Search results for: Discrete location problems

Authors: Mhand Hifi, Hedi Mhalla

Abstract:

In this paper, we study the knapsack sharing problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of a tree search for optimally solving the problem. The used method combines two complementary phases: a reduction interval search phase and a branch and bound procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for decomposing the problem into a series of knapsack problems. Second, the tree search procedure is applied in order to attain a set of optimal capacities characterizing the knapsack problems. Finally, the performance of the proposed optimal algorithm is evaluated on a set of instances of the literature and its runtime is compared to the best exact algorithm of the literature.

Keywords: Branch and bound, combinatorial optimization, knap¬sack, knapsack sharing, heuristics, interval reduction.

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Authors: Chein-Shung Hwang, Ruei-Siang Fong

Abstract:

User-based Collaborative filtering (CF), one of the most prevailing and efficient recommendation techniques, provides personalized recommendations to users based on the opinions of other users. Although the CF technique has been successfully applied in various applications, it suffers from serious sparsity problems. The cloud-model approach addresses the sparsity problems by constructing the user-s global preference represented by a cloud eigenvector. The user-based CF approach works well with dense datasets while the cloud-model CF approach has a greater performance when the dataset is sparse. In this paper, we present a hybrid approach that integrates the predictions from both the user-based CF and the cloud-model CF approaches. The experimental results show that the proposed hybrid approach can ameliorate the sparsity problem and provide an improved prediction quality.

Keywords: Cloud model, Collaborative filtering, Hybridrecommender system

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Authors: G. Saxena, D. Singh, M. Kaushik,

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Inspired by the recent experiments [1]-[3] indicating unusual doubly magic nucleus 24O which lies just at the neutron drip-line and encouraged by the success of our relativistic mean-field (RMF) plus state dependent BCS approach for the description of the ground state properties of the drip-line nuclei [23]-[27], we have further employed this approach, across the entire periodic table, to explore the unusual shell closures in exotic nuclei. In our RMF+BCS approach the single particle continuum corresponding to the RMF is replaced by a set of discrete positive energy states for the calculations of pairing energy. Detailed analysis of the single particle spectrum, pairing energies and densities of the nuclei predict the unusual proton shell closures at Z = 6, 14, 16, 34, and unusual neutron shell closures at N = 6, 14, 16, 34, 40, 70, 112.

Keywords: Relativistic Mean Field theory, Magic Nucleus, Si isotopes, Shell Closure.

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Authors: Souleymane Oumtanaga, Kadjo Tanon Lambert, Koné Tiémoman, Tety Pierre, Kimou KouadioProsper

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Multicast transmissions allow an host (the source) to send only one flow bound for a group of hosts (the receivers). Any equipment eager to belong to the group may explicitly register itself to that group via its multicast router. This router will be given the responsibility to convey all information relating to the group to all registered hosts. However in an environment in which the final receiver or the source frequently moves, the multicast flows need particular treatment. This constitutes one of the multicast transmissions problems around which several proposals were made in the Mobile IPv6 case in general. In this article, we describe the problems involved in this IPv6 multicast mobility and the existing proposals for their resolution. Then architecture will be proposed aiming to satisfy and optimize these transmissions in the specific case of a mobile multicast receiver in NC-HMIPv6 environment.

Keywords: Mobile IP, NC-HMIPv6, Multicast, MLD, PIM, SSM, Rendezvous Point.

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Authors: Khaled M. EL-Naggar

Abstract:

This paper presents a fast and efficient on-line technique for estimating impedance of unbalanced loads in power systems. The proposed technique is an application of a discrete timedynamic filter based on stochastic estimation theory which is suitable for estimating parameters in noisy environment. The algorithm uses sets of digital samples of the distorted voltage and current waveforms of the non-linear load to estimate the harmonic contents of these two signal. The non-linear load impedance is then calculated from these contents. The method is tested using practical data. Results are reported and compared with those obtained using the conventional least error squares technique. In addition to the very accurate results obtained, the method can detect and reject bad measurements. This can be considered as a very important advantage over the conventional static estimation methods such as the least error square method.

