10 features were extracted and 4 sample sets that contained 9 sliding windows were made according to features. These 4 sample sets were calculated by Radial Basis Functional neutral networks which were optimized by Particle Swarm Optimization respectively. Then 4 groups of results were obtained. Finally, these 4 groups of results were integrated by decision fusion (DF) and Genetic Algorithm based Selected Ensemble (GASEN). A better accuracy was got by DF and GASEN. So, the integrated methods were proved to be effective.

Keywords: protein interaction sites, features, sliding windows, radial basis functional neutral networks, genetic algorithm basedselected ensemble.

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Authors: Seifedine Kadry

Abstract:

In this article, our objective is the analysis of the resolution of non-linear differential systems by combining Newton and Continuation (N-C) method. The iterative numerical methods converge where the initial condition is chosen close to the exact solution. The question of choosing the initial condition is answered by N-C method.

Keywords: Continuation Method, Newton Method, Finite Difference Method, Numerical Analysis and Non-Linear partial Differential Equation.

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Authors: H. Shayeghi, H. Hosseini, A. Shabani, M. Mahdavi

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In this paper, optimal generation expansion planning (GEP) is investigated considering purchase prices, profits of independent power producers (IPPs) and reliability criteria using a new method based on hybrid coded Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). In this approach, optimal purchase price of each IPP is obtained by HCGA and reliability criteria are calculated by PSO technique. It should be noted that reliability criteria and the rate of carbon dioxide (CO2) emission have been considered as constraints of the GEP problem. Finally, the proposed method has been tested on the case study system. The results evaluation show that the proposed method can simply obtain optimal purchase prices of IPPs and is a fast method for calculation of reliability criteria in expansion planning. Also, considering the optimal purchase prices and profits of IPPs in generation expansion planning are caused that the expansion costs are decreased and the problem is solved more exactly.

Keywords: GEP Problem, IPPs, Reliability Criteria, GA, PSO.

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Authors: Yizhi Gai, Yukinori Kobayashi, Yohei Hoshino, Takanori Emaru

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Motion control of flexible arms is more difficult than that of rigid arms, however utilizing its dynamics enables improved performance such as a fast motion in short operation time. This paper investigates a ball throwing robot with one rigid link and one flexible link. This robot throws a ball at a set speed with a proper control torque. A mathematical model of this ball throwing robot is derived through Hamilton’s principle. Several patterns of torque input are designed and tested through the proposed simulation models. The parameters of each torque input pattern is optimized and determined by chaos embedded vector evaluated particle swarm optimization (CEVEPSO). Then, the residual vibration of the manipulator after throwing is suppressed with input shaping technique. Finally, a real experiment is set up for the model checking.

Keywords: Motion control, flexible robotic arm, CEVEPSO, ball throwing robot.

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Authors: Jingya Liu, Yue Wu, Jiabin Luo

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This work investigates an intermodal transportation system for delivering goods from a Regional Distribution Centre to supermarkets on the Isle of Wight (IOW) via the port of Southampton or Portsmouth in the UK. We consider this integrated logistics chain as a 3-echelon transportation system. In such a system, there are two types of transport methods used to deliver goods across the Solent Channel: one is accompanied transport, which is used by most supermarkets on the IOW, such as Spar, Lidl and Co-operative food; the other is unaccompanied transport, which is used by Aldi. Five transport scenarios are studied based on different transport modes and ferry routes. The aim is to determine an optimal delivery plan for supermarkets of different business scales on IOW, in order to minimise the total running cost, fuel consumptions and carbon emissions. The problem is modelled as a vehicle routing problem with time windows and solved by genetic algorithm. The computing results suggested that accompanied transport is more cost efficient for small and medium business-scale supermarket chains on IOW, while unaccompanied transport has the potential to improve the efficiency and effectiveness of large business scale supermarket chains.

Keywords: Genetic algorithm, intermodal transport system, Isle of Wight, optimization, supermarket.

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Authors: Sufian Ashraf Mazhari, Surendra Kumar

Abstract:

This paper compares the heuristic Global Search Techniques; Genetic Algorithm, Particle Swarm Optimization, Simulated Annealing, Generalized Pattern Search, genetic algorithm hybridized with Nelder–Mead and Generalized pattern search technique for tuning of fuzzy PID controller for Puma 560. Since the actual control is in joint space ,inverse kinematics is used to generate various joint angles correspoding to desired cartesian space trajectory. Efficient dynamics and kinematics are modeled on Matlab which takes very less simulation time. Performances of all the tuning methods with and without disturbance are compared in terms of ITSE in joint space and ISE in cartesian space for spiral trajectory tracking. Genetic Algorithm hybridized with Generalized Pattern Search is showing best performance.

Keywords: Controller tuning, Fuzzy Control, Genetic Algorithm, Heuristic search, Robot control.

