Search results for: Evolutionary Algorithm (EA)

Authors: Hany Osman, M. F. Baki

Abstract:

We address the balancing problem of transfer lines in this paper to find the optimal line balancing that minimizes the nonproductive time. We focus on the tool change time and face orientation change time both of which influence the makespane. We consider machine capacity limitations and technological constraints associated with the manufacturing process of auto cylinder heads. The problem is represented by a mixed integer programming model that aims at distributing the design features to workstations and sequencing the machining processes at a minimum non-productive time. The proposed model is solved by an algorithm established using linearization schemes and Benders- decomposition approach. The experiments show the efficiency of the algorithm in reaching the exact solution of small and medium problem instances at reasonable time.

Keywords: Transfer line balancing, Benders' decomposition, Linearization.

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Authors: Rizauddin Ramli, Jaber Abu Qudeiri, Hidehiko Yamamoto

Abstract:

Nowadays the market for industrial companies is becoming more and more globalized and highly competitive, forcing them to shorten the duration of the manufacturing system development time in order to reduce the time to market. In order to achieve this target, the hierarchical systems used in previous manufacturing systems are not enough because they cannot deal effectively with unexpected situations. To achieve flexibility in manufacturing systems, the concept of an Autonomous Decentralized Flexible Manufacturing System (AD-FMS) is useful. In this paper, we introduce a hypothetical reasoning based algorithm called the Algorithm for Future Anticipative Reasoning (AFAR) which is able to decide on a conceivable next action of an Automated Guided Vehicle (AGV) that works autonomously in the AD-FMS.

Keywords: Flexible Manufacturing System, Automated GuidedVehicle, Hypothetical Reasoning, Autonomous Decentralized.

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Authors: V. Sudha, D. Sriram Kumar

Abstract:

In this paper, we present a low complexity hybrid scheme using conventional selective mapping (C-SLM) and clipping algorithms to reduce the high peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signal. In the proposed scheme, the input data sequence (X) is divided into two sub-blocks, then clipping algorithm is applied to the first sub-block, whereas C-SLM algorithm is applied to the second sub-block in order to reduce both computational complexity and PAPR. The resultant time domain OFDM signal is obtained by combining the output of two sub-blocks. The simulation results show that the proposed hybrid scheme provides 0.45 dB PAPR reduction gain at CCDF value of 10-2 and 52% of computational complexity reduction when compared to C-SLM scheme at the expense of slight degradation in bit error rate (BER) performance.

Keywords: CCDF, Clipping, OFDM, PAPR, SLM.

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Authors: Jianfeng Li, Feng Jin, Xiaoyu Yang

Abstract:

This paper applies fuzzy clustering algorithm in classifying real estate companies in China according to some general financial indexes, such as income per share, share accumulation fund, net profit margins, weighted net assets yield and shareholders' equity. By constructing and normalizing initial partition matrix, getting fuzzy similar matrix with Minkowski metric and gaining the transitive closure, the dynamic fuzzy clustering analysis for real estate companies is shown clearly that different clustered result change gradually with the threshold reducing, and then, it-s shown there is the similar relationship with the prices of those companies in stock market. In this way, it-s great valuable in contrasting the real estate companies- financial condition in order to grasp some good chances of investment, and so on.

Keywords: Fuzzy clustering algorithm, data mining, real estate company, financial analysis.

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Authors: Paulo Gomes, Adelaide Figueiredo

Abstract:

We consider n individuals described by p standardized variables, represented by points of the surface of the unit hypersphere S_n-1. For a previous choice of n individuals we suppose that the set of observables variables comes from a mixture of bipolar Watson distribution defined on the hypersphere. EM and Dynamic Clusters algorithms are used for identification of such mixture. We obtain estimates of parameters for each Watson component and then a partition of the set of variables into homogeneous groups of variables. Additionally we will present a factor analysis model where unobservable factors are just the maximum likelihood estimators of Watson directional parameters, exactly the first principal component of data matrix associated to each group previously identified. Such alternative model it will yield us to directly interpretable solutions (simple structure), avoiding factors rotations.