Keywords: Estimation, identification, Harmonics, Dynamic Filter.

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Authors: Mohammad Modarres, Shirin Aslani

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The goal of this paper is to develop a model to integrate “pricing" and “advertisement" for short life cycle products, such as branded fashion clothing products. To achieve this goal, we apply the concept of “Dynamic Pricing". There are two classes of advertisements, for the brand (regardless of product) and for a particular product. Advertising the brand affects the demand and price of all the products. Thus, the model considers all these products in relation with each other. We develop two different methods to integrate both types of advertisement and pricing. The first model is developed within the framework of dynamic programming. However, due to the complexity of the model, this method cannot be applicable for large size problems. Therefore, we develop another method, called hieratical approach, which is capable of handling the real world problems. Finally, we show the accuracy of this method, both theoretically and also by simulation.

Keywords: Advertising, Dynamic programming, Dynamic pricing, Promotion.

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Authors: Michael G. Pantelyat

Abstract:

Fundamental basics of pure and applied research in the area of magneto-thermo-mechanical numerical analysis and design of innovative electromagnetic devices (modern induction heaters, novel thermoelastic actuators, rotating electrical machines, induction cookers, electrophysical devices) are elaborated. Thus, mathematical models of magneto-thermo-mechanical processes in electromagnetic devices taking into account main interactions of interrelated phenomena are developed. In addition, graphical representation of coupled (multiphysics) phenomena under consideration is proposed. Besides, numerical techniques for nonlinear problems solution are developed. On this base, effective numerical algorithms for solution of actual problems of practical interest are proposed, validated and implemented in applied 2D and 3D computer codes developed. Many applied problems of practical interest regarding modern electrical engineering devices are numerically solved. Investigations of the influences of various interrelated physical phenomena (temperature dependences of material properties, thermal radiation, conditions of convective heat transfer, contact phenomena, etc.) on the accuracy of the electromagnetic, thermal and structural analyses are conducted. Important practical recommendations on the choice of rational structures, materials and operation modes of electromagnetic devices under consideration are proposed and implemented in industry.

Keywords: Electromagnetic devices, multiphysics, numerical analysis, simulation and design.

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Authors: Sayyed R Mousavi

Abstract:

The Far From Most Strings Problem (FFMSP) is to obtain a string which is far from as many as possible of a given set of strings. All the input and the output strings are of the same length, and two strings are said to be far if their hamming distance is greater than or equal to a given positive integer. FFMSP belongs to the class of sequences consensus problems which have applications in molecular biology. The problem is NP-hard; it does not admit a constant-ratio approximation either, unless P = NP. Therefore, in addition to exact and approximate algorithms, (meta)heuristic algorithms have been proposed for the problem in recent years. On the other hand, in the recent years, hybrid algorithms have been proposed and successfully used for many hard problems in a variety of domains. In this paper, a new metaheuristic algorithm, called Constructive Beam and Local Search (CBLS), is investigated for the problem, which is a hybridization of constructive beam search and local search algorithms. More specifically, the proposed algorithm consists of two phases, the first phase is to obtain several candidate solutions via the constructive beam search and the second phase is to apply local search to the candidate solutions obtained by the first phase. The best solution found is returned as the final solution to the problem. The proposed algorithm is also similar to memetic algorithms in the sense that both use local search to further improve individual solutions. The CBLS algorithm is compared with the most recent published algorithm for the problem, GRASP, with significantly positive results; the improvement is by order of magnitudes in most cases.

Keywords: Bioinformatics, Far From Most Strings Problem, Hybrid metaheuristics, Matheuristics, Sequences consensus problems.

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Authors: Ivan Yatchev, Ewen Ritchie

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Comparison of two approaches for the simulation of the dynamic behaviour of a permanent magnet linear actuator is presented. These are full coupled model, where the electromagnetic field, electric circuit and mechanical motion problems are solved simultaneously, and decoupled model, where first a set of static magnetic filed analysis is carried out and then the electric circuit and mechanical motion equations are solved employing bi-cubic spline approximations of the field analysis results. The results show that the proposed decoupled model is of satisfactory accuracy and gives more flexibility when the actuator response is required to be estimated for different external conditions, e.g. external circuit parameters or mechanical loads.

