Search results for: Ant Algorithms

Authors: M’hamed Outanoute, Mohamed Baslam, Belaid Bouikhalene

Abstract:

The customers use the best compromise criterion between price and quality of service (QoS) to select or change their Service Provider (SP). The SPs share the same market and are competing to attract more customers to gain more profit. Due to the divergence of SPs interests, we believe that this situation is a non-cooperative game of price and QoS. The game converges to an equilibrium position known Nash Equilibrium (NE). In this work, we formulate a game theoretic framework for the dynamical behaviors of SPs. We use Genetic Algorithms (GAs) to find the price and QoS strategies that maximize the profit for each SP and illustrate the corresponding strategy in NE. In order to quantify how this NE point is performant, we perform a detailed analysis of the price of anarchy induced by the NE solution. Finally, we provide an extensive numerical study to point out the importance of considering price and QoS as a joint decision parameter.

Keywords: Pricing, QoS, Market share game, Genetic algorithms, Nash equilibrium, Learning, Price of anarchy.

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Authors: S.A.Ahmad, M.N.Taib, N.E.A.Khalid, R.Ahmad, H.Taib

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The purpose of this research is to compare the original intra-oral digital dental radiograph images with images that are enhanced using a combination of image processing algorithms. Intraoral digital dental radiograph images are often noisy, blur edges and low in contrast. A combination of sharpening and enhancement method are used to overcome these problems. Three types of proposed compound algorithms used are Sharp Adaptive Histogram Equalization (SAHE), Sharp Median Adaptive Histogram Equalization (SMAHE) and Sharp Contrast adaptive histogram equalization (SCLAHE). This paper presents an initial study of the perception of six dentists on the details of abnormal pathologies and improvement of image quality in ten intra-oral radiographs. The research focus on the detection of only three types of pathology which is periapical radiolucency, widen periodontal ligament space and loss of lamina dura. The overall result shows that SCLAHE-s slightly improve the appearance of dental abnormalities- over the original image and also outperform the other two proposed compound algorithms.

Keywords: intra-oral dental radiograph, histogram equalization, sharpening, CLAHE.

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Authors: Tami Alghamdi, Terence Soule

Abstract:

To study how to transfer knowledge from multiple source problems to the target problem, we modeled the Transfer Learning (TL) process using Genetic Algorithms as the model solver. TL is the process that aims to transfer learned data from one problem to another problem. The TL process aims to help Machine Learning (ML) algorithms find a solution to the problems. The Genetic Algorithms (GA) give researchers access to information that we have about how the old problem is solved. In this paper, we have five different source problems, and we transfer the knowledge to the target problem. We studied different scenarios of the target problem. The results showed that combined knowledge from multiple source problems improves the GA performance. Also, the process of combining knowledge from several problems results in promoting diversity of the transferred population.

Keywords: Transfer Learning, Multiple Sources, Knowledge Transfer, Domain Adaptation, Source, Target.

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Authors: Nayera E. El-Gharably, Khaled S. El-Kilany, Aziz E. El-Sayed

Abstract:

A key element of many distribution systems is the routing and scheduling of vehicles servicing a set of customers. A wide variety of exact and approximate algorithms have been proposed for solving the vehicle routing problems (VRP). Exact algorithms can only solve relatively small problems of VRP, which is classified as NP-Hard. Several approximate algorithms have proven successful in finding a feasible solution not necessarily optimum. Although different parts of the problem are stochastic in nature; yet, limited work relevant to the application of discrete event system simulation has addressed the problem. Presented here is optimization using simulation of VRP; where, a simplified problem has been developed in the ExtendSimTM simulation environment; where, ExtendSimTM evolutionary optimizer is used to minimize the total transportation cost of the problem. Results obtained from the model are very satisfactory. Further complexities of the problem are proposed for consideration in the future.

Keywords: Discrete event system simulation, optimization using simulation, vehicle routing problem.

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Authors: Valeriy Naumov, Olli Martikainen

Abstract:

In this paper we propose new method for simultaneous generating multiple quantiles corresponding to given probability levels from data streams and massive data sets. This method provides a basis for development of single-pass low-storage quantile estimation algorithms, which differ in complexity, storage requirement and accuracy. We demonstrate that such algorithms may perform well even for heavy-tailed data.