Keywords: Dynamic Clusters algorithm, EM algorithm, Factor analysis model, Hierarchical Clustering, Watson distribution.

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Authors: Jiming Yang

Abstract:

A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.

Keywords: Convergence analysis, green's function, singularly perturbed, equi-distribution, moving mesh.

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Authors: Srinivasan Aruchamy, Partha Bhattacharjee, Goutam Sanyal

Abstract:

Optic disk segmentation plays a key role in the mass screening of individuals with diabetic retinopathy and glaucoma ailments. An efficient hardware-based algorithm for optic disk localization and segmentation would aid for developing an automated retinal image analysis system for real time applications. Herein, TMS320C6416DSK DSP board pixel intensity based fractal analysis algorithm for an automatic localization and segmentation of the optic disk is reported. The experiment has been performed on color and fluorescent angiography retinal fundus images. Initially, the images were pre-processed to reduce the noise and enhance the quality. The retinal vascular tree of the image was then extracted using canny edge detection technique. Finally, a pixel intensity based fractal analysis is performed to segment the optic disk by tracing the origin of the vascular tree. The proposed method is examined on three publicly available data sets of the retinal image and also with the data set obtained from an eye clinic. The average accuracy achieved is 96.2%. To the best of the knowledge, this is the first work reporting the use of TMS320C6416DSK DSP board and pixel intensity based fractal analysis algorithm for an automatic localization and segmentation of the optic disk. This will pave the way for developing devices for detection of retinal diseases in the future.

Keywords: Color retinal fundus images, Diabetic retinopathy, Fluorescein angiography retinal fundus images, Fractal analysis.

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Authors: Mario Mastriani, Marcelo Naiouf

Abstract:

This paper introduces a Quantum Correlation Matrix Memory (QCMM) and Enhanced QCMM (EQCMM), which are useful to work with quantum memories. A version of classical Gram-Schmidt orthogonalisation process in Dirac notation (called Quantum Orthogonalisation Process: QOP) is presented to convert a non-orthonormal quantum basis, i.e., a set of non-orthonormal quantum vectors (called qudits) to an orthonormal quantum basis, i.e., a set of orthonormal quantum qudits. This work shows that it is possible to improve the performance of QCMM thanks QOP algorithm. Besides, the EQCMM algorithm has a lot of additional fields of applications, e.g.: Steganography, as a replacement Hopfield Networks, Bilevel image processing, etc. Finally, it is important to mention that the EQCMM is an extremely easy to implement in any firmware.

Keywords: Quantum Algebra, correlation matrix memory, Dirac notation, orthogonalisation.

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Authors: Ghassan A. Abed, Akbal O. Salman, Bayan M. Sabbar

Abstract:

Transmission Control Protocol (TCP) among the wired and wireless networks, it still has a practical problem; where the congestion control mechanism does not permit the data stream to get complete bandwidth over the existing network links. To solve this problem, many TCP protocols have been introduced with high speed performance. Therefore, an enhanced congestion window (cwnd) for the congestion control mechanism is proposed in this article to improve the performance of TCP by increasing the number of cycles of the new window to improve the transmitted packet number. The proposed algorithm used a new mechanism based on the available bandwidth of the connection to detect the capacity of network path in order to improve the regular clocking of congestion avoidance mechanism. The work in this paper based on using Network Simulator 2 (NS-2) to simulate the proposed algorithm.

Keywords: TCP, cwnd, Congestion Control, NS-2.

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Authors: Suryanto, Hyo-Kak Kim, Sang-Hee Park, Dae-Hwan Kim, Sung-Jea Ko

Abstract:

In this paper, we introduce a novel algorithm for object tracking in video sequence. In order to represent the object to be tracked, we propose a spatial color histogram model which encodes both the color distribution and spatial information. The object tracking from frame to frame is accomplished via center voting and back projection method. The center voting method has every pixel in the new frame to cast a vote on whereabouts the object center is. The back projection method segments the object from the background. The segmented foreground provides information on object size and orientation, omitting the need to estimate them separately. We do not put any assumption on camera motion; the proposed algorithm works equally well for object tracking in both static and moving camera videos.