Keywords: Coupled problems, dynamic models, finite elementanalysis, linear actuators, permanent magnets.

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Authors: S. Mohan Kumar, Rajashekar Patil, Tanuja Ajit Desphande

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It is necessary to incorporate technological advances achieved in the field of engineering into dentistry in order to enhance the process of diagnosis, treatment planning and enable the doctors to render better treatment to their patients. To achieve this ultimate goal long distance collaborations are often necessary. This paper discusses the various collaborative tools and their applications to solve a few burning problems confronted by the dentists. Customization is often the solution to most of the problems. But rapid designing, development and cost effective manufacturing is a difficult task to achieve. This problem can be solved using the technique of digital manufacturing. Cases from 6 major branches of dentistry have been discussed and possible solutions with the help of state of art technology using rapid digital manufacturing have been proposed in the present paper. The paper also entails the usage of existing tools in collaborative and digital manufacturing area.

Keywords: Customisation, collaborative tools, dentistry, digital manufacturing.

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Authors: Attila Vámosi, Tamás Mankovits, Dávid Huri, Imre Kocsis, Tamás Szabó

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Non-linear FEM calculations are indispensable when important technical information like operating performance of a rubber component is desired. For example rubber bumpers built into air-spring structures may undergo large deformations under load, which in itself shows non-linear behavior. The changing contact range between the parts and the incompressibility of the rubber increases this non-linear behavior further. The material characterization of an elastomeric component is also a demanding engineering task. The shape optimization problem of rubber parts led to the study of FEM based calculation processes. This type of problems was posed and investigated by several authors. In this paper the time demand of certain calculation methods are studied and the possibilities of time reduction is presented.

Keywords: Rubber bumper, data acquisition, finite element analysis, support vector regression.

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Authors: Anil Kumar Tripathi, Ratneshwer

Abstract:

All the software engineering researches and best industry practices aim at providing software products with high degree of quality and functionality at low cost and less time. These requirements are addressed by the Component Based Software Engineering (CBSE) as well. CBSE, which deals with the software construction by components’ assembly, is a revolutionary extension of Software Engineering. CBSE must define and describe processes to assure timely completion of high quality software systems that are composed of a variety of pre built software components. Though these features provide distinct and visible benefits in software design and programming, they also raise some challenging problems. The aim of this work is to summarize the pertinent issues and considerations in CBSE to make an understanding in forms of concepts and observations that may lead to development of newer ways of dealing with the problems and challenges in CBSE.

Keywords: Software Component, Component Based Software Engineering, Software Process, Testing, Maintenance.

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Authors: Mario Mastriani

Abstract:

We describe a novel method for removing noise (in wavelet domain) of unknown variance from microarrays. The method is based on the following procedure: We apply 1) Bidimentional Discrete Wavelet Transform (DWT-2D) to the Noisy Microarray, 2) scaling and rounding to the coefficients of the highest subbands (to obtain integer and positive coefficients), 3) bit-slicing to the new highest subbands (to obtain bit-planes), 4) then we apply the Systholic Boolean Orthonormalizer Network (SBON) to the input bit-plane set and we obtain two orthonormal otput bit-plane sets (in a Boolean sense), we project a set on the other one, by means of an AND operation, and then, 5) we apply re-assembling, and, 6) rescaling. Finally, 7) we apply Inverse DWT-2D and reconstruct a microarray from the modified wavelet coefficients. Denoising results compare favorably to the most of methods in use at the moment.