Keywords: Quantile estimation, data stream, heavy-taileddistribution, tail index.

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Authors: ER. Yashpaul Singh, A. Swarup

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This research paper evaluates and compares the performance of equal cost adaptive multi-path routing algorithms taking the transport protocols TCP (Transmission Control Protocol) and UDP (User Datagram Protocol) using network simulator ns2 and concludes which one is better.

Keywords: Multi-path routing algorithm, Datagram, Virtual Circuit, Throughput, Network services.

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Authors: Shashank N. Mathur, Anil K. Ahlawat, Virendra P. Vishwakarma

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In this paper, a comparative study of application of supervised and unsupervised learning algorithms on illumination invariant face recognition has been carried out. The supervised learning has been carried out with the help of using a bi-layered artificial neural network having one input, two hidden and one output layer. The gradient descent with momentum and adaptive learning rate back propagation learning algorithm has been used to implement the supervised learning in a way that both the inputs and corresponding outputs are provided at the time of training the network, thus here is an inherent clustering and optimized learning of weights which provide us with efficient results.. The unsupervised learning has been implemented with the help of a modified Counterpropagation network. The Counterpropagation network involves the process of clustering followed by application of Outstar rule to obtain the recognized face. The face recognition system has been developed for recognizing faces which have varying illumination intensities, where the database images vary in lighting with respect to angle of illumination with horizontal and vertical planes. The supervised and unsupervised learning algorithms have been implemented and have been tested exhaustively, with and without application of histogram equalization to get efficient results.

Keywords: Artificial Neural Networks, back propagation, Counterpropagation networks, face recognition, learning algorithms.

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Authors: V. B. Bastos, M. P. Lima, P. R. G. Kurka

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This paper applies to the creation of virtual 3D environments for the study and development of mobile robot image based navigation algorithms and techniques, which need to operate robustly and efficiently. The test of these algorithms can be performed in a physical way, from conducting experiments on a prototype, or by numerical simulations. Current simulation platforms for robotic applications do not have flexible and updated models for image rendering, being unable to reproduce complex light effects and materials. Thus, it is necessary to create a test platform that integrates sophisticated simulated applications of real environments for navigation, with data and image processing. This work proposes the development of a high-level platform for building 3D model’s environments and the test of image-based navigation algorithms for mobile robots. Techniques were used for applying texture and lighting effects in order to accurately represent the generation of rendered images regarding the real world version. The application will integrate image processing scripts, trajectory control, dynamic modeling and simulation techniques for physics representation and picture rendering with the open source 3D creation suite - Blender.

Keywords: Simulation, visual navigation, mobile robot, data visualization.

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Authors: Helen Zhang

Abstract:

Accurate segmentation of the airways from CT scans is crucial for early diagnosis of lung cancer. However, the existing airway segmentation algorithms often rely on thin-slice CT scans, which can be inconvenient and costly. This paper presents a set of machine learning-based 3D super-resolution algorithms along heterogenous dimensions to improve the resolution of thicker CT scans to reduce the reliance on thin-slice scans. To evaluate the efficacy of the super-resolution algorithms, quantitative assessments using PSNR (Peak Signal to Noise Ratio) and SSIM (Structural SIMilarity index) were performed. The impact of super-resolution on airway segmentation accuracy is also studied. The proposed approach has the potential to make airway segmentation more accessible and affordable, thereby facilitating early diagnosis and treatment of lung cancer.

Keywords: 3D super-resolution, airway segmentation, thin-slice CT scans, machine learning.

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Authors: Abdallah Al Sabbagh

Abstract:

Next Generation Wireless Network (NGWN) is expected to be a heterogeneous network which integrates all different Radio Access Technologies (RATs) through a common platform. A major challenge is how to allocate users to the most suitable RAT for them. An optimized solution can lead to maximize the efficient use of radio resources, achieve better performance for service providers and provide Quality of Service (QoS) with low costs to users. Currently, Radio Resource Management (RRM) is implemented efficiently for the RAT that it was developed. However, it is not suitable for a heterogeneous network. Common RRM (CRRM) was proposed to manage radio resource utilization in the heterogeneous network. This paper presents a user level Markov model for a three co-located RAT networks. The load-balancing based and service based CRRM algorithms have been studied using the presented Markov model. A comparison for the performance of load-balancing based and service based CRRM algorithms is studied in terms of traffic distribution, new call blocking probability, vertical handover (VHO) call dropping probability and throughput.