Keywords: center voting, back projection, object tracking, size adaptation, non-stationary camera tracking.

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Authors: Sello Mokwena, Monyepao Thabang

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In this study, we propose a comprehensive approach to address the challenges in person re-identification models. By combining a centroid tracking algorithm with a Siamese convolutional neural network model, our method excels in detecting, tracking, and capturing robust person features across non-overlapping camera views. The algorithm efficiently identifies individuals in the camera network, while the neural network extracts fine-grained global features for precise cross-image comparisons. The approach's effectiveness is further accentuated by leveraging the camera network topology for guidance. Our empirical analysis of benchmark datasets highlights its competitive performance, particularly evident when background subtraction techniques are selectively applied, underscoring its potential in advancing person re-identification techniques.

Keywords: Camera network, convolutional neural network topology, person tracking, person re-identification, Siamese.

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Authors: Zhihan Li

Abstract:

Nowadays, most universities use the course enrollment system considering students’ registration orders. However, the students’ preference level to certain courses is also one important factor to consider. In this research, the possibility of applying a preference-first system has been discussed and analyzed compared to the order-first system. A bipartite graph is applied to resemble the relationship between students and courses they tend to register. With the graph set up, we apply Ford-Fulkerson (F.F.) Algorithm to maximize parings between two sets of nodes, in our case, students and courses. Two models are proposed in this paper: the one considered students’ order first, and the one considered students’ preference first. By comparing and contrasting the two models, we highlight the usability of models which potentially leads to better designs for school course registration systems.

Keywords: Bipartite graph, Ford-Fulkerson Algorithm, graph theory, maximum matching.

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Authors: Belabbas Yagoubi, Yahya Slimani

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Workload and resource management are two essential functions provided at the service level of the grid software infrastructure. To improve the global throughput of these software environments, workloads have to be evenly scheduled among the available resources. To realize this goal several load balancing strategies and algorithms have been proposed. Most strategies were developed in mind, assuming homogeneous set of sites linked with homogeneous and fast networks. However for computational grids we must address main new issues, namely: heterogeneity, scalability and adaptability. In this paper, we propose a layered algorithm which achieve dynamic load balancing in grid computing. Based on a tree model, our algorithm presents the following main features: (i) it is layered; (ii) it supports heterogeneity and scalability; and, (iii) it is totally independent from any physical architecture of a grid.

Keywords: Grid computing, load balancing, workload, tree based model.

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Authors: Ali Abdrhman Ukasha

Abstract:

This paper presented two new efficient algorithms for contour approximation. The proposed algorithm is compared with Ramer (good quality), Triangle (faster) and Trapezoid (fastest) in this work; which are briefly described. Cartesian co-ordinates of an input contour are processed in such a manner that finally contours is presented by a set of selected vertices of the edge of the contour. In the paper the main idea of the analyzed procedures for contour compression is performed. For comparison, the mean square error and signal-to-noise ratio criterions are used. Computational time of analyzed methods is estimated depending on a number of numerical operations. Experimental results are obtained both in terms of image quality, compression ratios, and speed. The main advantages of the analyzed algorithm is small numbers of the arithmetic operations compared to the existing algorithms.

Keywords: Polygonal approximation, Ramer, Triangle and Trapezoid methods.

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Authors: Min-Hsun Kuo, Yun-Shiow Chen

Abstract:

The running logs of a process hold valuable information about its executed activity behavior and generated activity logic structure. Theses informative logs can be extracted, analyzed and utilized to improve the efficiencies of the process's execution and conduction. One of the techniques used to accomplish the process improvement is called as process mining. To mine similar processes is such an improvement mission in process mining. Rather than directly mining similar processes using a single comparing coefficient or a complicate fitness function, this paper presents a simplified heuristic process mining algorithm with two similarity comparisons that are able to relatively conform the activity logic sequences (traces) of mining processes with those of a normalized (regularized) one. The relative process conformance is to find which of the mining processes match the required activity sequences and relationships, further for necessary and sufficient applications of the mined processes to process improvements. One similarity presented is defined by the relationships in terms of the number of similar activity sequences existing in different processes; another similarity expresses the degree of the similar (identical) activity sequences among the conforming processes. Since these two similarities are with respect to certain typical behavior (activity sequences) occurred in an entire process, the common problems, such as the inappropriateness of an absolute comparison and the incapability of an intrinsic information elicitation, which are often appeared in other process conforming techniques, can be solved by the relative process comparison presented in this paper. To demonstrate the potentiality of the proposed algorithm, a numerical example is illustrated.