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Authors: C. Rajan, K. Geetha, C. Rasi Priya, R. Sasikala

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Nature is a great source of inspiration for solving complex problems in networks. It helps to find the optimal solution. Metaheuristic algorithm is one of the nature-inspired algorithm which helps in solving routing problem in networks. The dynamic features, changing of topology frequently and limited bandwidth make the routing, challenging in MANET. Implementation of appropriate routing algorithms leads to the efficient transmission of data in mobile ad hoc networks. The algorithms that are inspired by the principles of naturally-distributed/collective behavior of social colonies have shown excellence in dealing with complex optimization problems. Thus some of the bio-inspired metaheuristic algorithms help to increase the efficiency of routing in ad hoc networks. This survey work presents the overview of bio-inspired metaheuristic algorithms which support the efficiency of routing in mobile ad hoc networks.

Keywords: Ant colony optimization algorithm, Genetic algorithm, naturally inspired algorithms and particle swarm optimization algorithm.

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Authors: Andrey V. Timofeev, Dmitry V. Egorov

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This paper introduces an original method of parametric optimization of the structure for multimodal decisionlevel fusion scheme which combines the results of the partial solution of the classification task obtained from assembly of the mono-modal classifiers. As a result, a multimodal fusion classifier which has the minimum value of the total error rate has been obtained.

Keywords: Сlassification accuracy, fusion solution, total error rate.

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Authors: Saba Shams Bidhendi, Steven Goh, Andrew Wandel

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The implementation of lean manufacturing initiatives has produced significant impacts in improving operational performance and reducing manufacturing wastes in the production process. However, selecting an appropriate set of lean strategies is critical to avoid misapplication of the lean manufacturing techniques and consequential increase in non-value-adding activities. To the author’s best knowledge, there is currently no methodology to select lean strategies that considers their impacts on manufacturing wastes and performance metrics simultaneously. In this research, a multi-objective methodology is proposed that suggests an appropriate set of lean initiatives based on their impacts on performance metrics and manufacturing wastes and within manufacturers’ resource limitation. The proposed methodology in this research suggests the best set of lean initiatives for implementation that have highest impacts on identified critical performance metrics and manufacturing wastes. Therefore, manufacturers can assure that implementing suggested lean tools improves their production performance and reduces manufacturing wastes at the same time. A case study was conducted to show the effectiveness and validate the proposed model and methodologies.

Keywords: Lean manufacturing, Lean strategies, manufacturing wastes, manufacturing performance metrics, decision making, optimisation.

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Authors: Philip Symonds, Jon Taylor, Zaid Chalabi, Michael Davies

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Average temperatures worldwide are expected to continue to rise. At the same time, major cities in developing countries are becoming increasingly populated and polluted. Governments are tasked with the problem of overheating and air quality in residential buildings. This paper presents the development of a model, which is able to estimate the occupant exposure to extreme temperatures and high air pollution within domestic buildings. Building physics simulations were performed using the EnergyPlus building physics software. An accurate metamodel is then formed by randomly sampling building input parameters and training on the outputs of EnergyPlus simulations. Metamodels are used to vastly reduce the amount of computation time required when performing optimisation and sensitivity analyses. Neural Networks (NNs) have been compared to a Radial Basis Function (RBF) algorithm when forming a metamodel. These techniques were implemented using the PyBrain and scikit-learn python libraries, respectively. NNs are shown to perform around 15% better than RBFs when estimating overheating and air pollution metrics modelled by EnergyPlus.

Keywords: Neural Networks, Radial Basis Functions, Metamodelling, Python machine learning libraries.

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Authors: R. Srinivasa Rao

Abstract:

This paper presents a new method which applies an artificial bee colony algorithm (ABC) for capacitor placement in distribution systems with an objective of improving the voltage profile and reduction of power loss. The ABC algorithm is a new population based meta heuristic approach inspired by intelligent foraging behavior of honeybee swarm. The advantage of ABC algorithm is that it does not require external parameters such as cross over rate and mutation rate as in case of genetic algorithm and differential evolution and it is hard to determine these parameters in prior. The other advantage is that the global search ability in the algorithm is implemented by introducing neighborhood source production mechanism which is a similar to mutation process. To demonstrate the validity of the proposed algorithm, computer simulations are carried out on 69-bus system and compared the results with the other approach available in the literature. The proposed method has outperformed the other methods in terms of the quality of solution and computational efficiency.

Keywords: Distribution system, Capacitor Placement, Loss reduction, Artificial Bee Colony Algorithm.

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Authors: Jaroslav Žák, Aleš Florian

Abstract:

Green bridges enable wildlife to pass through linear structures, especially freeways. The term migration potential is used to quantify their functionality. The proposed methodology for determining migration potential eliminates the mathematical, systematic and ecological inaccuracies of previous methodologies and provides a reliable tool for designers and environmentalists. The methodology is suited especially to medium-sized and large mammals, is mathematically correct, and its correspondence with reality was tested by monitoring existing green bridges. 