Keywords: Heterogeneous Wireless Network, Markov chain model, load-balancing based and service based algorithm, CRRM algorithms, Beyond 3G network.

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Authors: Daliyah S. Aljutaili, Redna A. Almutlaq, Suha A. Alharbi, Dina M. Ibrahim

Abstract:

All currencies around the world look very different from each other. For instance, the size, color, and pattern of the paper are different. With the development of modern banking services, automatic methods for paper currency recognition become important in many applications like vending machines. One of the currency recognition architecture’s phases is Feature detection and description. There are many algorithms that are used for this phase, but they still have some disadvantages. This paper proposes a feature detection algorithm, which merges the advantages given in the current SIFT and SURF algorithms, which we call, Speeded up Robust Scale-Invariant Feature Transform (SR-SIFT) algorithm. Our proposed SR-SIFT algorithm overcomes the problems of both the SIFT and SURF algorithms. The proposed algorithm aims to speed up the SIFT feature detection algorithm and keep it robust. Simulation results demonstrate that the proposed SR-SIFT algorithm decreases the average response time, especially in small and minimum number of best key points, increases the distribution of the number of best key points on the surface of the currency. Furthermore, the proposed algorithm increases the accuracy of the true best point distribution inside the currency edge than the other two algorithms.

Keywords: Currency recognition, feature detection and description, SIFT algorithm, SURF algorithm, speeded up and robust features.

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Authors: Ying-Wen Bai, Ju-Maw Chen

Abstract:

To successfully provide a fast FIR filter with FTT algorithms, overlapped-save algorithms can be used to lower the computational complexity and achieve the desired real-time processing. As the length of the input block increases in order to improve the efficiency, a larger volume of zero padding will greatly increase the computation length of the FFT. In this paper, we use the overlapped block digital filtering to construct a parallel structure. As long as the down-sampling (or up-sampling) factor is an exact multiple lengths of the impulse response of a FIR filter, we can process the input block by using a parallel structure and thus achieve a low-complex fast FIR filter with overlapped-save algorithms. With a long filter length, the performance and the throughput of the digital filtering system will also be greatly enhanced.

Keywords: FIR Filter, Overlapped-save Algorithm, ParallelStructure

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Authors: Vichai Rungreunganaun, Chirawat Woarawichai

Abstract:

The objective of this research is to calculate the optimal inventory lot-sizing for each supplier and minimize the total inventory cost which includes joint purchase cost of the products, transaction cost for the suppliers, and holding cost for remaining inventory. Genetic algorithms (GAs) are applied to the multi-product and multi-period inventory lot-sizing problems with supplier selection under storage space. Also a maximum storage space for the decision maker in each period is considered. The decision maker needs to determine what products to order in what quantities with which suppliers in which periods. It is assumed that demand of multiple products is known over a planning horizon. The problem is formulated as a mixed integer programming and is solved with the GAs. The detailed computation results are presented.

Keywords: Genetic Algorithms, Inventory lot-sizing, Supplier selection, Storage space.

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Authors: Guilherme Ribeiro, Alexandre Oliveira, Antonio Ferreira, Shyam Visweswaran, Gregory Cooper

Abstract:

Patient-specific models are instance-based learning algorithms that take advantage of the particular features of the patient case at hand to predict an outcome. We introduce two patient-specific algorithms based on decision tree paradigm that use AUC as a metric to select an attribute. We apply the patient specific algorithms to predict outcomes in several datasets, including medical datasets. Compared to the patient-specific decision path (PSDP) entropy-based and CART methods, the AUC-based patient-specific decision path models performed equivalently on area under the ROC curve (AUC). Our results provide support for patient-specific methods being a promising approach for making clinical predictions.

Keywords: Approach instance-based, area Under the ROC Curve, Patient-specific Decision Path, clinical predictions.