Keywords: process mining, process similarity, artificial intelligence, process conformance.

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Authors: Lana Dalawr Jalal

Abstract:

This paper addresses the problem of offline path planning for Unmanned Aerial Vehicles (UAVs) in complex threedimensional environment with obstacles, which is modelled by 3D Cartesian grid system. Path planning for UAVs require the computational intelligence methods to move aerial vehicles along the flight path effectively to target while avoiding obstacles. In this paper Modified Particle Swarm Optimization (MPSO) algorithm is applied to generate the optimal collision free 3D flight path for UAV. The simulations results clearly demonstrate effectiveness of the proposed algorithm in guiding UAV to the final destination by providing optimal feasible path quickly and effectively.

Keywords: Obstacle Avoidance, Particle Swarm Optimization, Three-Dimensional Path Planning Unmanned Aerial Vehicles.

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Authors: Sun H. Hwang, Young E. Lee, Yunhan Ga, Gilwon Yoon

Abstract:

EEG is a very complex signal with noises and other bio-potential interferences. EOG is the most distinct interfering signal when EEG signals are measured and analyzed. It is very important how to process raw EEG signals in order to obtain useful information. In this study, the EEG signal processing techniques such as EOG filtering and outlier removal were examined to minimize unwanted EOG signals and other noises. The two different mental states of resting and focusing were examined through EEG analysis. A focused state was induced by letting subjects to watch a red dot on the white screen. EEG data for 32 healthy subjects were measured. EEG data after 60-Hz notch filtering were processed by a commercially available EOG filtering and our presented algorithm based on the removal of outliers. The ratio of beta wave to theta wave was used as a parameter for determining the degree of focusing. The results show that our algorithm was more appropriate than the existing EOG filtering.

Keywords: EEG, focus, mental state, outlier, signal processing.

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Authors: Vadims Goremikins, Karlis Rocens, Dmitrijs Serdjuks

Abstract:

A suspension bridge is the most suitable type of structure for a long-span bridge due to rational use of structural materials. Increased deformability, which is conditioned by appearance of the elastic and kinematic displacements, is the major disadvantage of suspension bridges. The problem of increased kinematic displacements under the action of non-symmetrical load can be solved by prestressing. The prestressed suspension bridge with the span of 200 m was considered as an object of investigations. The cable truss with the cross web was considered as the main load carrying structure of the prestressed suspension bridge. The considered cable truss was optimized by 47 variable factors using Genetic algorithm and FEM program ANSYS. It was stated, that the maximum total displacements are reduced up to 29.9% by using of the cable truss with the rational characteristics instead of the single cable in the case of the worst situated load.

Keywords: Decreasing displacements, Genetic algorithm.

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Authors: Jianwei Wang, Timo Korhonen, Yuping Zhao

Abstract:

Cross layer optimization based on utility functions has been recently studied extensively, meanwhile, numerous types of utility functions have been examined in the corresponding literature. However, a major drawback is that most utility functions take a fixed mathematical form or are based on simple combining, which can not fully exploit available information. In this paper, we formulate a framework of cross layer optimization based on Adaptively Weighted Utility Functions (AWUF) for fairness balancing in OFDMA networks. Under this framework, a two-step allocation algorithm is provided as a sub-optimal solution, whose control parameters can be updated in real-time to accommodate instantaneous QoS constrains. The simulation results show that the proposed algorithm achieves high throughput while balancing the fairness among multiple users.

Keywords: OFDMA, Fairness, AWUF, QoS.

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Authors: Yasser M. Abd El-Latif, Fatma S.Abousaleh, Daoud S. S.