Keywords: Bit-Plane, Boolean Orthonormalization Process, Denoising, Microarrays, Wavelets

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Authors: Krisada Sungkhamanee

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The objectives of this research are to search the management pattern of Bang Khonthi lodging entrepreneurs for sufficient economy ways, to know the threat that affects this sector and design fit arrangement model to sustain their business with Samut Songkram style. What will happen if they do not use this approach? Will they have a financial crisis? The data and information are collected by informal discussions with 8 managers and 400 questionnaires. A mixed methods of both qualitative research and quantitative research are used. Bent Flyvbjerg-s phronesis is utilized for this analysis. Our research will prove that sufficient economy can help small business firms to solve their problems. We think that the results of our research will be a financial model to solve many problems of the entrepreneurs and this way will can be a model for other provinces of Thailand.

Keywords: Bang Khonthi, Lodging Business, Sufficient Economy.

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Authors: M. Zareiee, A. Dideban, P. Nazemzadeh

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This paper deals with the problem of constructing constraints in non safe Petri Nets and then reducing the number of the constructed constraints. In a system, assigning some linear constraints to forbidden states is possible. Enforcing these constraints on the system prevents it from entering these states. But there is no a systematic method for assigning constraints to forbidden states in non safe Petri Nets. In this paper a useful method is proposed for constructing constraints in non safe Petri Nets. But when the number of these constraints is large enforcing them on the system may complicate the Petri Net model. So, another method is proposed for reducing the number of constructed constraints.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

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Authors: Alluri Swaroopa, Lakkakula Venkata Narasimha Prasad

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Alone with fast urbanization in world, traffic control became a big issue in urban construction. Having an efficient and reliable traffic control system is crucial to macro-traffic control. Traffic signal is used to manage conflicting requirement by allocating different sets of mutually compatible traffic movement during distinct time interval. Many approaches have been made proposed to solve this discrete stochastic problem. Recognizing the need to minimize right-of-way impacts while efficiently handling the anticipated high traffic volumes, the proposed alternative system gives effective design. This model allows for increased traffic capacity and reduces delays by eliminating a step in maneuvering through the freeway interchange. The concept proposed in this paper involves construction of bridges and ramps at intersection of four roads to control the vehicular congestion and to prevent traffic breakdown.

Keywords: Bridges, junctions, ramps, urban traffic control.

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Authors: Wen-Pai Wang, Mei-Ching Tang

Abstract:

The service sector continues to grow and the percentage of GDP accounted for by service industries keeps increasing. The growth and importance of service to an economy is not just a phenomenon of advanced economies, service is now a majority of the world gross domestic products. However, the performance evaluation process of new service development problems generally involves uncertain and imprecise data. This paper presents a 2-tuple fuzzy linguistic computing approach to dealing with heterogeneous information and information loss problems while the processes of subjective evaluation integration. The proposed method based on group decision-making scenario to assist business managers in measuring performance of new service development manipulates the heterogeneity integration processes and avoids the information loss effectively.

Keywords: Heterogeneity, Multigranular linguistic computing, New service development, Performance evaluation.

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Authors: M. Aslam, Farrukh, A. R. Gardezi, Nasir Hayat

Abstract:

Automated material handling is given prime importance in the semi automated and automated facilities since it provides solution to the gigantic problems related to inventory and also support the latest philosophies like just in time production JIT and lean production. Automated storage and retrieval system is an antidote (if designed properly) to the facility sufferings like getting the right material , materials getting perished, long cycle times or many other similar kind of problems. A working model of automated storage and retrieval system (AS/RS) is designed and developed under the design parameters specified by Material Handling Industry of America (MHIA). Later on analysis was carried out to calculate the throughput and size of the machine. The possible implementation of this technology in local scenario is also discussed in this paper.

Keywords: Automated storage and retrieval system (AS/RS), Material handling, Computer integrated manufacturing (CIM), Lightdependent resistor (LDR)

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Authors: Piyush Samant, Ravinder Agarwal

Abstract:

Complementary and Alternative Medicine (CAM) techniques are quite popular and effective for chronic diseases. Iridology is more than 150 years old CAM technique which analyzes the patterns, tissue weakness, color, shape, structure, etc. for disease diagnosis. The objective of this paper is to validate the use of iridology for the diagnosis of the diabetes. The suggested model was applied in a systemic disease with ocular effects. 200 subject data of 100 each diabetic and non-diabetic were evaluated. Complete procedure was kept very simple and free from the involvement of any iridologist. From the normalized iris, the region of interest was cropped. All 63 features were extracted using statistical, texture analysis, and two-dimensional discrete wavelet transformation. A comparison of accuracies of six different classifiers has been presented. The result shows 89.66% accuracy by the random forest classifier.

