Search results for: preference programming. MCDM

Authors: José Paulo Leal, Ricardo Queirós

Abstract:

Standards for learning objects focus primarily on content presentation. They were already extended to support automatic evaluation but it is limited to exercises with a predefined set of answers. The existing standards lack the metadata required by specialized evaluators to handle types of exercises with an indefinite set of solutions. To address this issue existing learning object standards were extended to the particular requirements of a specialized domain. A definition of programming problems as learning objects, compatible both with Learning Management Systems and with systems performing automatic evaluation of programs, is presented in this paper. The proposed definition includes metadata that cannot be conveniently represented using existing standards, such as: the type of automatic evaluation; the requirements of the evaluation engine; and the roles of different assets - tests cases, program solutions, etc. The EduJudge project and its main services are also presented as a case study on the use of the proposed definition of programming problems as learning objects.

Keywords: Content Packaging, eLearning Services, Interoperability, Learning Objects.

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Authors: K. Balamurugan, R. Muralisachithanandam, V. Dharmalingam, R. Srikanth

Abstract:

This paper deals with the optimal choice and allocation of multi FACTS devices in Deregulated power system using Evolutionary Programming method. The objective is to achieve the power system economic generation allocation and dispatch in deregulated electricity market. Using the proposed method, the locations of the FACTS devices, their types and ratings are optimized simultaneously. Different kinds of FACTS devices are simulated in this study such as UPFC, TCSC, TCPST, and SVC. Simulation results validate the capability of this new approach in minimizing the overall system cost function, which includes the investment costs of the FACTS devices and the bid offers of the market participants. The proposed algorithm is an effective and practical method for the choice and allocation of FACTS devices in deregulated electricity market environment. The standard data of IEEE 14 Bus systems has been taken into account and simulated with aid of MAT-lab software and results were obtained.

Keywords: FACTS devices, Optimal allocation, Deregulated electricity market, Evolutionary programming, Mat Lab.

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Authors: Abdolsalam Ghaderi

Abstract:

In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. This problem has many applications, especially in the area of supply chain management and distribution systems. To get closer to real-world situations, travel time of vehicles, the fixed cost of vehicles usage and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a heuristic algorithm based on Variable Neighborhood Search(VNS) is presented to solve the model. Finally, the computational results are presented and future research directions are discussed.

Keywords: Location-routing problem, robust optimization, Stochastic Programming, variable neighborhood search.

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Authors: Jain-Shing Liu

Abstract:

In this paper, we present a matrix game-theoretic cross-layer optimization formulation to maximize the network lifetime in wireless ad hoc networks with network coding. To this end, we introduce a cross-layer formulation of general NUM (network utility maximization) that accommodates routing, scheduling, and stream control from different layers in the coded networks. Specifically, for the scheduling problem and then the objective function involved, we develop a matrix game with the strategy sets of the players corresponding to hyperlinks and transmission modes, and design the payoffs specific to the lifetime. In particular, with the inherit merit that matrix game can be solved with linear programming, our cross-layer programming formulation can benefit from both game-based and NUM-based approaches at the same time by cooperating the programming model for the matrix game with that for the other layers in a consistent framework. Finally, our numerical example demonstrates its performance results on a well-known wireless butterfly network to verify the cross-layer optimization scheme.

Keywords: Cross-layer design, Lifetime maximization, Matrix game, Network coding

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Authors: Abdulqader M. Mohsen, Ahamad Tajudin Khader, Dhanesh Ramachandram, Abdullatif Ghallab

Abstract:

The physical methods for RNA secondary structure prediction are time consuming and expensive, thus methods for computational prediction will be a proper alternative. Various algorithms have been used for RNA structure prediction including dynamic programming and metaheuristic algorithms. Musician's behaviorinspired harmony search is a recently developed metaheuristic algorithm which has been successful in a wide variety of complex optimization problems. This paper proposes a harmony search algorithm (HSRNAFold) to find RNA secondary structure with minimum free energy and similar to the native structure. HSRNAFold is compared with dynamic programming benchmark mfold and metaheuristic algorithms (RnaPredict, SetPSO and HelixPSO). The results showed that HSRNAFold is comparable to mfold and better than metaheuristics in finding the minimum free energies and the number of correct base pairs.

Keywords: Metaheuristic algorithms, dynamic programming algorithms, harmony search optimization, RNA folding, Minimum free energy.