Abstract:

L-system is a tool commonly used for modeling and simulating the growth of fractal plants. The aim of this paper is to join some problems of the computational geometry with the fractal geometry by using the L-system technique to generate fractal plant in 3D. L-system constructs the fractal structure by applying rewriting rules sequentially and this technique depends on recursion process with large number of iterations to get different shapes of 3D fractal plants. Instead, it was reiterated a specific number of iterations up to three iterations. The vertices generated from the last stage of the Lsystem rewriting process are used as input to the triangulation algorithm to construct the triangulation shape of these vertices. The resulting shapes can be used as covers for the architectural objects and in different computer graphics fields. The paper presents a gallery of triangulation forms which application in architecture creates an alternative for domes and other traditional types of roofs.

Keywords: Computational geometry, fractal geometry, L-system, triangulation.

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, Decomposition Method, Generalized Thermoelasticity, algorithm, empirical parameter, lattice design.

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Authors: Mohamed Abdel Fattah, Fuji Ren

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This work proposes an approach to address automatic text summarization. This approach is a trainable summarizer, which takes into account several features, including sentence position, positive keyword, negative keyword, sentence centrality, sentence resemblance to the title, sentence inclusion of name entity, sentence inclusion of numerical data, sentence relative length, Bushy path of the sentence and aggregated similarity for each sentence to generate summaries. First we investigate the effect of each sentence feature on the summarization task. Then we use all features score function to train genetic algorithm (GA) and mathematical regression (MR) models to obtain a suitable combination of feature weights. The proposed approach performance is measured at several compression rates on a data corpus composed of 100 English religious articles. The results of the proposed approach are promising.

Keywords: Automatic Summarization, Genetic Algorithm, Mathematical Regression, Text Features.

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Authors: Jan Busch, Maurice Schmidt, Peter Nyhuis

Abstract:

The change of conditions for production companies in high-wage countries is characterized by the globalization of competition and the transition of a supplier´s to a buyer´s market. The companies need to face the challenges of reacting flexibly to these changes. Due to the significant and increasing degree of automation, assembly has become the most expensive production process. Regarding the reduction of production cost, assembly consequently offers a considerable rationalizing potential. Therefore, an aerodynamic feeding system has been developed at the Institute of Production Systems and Logistics (IFA), Leibniz Universitaet Hannover. This system has been enabled to adjust itself by using a genetic algorithm. The longer this genetic algorithm is executed the better is the feeding quality. In this paper, the relation between the system´s setting time and the feeding quality is observed and a function which enables the user to achieve the minimum of the total feeding time is presented.

Keywords: Aerodynamic feeding system, batch size, optimisation, setting time.

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Authors: T. S. Chou, K. K. Yen, J. Luo

Abstract:

The network traffic data provided for the design of intrusion detection always are large with ineffective information and enclose limited and ambiguous information about users- activities. We study the problems and propose a two phases approach in our intrusion detection design. In the first phase, we develop a correlation-based feature selection algorithm to remove the worthless information from the original high dimensional database. Next, we design an intrusion detection method to solve the problems of uncertainty caused by limited and ambiguous information. In the experiments, we choose six UCI databases and DARPA KDD99 intrusion detection data set as our evaluation tools. Empirical studies indicate that our feature selection algorithm is capable of reducing the size of data set. Our intrusion detection method achieves a better performance than those of participating intrusion detectors.

Keywords: Intrusion detection, feature selection, k-nearest neighbors, fuzzy clustering, Dempster-Shafer theory

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Authors: Sorin Valcan, Mihail Găianu

Abstract:

Labeling is a very costly and time consuming process which aims to generate datasets for training neural networks in several functionalities and projects. For driver monitoring system projects, the need of labeled images has a significant impact on the budget and distribution of effort. This paper presents the modifications done to a ground truth data generation algorithm for 2D eyes location on infrared images with drivers in order to improve the quality of the data and performance of the trained neural networks. The algorithm restrictions become tougher which makes it more accurate but also less constant. The resulting dataset becomes smaller and shall not be altered by any kind of manual labels adjustment before being used in the neural networks training process. These changes resulted in a much better performance of the trained neural networks.