Keywords: Green bridges, migration potential, partial probabilities, wildlife migration.

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

Abstract:

On the basis of the linearized Phillips-Herffron model of a single-machine power system, a novel method for designing unified power flow controller (UPFC) based output feedback controller is presented. The design problem of output feedback controller for UPFC is formulated as an optimization problem according to with the time domain-based objective function which is solved by iteration particle swarm optimization (IPSO) that has a strong ability to find the most optimistic results. To ensure the robustness of the proposed damping controller, the design process takes into account a wide range of operating conditions and system configurations. The simulation results prove the effectiveness and robustness of the proposed method in terms of a high performance power system. The simulation study shows that the designed controller by Iteration PSO performs better than Classical PSO in finding the solution.

Keywords: UPFC, IPSO, output feedback Controller.

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Authors: M. Padmavathi, R. M. Suresh

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Every machine plays roles of client and server simultaneously in a peer-to-peer (P2P) network. Though a P2P network has many advantages over traditional client-server models regarding efficiency and fault-tolerance, it also faces additional security threats. Users/IT administrators should be aware of risks from malicious code propagation, downloaded content legality, and P2P software’s vulnerabilities. Security and preventative measures are a must to protect networks from potential sensitive information leakage and security breaches. Bit Torrent is a popular and scalable P2P file distribution mechanism which successfully distributes large files quickly and efficiently without problems for origin server. Bit Torrent achieved excellent upload utilization according to measurement studies, but it also raised many questions as regards utilization in settings, than those measuring, fairness, and Bit Torrent’s mechanisms choice. This work proposed a block selection technique using Fuzzy ACO with optimal rules selected using ACO.

Keywords: Ant Colony Optimization (ACO), Bit Torrent, Download time, Peer-to-Peer (P2P) network, Performance.

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Authors: Chunshien Li, Jhao-Wun Hu, Tai-Wei Chiang, Tsunghan Wu

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Time series forecasting is an important and widely popular topic in the research of system modeling. This paper describes how to use the hybrid PSO-RLSE neuro-fuzzy learning approach to the problem of time series forecasting. The PSO algorithm is used to update the premise parameters of the proposed prediction system, and the RLSE is used to update the consequence parameters. Thanks to the hybrid learning (HL) approach for the neuro-fuzzy system, the prediction performance is excellent and the speed of learning convergence is much faster than other compared approaches. In the experiments, we use the well-known Mackey-Glass chaos time series. According to the experimental results, the prediction performance and accuracy in time series forecasting by the proposed approach is much better than other compared approaches, as shown in Table IV. Excellent prediction performance by the proposed approach has been observed.

Keywords: forecasting, hybrid learning (HL), Neuro-FuzzySystem (NFS), particle swarm optimization (PSO), recursiveleast-squares estimator (RLSE), time series

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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: Sagir M. Yusuf, Chris Baber

Abstract:

We describe issues bedeviling the coordination of heterogeneous (different sensors carrying agents) multi-agent missions such as belief conflict, situation reasoning, etc. We applied Bayesian and agents' presumptions inferential reasoning to solve the outlined issues with the heterogeneous multi-agent belief variation and situational-base reasoning. Bayesian Belief Network (BBN) was used in modeling the agents' belief conflict due to sensor variations. Simulation experiments were designed, and cases from agents’ missions were used in training the BBN using gradient descent and expectation-maximization algorithms. The output network is a well-trained BBN for making inferences for both agents and human experts. We claim that the Bayesian learning algorithm prediction capacity improves by the number of training data and argue that it enhances multi-agents robustness and solve agents’ sensor conflicts.

Keywords: Distributed constraint optimization problem, multi-agent system, multi-robot coordination, autonomous system, swarm intelligence.

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Authors: P. Luangpaiboon, S. Boonhao

Abstract:

This study proposes a multi-response surface optimization problem (MRSOP) for determining the proper choices of a process parameter design (PPD) decision problem in a noisy environment of a grease position process in an electronic industry. The proposed models attempts to maximize dual process responses on the mean of parts between failure on left and right processes. The conventional modified simplex method and its hybridization of the stochastic operator from the hunting search algorithm are applied to determine the proper levels of controllable design parameters affecting the quality performances. A numerical example demonstrates the feasibility of applying the proposed model to the PPD problem via two iterative methods. Its advantages are also discussed. Numerical results demonstrate that the hybridization is superior to the use of the conventional method. In this study, the mean of parts between failure on left and right lines improve by 39.51%, approximately. All experimental data presented in this research have been normalized to disguise actual performance measures as raw data are considered to be confidential.

Keywords: Grease Position Process, Multi-response Surfaces, Modified Simplex Method, Hunting Search Method, Desirability Function Approach.

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