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Authors: T. Ganesan, M. S. Aris, I. Elamvazuthi, Momen Kamal Tageldeen

Abstract:

Terms set in power purchase agreements (PPA) challenge power utility companies in balancing between the returns (from maximizing power production) and securing long term supply contracts at capped production. The production limitation set in the PPA has driven efforts to maximize profits through efficient and economic power production. In this paper, a combined industrial-scale gas turbine (GT) - absorption chiller (AC) system is considered to cool the GT air intake for reducing the plant’s heat rate (HR). This GT-AC system is optimized while considering power output limitations imposed by the PPA. In addition, the proposed formulation accounts for uncertainties in the ambient temperature using Type-2 fuzzy programming. Using the enhanced chaotic differential evolution (CEDE), the Pareto frontier was constructed and the optimization results are analyzed in detail.

Keywords: Absorption chillers, turbine inlet air cooling, power purchase agreement, multiobjective optimization, type-2 fuzzy programming, chaotic differential evolution.

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

Abstract:

In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: Grey relational degree, multiple linear regression, membership function, nonlinear programming.

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Authors: Omid S. Fard, Akbar H. Borzabadi

Abstract:

In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.

Keywords: Optimal control, Integer programming, Genetic algorithm, Discrete approximation, Linear programming.

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Authors: Phruksaphanrat B.

Abstract:

This research proposes a Preemptive Possibilistic Linear Programming (PPLP) approach for solving multiobjective Aggregate Production Planning (APP) problem with interval demand and imprecise unit price and related operating costs. The proposed approach attempts to maximize profit and minimize changes of workforce. It transforms the total profit objective that has imprecise information to three crisp objective functions, which are maximizing the most possible value of profit, minimizing the risk of obtaining the lower profit and maximizing the opportunity of obtaining the higher profit. The change of workforce level objective is also converted. Then, the problem is solved according to objective priorities. It is easier than simultaneously solve the multiobjective problem as performed in existing approach. Possible range of interval demand is also used to increase flexibility of obtaining the better production plan. A practical application of an electronic company is illustrated to show the effectiveness of the proposed model.

Keywords: Aggregate production planning, Fuzzy sets theory, Possibilistic linear programming, Preemptive priority

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Authors: C. Ardil

Abstract:

This paper presents a multiple criteria evaluation analysis for airline quality rating using the preference analysis for reference ideal solution (PARIS) and the technique for order of preference by similarity to ideal solution (TOPSIS) approaches. The airline quality rating was developed as an objective method for assessing airline quality on combined multiple performance criteria and the importance weights of criteria. The selected multiple performance criteria were determined as on-time arrivals, mishandled baggage, involuntary denied boardings, and consumer complaints. The multiple criteria decision making analysis results show that the alternative ( a2) airline is the best-rated airline.

Keywords: airline quality rating, multiple criteria decision making, multiple criteria decision making analysis, entropy weight, MCDMA, PARIS, TOPSIS

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Authors: André Trudel, Haiyi Zhang

Abstract:

Over the years, many implementations have been proposed for solving IA networks. These implementations are concerned with finding a solution efficiently. The primary goal of our implementation is simplicity and ease of use. We present an IA network implementation based on finite domain non-binary CSPs, and constraint logic programming. The implementation has a GUI which permits the drawing of arbitrary IA networks. We then show how the implementation can be extended to find all the solutions to an IA network. One application of finding all the solutions, is solving probabilistic IA networks.

Keywords: Constraint logic programming, CSP, logic, temporalreasoning.

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Authors: A. Sina, A. Aeenmehr, H. Mohamadian

Abstract:

Optimization and control of reactive power distribution in the power systems leads to the better operation of the reactive power resources. Reactive power control reduces considerably the power losses and effective loads and improves the power factor of the power systems. Another important reason of the reactive power control is improving the voltage profile of the power system. In this paper, voltage and reactive power control using Neural Network techniques have been applied to the 33 shines- Tehran Electric Company. In this suggested ANN, the voltages of PQ shines have been considered as the input of the ANN. Also, the generators voltages, tap transformers and shunt compensators have been considered as the output of ANN. Results of this techniques have been compared with the Linear Programming. Minimization of the transmission line power losses has been considered as the objective function of the linear programming technique. The comparison of the results of the ANN technique with the LP shows that the ANN technique improves the precision and reduces the computation time. ANN technique also has a simple structure and this causes to use the operator experience.