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Authors: Shonak Bansal, Prince Jain, Arun Kumar Singh, Neena Gupta

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Recently nature–inspired algorithms have widespread use throughout the tough and time consuming multi–objective scientific and engineering design optimization problems. In this paper, we present extended forms of firefly algorithm to find optimal Golomb ruler (OGR) sequences. The OGRs have their one of the major application as unequally spaced channel–allocation algorithm in optical wavelength division multiplexing (WDM) systems in order to minimize the adverse four–wave mixing (FWM) crosstalk effect. The simulation results conclude that the proposed optimization algorithm has superior performance compared to the existing conventional computing and nature–inspired optimization algorithms to find OGRs in terms of ruler length, total optical channel bandwidth and computation time.

Keywords: Channel allocation, conventional computing, four–wave mixing, nature–inspired algorithm, optimal Golomb ruler, Lévy flight distribution, optimization, improved multi–objective Firefly algorithms, Pareto optimal.

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Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

Abstract:

In this paper, a novel associative memory model will be proposed and applied to memory retrievals based on the conventional continuous time model. The conventional model presents memory capacity is very low and retrieval process easily converges to an equilibrium state which is very different from the stored patterns. Genetic Algorithms is well-known with the capability of global optimal search escaping local optimum on progress to reach a global optimum. Based on the well-known idea of Genetic Algorithms, this work proposes a heuristic rule to make a mutation when the state of the network is trapped in a spurious memory. The proposal heuristic associative memory show the stored capacity does not depend on the number of stored patterns and the retrieval ability is up to ~ 1.

Keywords: Artificial Intelligent, Soft Computing, NeuralNetworks, Genetic Algorithms, Hopfield Neural Networks, andAssociative Memories.

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Authors: Dalibor Fiala, Karel Jezek, Francois Rousselot

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In this paper, we present a methodology for finding authoritative researchers by analyzing academic Web sites. We show a case study in which we concentrate on a set of Czech computer science departments- Web sites. We analyze the relations between them via hyperlinks and find the most important ones using several common ranking algorithms. We then examine the contents of the research papers present on these sites and determine the most authoritative Czech authors.

Keywords: Authorities, citation analysis, prestige, ranking algorithms, Web mining.

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Authors: Akhilesh G. Naik, Dipankar Pal

Abstract:

In today’s scenario, the complexity of digital signal processing (DSP) applications and various microcontroller architectures have been increasing to such an extent that the traditional approaches to multiplier design in most processors are becoming outdated for being comparatively slow. Modern processing applications require suitable pipelined approaches, and therefore, algorithms that are friendlier with pipelined architectures. Traditional algorithms like Wallace Tree, Radix-4 Booth, Radix-8 Booth, Dadda architectures have been proven to be comparatively slow for pipelined architectures. These architectures, therefore, need to be optimized or combined with other architectures amongst them to enhance its performances and to be made suitable for pipelined hardware/architectures. Recently, Vedic algorithm mathematically has proven to be efficient by appearing to be less complex and with fewer steps for its output establishment and have assumed renewed importance. This paper describes and shows how the Vedic algorithm can be better suited for pipelined architectures and also can be combined with traditional architectures and algorithms for enhancing its ability even further. In this paper, we also established that for complex applications on DSP and other microcontroller architectures, using Vedic approach for multiplication proves to be the best available and efficient option.

Keywords: Wallace tree, Radix-4 Booth, Radix-8 Booth, Dadda, Vedic, Single-Stage Karatsuba, Looped Karatsuba.

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Authors: Konstantinos Michail, Argyrios Zolotas, Roger Goodall, John Pearson

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In this paper a systematic method via H∞ control design is proposed to select a sensor set that satisfies a number of input criteria for a MAGLEV suspension system. The proposed method recovers a number of optimised controllers for each possible sensor set that satisfies the performance and constraint criteria using evolutionary algorithms.

Keywords: H-infinity, Sensor optimisation, Genetic algorithms, MAGLEV vehicles

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Authors: N. P. Waweru, D. B. O. Konditi, P. K. Langat

Abstract:

Direction of Arrival estimation refers to defining a mathematical function called a pseudospectrum that gives an indication of the angle a signal is impinging on the antenna array. This estimation is an efficient method of improving the quality of service in a communication system by focusing the reception and transmission only in the estimated direction thereby increasing fidelity with a provision to suppress interferers. This improvement is largely dependent on the performance of the algorithm employed in the estimation. Many DOA algorithms exists amongst which are MUSIC, Root-MUSIC and ESPRIT. In this paper, performance of these three algorithms is analyzed in terms of complexity, accuracy as assessed and characterized by the CRLB and memory requirements in various environments and array sizes. It is found that the three algorithms are high resolution and dependent on the operating environment and the array size. 