Keywords: Complementary and alternative medicine, Iridology, iris, feature extraction, classification, disease prediction.

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Authors: Mohammed Boutalline, Imad Badi, Belaid Bouikhalene, Said Safi

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In this paper we describe the Levenvberg-Marquardt (LM) algorithm for identification and equalization of CDMA signals received by an antenna array in communication channels. The synthesis explains the digital separation and equalization of signals after propagation through multipath generating intersymbol interference (ISI). Exploiting discrete data transmitted and three diversities induced at the reception, the problem can be composed by the Block Component Decomposition (BCD) of a tensor of order 3 which is a new tensor decomposition generalizing the PARAFAC decomposition. We optimize the BCD decomposition by Levenvberg-Marquardt method gives encouraging results compared to classical alternating least squares algorithm (ALS). In the equalization part, we use the Minimum Mean Square Error (MMSE) to perform the presented method. The simulation results using the LM algorithm are important.

Keywords: Identification and equalization, communication channel, Levenvberg-Marquardt, tensor decomposition

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Authors: Christopher Deekia Nwimae, Nigel Simms, Liyun Lao

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Erosion in a pipe bends caused by particles is a major concern in the oil and gas fields and might cause breakdown to production equipment. This work investigates the effect of sand particle transport in an elbow using computational fluid dynamics (CFD) approach. Two-way coupled Euler-Lagrange and discrete phase model is employed to calculate the air/solid particle flow in the elbow. Generic erosion model in Ansys fluent and three particle rebound models are used to predict the erosion rate on the 90° elbows. The model result is compared with experimental data from the open literature validating the CFD-based predictions which reveals that due to the sand particles impinging on the wall of the elbow at high velocity, a point on the pipe elbow were observed to have started turning red due to velocity increase and the maximum erosion locations occur at 48°.

Keywords: Erosion, prediction, elbow, computational fluid dynamics, CFD.

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Authors: I. Abuiziah, N. Shakarneh

Abstract:

Genetic Algorithm (GA) is a powerful technique for solving optimization problems. It follows the idea of survival of the fittest - Better and better solutions evolve from previous generations until a near optimal solution is obtained. GA uses the main three operations, the selection, crossover and mutation to produce new generations from the old ones. GA has been widely used to solve optimization problems in many applications such as traveling salesman problem, airport traffic control, information retrieval (IR), reactive power optimization, job shop scheduling, and hydraulics systems such as water pipeline systems. In water pipeline systems we need to achieve some goals optimally such as minimum cost of construction, minimum length of pipes and diameters, and the place of protection devices. GA shows high performance over the other optimization techniques, moreover, it is easy to implement and use. Also, it searches a limited number of solutions.

Keywords: Genetic Algorithm, optimization, pipeline systems, selection, cross over.

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Authors: Siriporn Meenanan

Abstract:

The objective of this study is to investigate the attitude of Thai students towards the Thai series "Hormones the Series Season 2". This study was conducted in the quantitative research, and the questionnaires were used to collect data from 400 people of the sample group. Descriptive statistics were used in data analysis. The findings reveal that most participants have positive comments regarding the series. They strongly agreed that the series reflects on the way of life and problems of teenagers in Thailand. Hence, the participants believe that if adults have a chance to watch the series, they will have the better understanding of the teenagers. In addition, the participants also agreed that the contents of the play are appropriate and satisfiable as the contents of “Hormones the Series Season 2” will raise awareness among the teens and use it as a guide to prevent problems that might happen during their teenage life.

Keywords: Content analysis, attitude, Thai series, Hormones the series.