Keywords: Labeling automation, infrared camera, driver monitoring, eye detection, Convolutional Neural Networks.

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Authors: A. Udomsakdigool, S. Bangsaranthip

Abstract:

This paper presents an algorithm which combining ant colony optimization in the dynamic programming for solving a dynamic facility layout problem. The problem is separated into 2 phases, static and dynamic phase. In static phase, ant colony optimization is used to find the best ranked of layouts for each period. Then the dynamic programming (DP) procedure is performed in the dynamic phase to evaluate the layout set during multi-period planning horizon. The proposed algorithm is tested over many problems with size ranging from 9 to 49 departments, 2 and 4 periods. The experimental results show that the proposed method is an alternative way for the plant layout designer to determine the layouts during multi-period planning horizon.

Keywords: Ant colony optimization, Dynamicprogramming, Dynamic facility layout planning, Metaheuristic

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Authors: Revathi Venkataraman, M. Pushpalatha, T. Rama Rao

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The lack of any centralized infrastructure in mobile ad hoc networks (MANET) is one of the greatest security concerns in the deployment of wireless networks. Thus communication in MANET functions properly only if the participating nodes cooperate in routing without any malicious intention. However, some of the nodes may be malicious in their behavior, by indulging in flooding attacks on their neighbors. Some others may act malicious by launching active security attacks like denial of service. This paper addresses few related works done on trust evaluation and establishment in ad hoc networks. Related works on flooding attack prevention are reviewed. A new trust approach based on the extent of friendship between the nodes is proposed which makes the nodes to co-operate and prevent flooding attacks in an ad hoc environment. The performance of the trust algorithm is tested in an ad hoc network implementing the Ad hoc On-demand Distance Vector (AODV) protocol.

Keywords: AODV, Flooding, MANETs, trust estimation

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Authors: Kyaw Myo Lin, Wunna Swe, Pyone Lai Swe

Abstract:

This paper presents the coordinated controller design of static synchronous compensator (STATCOM) and power system stabilizers (PSSs) for power system stability improvement. Coordinated design problem of STATCOM-based controller with multiple PSSs is formulated as an optimization problem and optimal controller parameters are obtained using bacteria foraging optimization algorithm. By minimizing the proposed objective function, in which the speed deviations between generators are involved; stability performance of the system is improved. The nonlinear simulation results show that coordinated design of STATCOM-based controller and PSSs improve greatly the system damping oscillations and consequently stability improvement.

Keywords: Bacteria Foraging, Coordinated Design, Power System Stability, PSSs, STATCOM.

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Authors: Muhammad Abrar, Xiang Gui, Amal Punchihewa

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In this paper we study the resource allocation problem for an OFDMA based cooperative two-way relaying (TWR) network. We focus on amplify and forward (AF) analog network coding (ANC) protocol. An optimization problem for two basic resources namely, sub-carrier and power is formulated for multi-user TWR networks. A joint optimal optimization problem is investigated and two-step low complexity sub-optimal resource allocation algorithm is proposed for multi-user TWR networks with ANC protocol. The proposed algorithm has been evaluated in term of total achievable system sum-rate and achievable individual sum-rate for each userpair. The good tradeoff between system sum-rate and fairness is observed in the two-step proportional resource allocation scheme.

Keywords: Relay Network, Relay Protocols, Resource Allocation, Two –way relaying.

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Authors: H.R.Goshayeshi, M.Fahim inia, M.M.Naserian

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In this research, the laminar heat transfer of natural convection on vertical surfaces has been investigated. Most of the studies on natural convection have been considered constantly whereas velocity and temperature domain, do not change with time, transient one are used a lot. Governing equations are solved using a finite volume approach. The convective terms are discretized using the power-law scheme, whereas for diffusive terms the central difference is employed. Coupling between the velocity and pressure is made with SIMPLE algorithm. The resultant system of discretized linear algebraic equations is solved with an alternating direction implicit scheme. Then a configuration of rectangular fins is put in different ways on the surface and heat transfer of natural convection on these surfaces without sliding is studied and finally optimization is done.

Keywords: Natural convection, vertical surfaces, SIMPLE algorithm, Rectangular fins.

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