Keywords: Direction of Arrival, Autocorrelation matrix, Eigenvalue decomposition, MUSIC, ESPRIT, CRLB.

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Authors: Lv Meibo, Naqvi Najam Abbas, Li YanJun

Abstract:

Attitude Determination (AD) of a spacecraft using the phase measurements of the Global Navigation Satellite System (GNSS) is an active area of research. Various attitude determination algorithms have been developed in yester years for spacecrafts using different sensors but the last two decades have witnessed a phenomenal increase in research related with GPS receivers as a stand-alone sensor for determining the attitude of satellite using the phase measurements of the signals from GNSS. The GNSS-based Attitude determination algorithms have been experimented in many real missions. The problem of AD algorithms using GNSS phase measurements has two important parts; the ambiguity resolution and the determining of attitude. Ambiguity resolution is the widely addressed topic in literature for implementing the AD algorithm using GNSS phase measurements for achieving the accuracy of millimeter level. This paper broadly overviews the different techniques for resolving the integer ambiguities encountered in AD using GNSS phase measurements.

Keywords: Attitude Determination, Ambiguity Resolution, GNSS, LAMBDA Method, Satellite.

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Authors: Diego Saqui, José H. Saito, José R. Campos, Lúcio A. de C. Jorge

Abstract:

Hyperspectral images and remote sensing are important for many applications. A problem in the use of these images is the high volume of data to be processed, stored and transferred. Dimensionality reduction techniques can be used to reduce the volume of data. In this paper, an approach to band selection based on clustering algorithms is presented. This approach allows to reduce the volume of data. The proposed structure is based on Fuzzy C-Means (or K-Means) and NWHFC algorithms. New attributes in relation to other studies in the literature, such as kurtosis and low correlation, are also considered. A comparison of the results of the approach using the Fuzzy C-Means and K-Means with different attributes is performed. The use of both algorithms show similar good results but, particularly when used attributes variance and kurtosis in the clustering process, however applicable in hyperspectral images.

Keywords: Band selection, fuzzy C-means, K-means, hyperspectral image.

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Authors: Reza Ghaemi , Md. Nasir Sulaiman , Hamidah Ibrahim , Norwati Mustapha

Abstract:

The clustering ensembles combine multiple partitions generated by different clustering algorithms into a single clustering solution. Clustering ensembles have emerged as a prominent method for improving robustness, stability and accuracy of unsupervised classification solutions. So far, many contributions have been done to find consensus clustering. One of the major problems in clustering ensembles is the consensus function. In this paper, firstly, we introduce clustering ensembles, representation of multiple partitions, its challenges and present taxonomy of combination algorithms. Secondly, we describe consensus functions in clustering ensembles including Hypergraph partitioning, Voting approach, Mutual information, Co-association based functions and Finite mixture model, and next explain their advantages, disadvantages and computational complexity. Finally, we compare the characteristics of clustering ensembles algorithms such as computational complexity, robustness, simplicity and accuracy on different datasets in previous techniques.

Keywords: Clustering Ensembles, Combinational Algorithm, Consensus Function, Unsupervised Classification.

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Authors: Jeng-Shin Sheu, Jenn-Kaie Lain, Tai-Kuo Woo, Jyh-Horng Wen

Abstract:

The least mean square (LMS) algorithmis one of the most well-known algorithms for mobile communication systems due to its implementation simplicity. However, the main limitation is its relatively slow convergence rate. In this paper, a booster using the concept of Markov chains is proposed to speed up the convergence rate of LMS algorithms. The nature of Markov chains makes it possible to exploit the past information in the updating process. Moreover, since the transition matrix has a smaller variance than that of the weight itself by the central limit theorem, the weight transition matrix converges faster than the weight itself. Accordingly, the proposed Markov-chain based booster thus has the ability to track variations in signal characteristics, and meanwhile, it can accelerate the rate of convergence for LMS algorithms. Simulation results show that the LMS algorithm can effectively increase the convergence rate and meantime further approach the Wiener solution, if the Markov-chain based booster is applied. The mean square error is also remarkably reduced, while the convergence rate is improved.