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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Authors: Laleh Taheri, Noraini C. Pa., Rusli Abdullah, Salfarina Abdullah

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Knowledge plays an important role to the success of any organization. Software development organizations are highly knowledge-intensive organizations especially in their requirement elicitation process (REP). There are several problems regarding communicating and using the knowledge in REP such as misunderstanding, being out of scope, conflicting information and changes of requirements. All of these problems occurred in transmitting the requirements knowledge during REP. Several researches have been done in REP in order to solve the problem towards requirements. Knowledge Audit (KA) approaches were proposed in order to solve managing knowledge in human resources, financial and manufacturing. There is lack of study applying the KA in requirements elicitation process. Therefore, this paper proposes a KA model for REP in supporting to acquire good requirements.

Keywords: Knowledge Audit, Requirement Elicitation Process, KA Model, Knowledge in Requirement Elicitation.

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Authors: Waleed Abohamad, Amr Arisha

Abstract:

Owing the fact that optimization of business process is a crucial requirement to navigate, survive and even thrive in today-s volatile business environment, this paper presents a framework for selecting a best-fit optimization package for solving complex business problems. Complexity level of the problem and/or using incorrect optimization software can lead to biased solutions of the optimization problem. Accordingly, the proposed framework identifies a number of relevant factors (e.g. decision variables, objective functions, and modeling approach) to be considered during the evaluation and selection process. Application domain, problem specifications, and available accredited optimization approaches are also to be regarded. A recommendation of one or two optimization software is the output of the framework which is believed to provide the best results of the underlying problem. In addition to a set of guidelines and recommendations on how managers can conduct an effective optimization exercise is discussed.

Keywords: Complex Business Problems, Optimization, Selection Criteria, Software Evaluation.

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Authors: Sunitha S. L., V. Udayashankara

Abstract:

Hearing impairment is the number one chronic disability affecting many people in the world. Background noise is particularly damaging to speech intelligibility for people with hearing loss especially for sensorineural loss patients. Several investigations on speech intelligibility have demonstrated sensorineural loss patients need 5-15 dB higher SNR than the normal hearing subjects. This paper describes Discrete Hartley Transform Power Normalized Least Mean Square algorithm (DHT-LMS) to improve the SNR and to reduce the convergence rate of the Least Means Square (LMS) for sensorineural loss patients. The DHT transforms n real numbers to n real numbers, and has the convenient property of being its own inverse. It can be effectively used for noise cancellation with less convergence time. The simulated result shows the superior characteristics by improving the SNR at least 9 dB for input SNR with zero dB and faster convergence rate (eigenvalue ratio 12) compare to time domain method and DFT-LMS.

Keywords: Hearing Impairment, DHT-LMS, Convergence rate, SNR improvement.

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Authors: Hadi Seyedarabi, Ali Aghagolzadeh, Sohrab Khanmohammadi

Abstract:

Face and facial expressions play essential roles in interpersonal communication. Most of the current works on the facial expression recognition attempt to recognize a small set of the prototypic expressions such as happy, surprise, anger, sad, disgust and fear. However the most of the human emotions are communicated by changes in one or two of discrete features. In this paper, we develop a facial expressions synthesis system, based on the facial characteristic points (FCP's) tracking in the frontal image sequences. Selected FCP's are automatically tracked using a crosscorrelation based optical flow. The proposed synthesis system uses a simple deformable facial features model with a few set of control points that can be tracked in original facial image sequences.

Keywords: Deformable face model, facial animation, facialcharacteristic points, optical flow.

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Authors: Nhon Do, Tam Pham

Abstract:

Knowledge bases are basic components of expert systems or intelligent computational programs. Knowledge bases provide knowledge, events that serve deduction activity, computation and control. Therefore, researching and developing of models for knowledge representation play an important role in computer science, especially in Artificial Intelligence Science and intelligent educational software. In this paper, the extensive deduction computational model is proposed to design knowledge bases whose attributes are able to be real values or functional values. The system can also solve problems based on knowledge bases. Moreover, the models and algorithms are applied to produce the educational software for solving alternating current problems or solving set of equations automatically.

Keywords: Educational software, artificial intelligence, knowledge base systems, knowledge representation.

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Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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