Keywords: LMS, Markov chain, convergence rate, accelerator.

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Authors: Jorge A. Ruiz-Vanoye, Ocotlán Díaz-Parra, Alejandro Fuentes-Penna, Daniel Vélez-Díaz, Edith Olaco García

Abstract:

In this paper, we present the use of the discriminant analysis to select evolutionary algorithms that better solve instances of the vehicle routing problem with time windows. We use indicators as independent variables to obtain the classification criteria, and the best algorithm from the generic genetic algorithm (GA), random search (RS), steady-state genetic algorithm (SSGA), and sexual genetic algorithm (SXGA) as the dependent variable for the classification. The discriminant classification was trained with classic instances of the vehicle routing problem with time windows obtained from the Solomon benchmark. We obtained a classification of the discriminant analysis of 66.7%.

Keywords: Intelligent transportation systems, data-mining techniques, evolutionary algorithms, discriminant analysis, machine learning.

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Authors: R. Matousek, S. Lang, P. Minar, P. Pivonka

Abstract:

In the control theory one attempts to find a controller that provides the best possible performance with respect to some given measures of performance. There are many sorts of controllers e.g. a typical PID controller, LQR controller, Fuzzy controller etc. In the paper will be introduced polynomial controller with novel tuning method which is based on the special pole placement encoding scheme and optimization by Genetic Algorithms (GA). The examples will show the performance of the novel designed polynomial controller with comparison to common PID controller.

Keywords: Evolutionary design, Genetic algorithms, PID controller, Pole placement, Polynomial controller

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Authors: Y. Abdelrazig

Abstract:

Evolutionary optimization methods such as genetic algorithms have been used extensively for the construction site layout problem. More recently, ant colony optimization algorithms, which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to benchmark combinatorial optimization problems. This paper proposes a formulation of the site layout problem in terms of a sequencing problem that is suitable for solution using an ant colony optimization algorithm. In the construction industry, site layout is a very important planning problem. The objective of site layout is to position temporary facilities both geographically and at the correct time such that the construction work can be performed satisfactorily with minimal costs and improved safety and working environment. During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the construction site layout problem. This paper proposes an ant colony optimization model for construction site layout. A simple case study for a highway project is utilized to illustrate the application of the model.

Keywords: Construction site layout, optimization, ant colony.

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Authors: P. Asadee

Abstract:

Multiplication algorithms have considerable effect on processors performance. A new high-speed, low-power multiplication algorithm has been presented using modified Dadda tree structure. Three important modifications have been implemented in inner product generation step, inner product reduction step and final addition step. Optimized algorithms have to be used into basic computation components, such as multiplication algorithms. In this paper, we proposed a new algorithm to reduce power, delay, and transistor count of a multiplication algorithm implemented using low power modified counter. This work presents a novel design for Dadda multiplication algorithms. The proposed multiplication algorithm includes structured parts, which have important effect on inner product reduction tree. In this paper, a 1.3V, 64-bit carry hybrid adder is presented for fast, low voltage applications. The new 64-bit adder uses a new circuit to implement the proposed carry hybrid adder. The new adder using 80 nm CMOS technology has been implemented on 700 MHz clock frequency. The proposed multiplication algorithm has achieved 14 percent improvement in transistor count, 13 percent reduction in delay and 12 percent modification in power consumption in compared with conventional designs.

Keywords: adder, CMOS, counter, Dadda tree, encoder.

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Authors: Ayman A. AbuBaker, Rami S.Qahwaji, Musbah J. Aqel, Mohmmad H. Saleh

Abstract:

Two algorithms are proposed to reduce the storage requirements for mammogram images. The input image goes through a shrinking process that converts the 16-bit images to 8-bits by using pixel-depth conversion algorithm followed by enhancement process. The performance of the algorithms is evaluated objectively and subjectively. A 50% reduction in size is obtained with no loss of significant data at the breast region.

Keywords: Breast cancer, Image processing, Image reduction, Mammograms, Image enhancement

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Authors: A.Tajaddini

Abstract:

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

Keywords: Bisymmetric matrices, Paige’s algorithms, Least square.

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