Keywords: voltage control, linear programming, artificial neural network, power systems

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Authors: Margareta Ilkova, Petr Teply

Abstract:

The article deals with dividends and their distribution from investors from a theoretical point of view. Some studies try to analyzed the reaction of the market on the dividend announcement and found out the change of dividend policy is associated with abnormal returns around the dividend announcement date. Another researches directly questioned the investors about their dividend preference and beliefs. Investors want the dividend from many reasons (e.g. some of them explain the dividend preference by the existence of transaction cost; investors prefer the dividend today, because there is less risky; the managers have private information about the firm). The most controversial theory of dividend policy was developed by Modigliani and Miller (1961) who demonstrated that in the perfect and complete capital markets the dividend policy is irrelevant and the value of the company is independent of its payout policy. Nevertheless, in the real world the capital markets are imperfect, because of asymmetric information, transaction costs, incomplete contracting possibilities and taxes.

Keywords: dividend distribution, taxation, payout policy, investor, Modigliani and Miller theorem

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Authors: Hadi Gholizadeh, Ali Tajdin

Abstract:

To have effective production planning, it is necessary to control the quality of processes. This paper aims at improving the performance of the disposable essentials process using statistical quality control and goal programming in a vague environment. That is expressed uncertainty because there is always a measurement error in the real world. Therefore, in this study, the conditions are examined in a vague environment that is a distance-based environment. The disposable essentials process in Kach Company was studied. Statistical control tools were used to characterize the existing process for four factor responses including the average of disposable glasses’ weights, heights, crater diameters, and volumes. Goal programming was then utilized to find the combination of optimal factors setting in a vague environment which is measured to apply uncertainty of the initial information when some of the parameters of the models are vague; also, the fuzzy regression model is used to predict the responses of the four described factors. Optimization results show that the process capability index values for disposable glasses’ average of weights, heights, crater diameters and volumes were improved. Such increasing the quality of the products and reducing the waste, which will reduce the cost of the finished product, and ultimately will bring customer satisfaction, and this satisfaction, will mean increased sales.

Keywords: Goal programming, quality control, vague environment, disposable glasses’ optimization, fuzzy regression.

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Authors: Paulo S. Caparelli, Eduardo Costa, Alexsandro S. Soares, Hipolito Barbosa

Abstract:

This paper presents an evolutionary method for designing electronic circuits and numerical methods associated with monitoring systems. The instruments described here have been used in studies of weather and climate changes due to global warming, and also in medical patient supervision. Genetic Programming systems have been used both for designing circuits and sensors, and also for determining sensor parameters. The authors advance the thesis that the software side of such a system should be written in computer languages with a strong mathematical and logic background in order to prevent software obsolescence, and achieve program correctness.

Keywords: Pattern recognition, evolutionary computation, biological signal, functional programming.

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Authors: Ashkan Izadi, Vic Ciesielski

Abstract:

We describe a work with an evolutionary computing algorithm for non photo–realistic rendering of a target image. The renderings are produced by genetic programming. We have used two different types of strokes: “empty triangle" and “filled triangle" in color level. We compare both empty and filled triangular strokes to find which one generates more aesthetic pleasing images. We found the filled triangular strokes have better fitness and generate more aesthetic images than empty triangular strokes.

Keywords: Artificial intelligence, Evolutionary programming, Geneticprogramming, Non photo–realistic rendering.

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Authors: S. T. Tan, H. Hashim, W. S. Ho, C. T. Lee

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Rapid economic development and population growth in Malaysia had accelerated the generation of solid waste. This issue gives pressure for effective management of municipal solid waste (MSW) to take place in Malaysia due to the increased cost of landfill. This paper discusses optimal planning of waste-to-energy (WTE) using a combinatorial simulation and optimization model through mixed integer linear programming (MILP) approach. The proposed multi-period model is tested in Iskandar Malaysia (IM) as case study for a period of 12 years (2011 -2025) to illustrate the economic potential and tradeoffs involved in this study. In this paper, 3 scenarios have been used to demonstrate the applicability of the model: (1) Incineration scenario (2) Landfill scenario (3) Optimal scenario. The model revealed that the minimum cost of electricity generation from 9,995,855 tonnes of MSW is estimated as USD 387million with a total electricity generation of 50MW /yr in the optimal scenario.

Keywords: Mixed Integer Linear Programming (MILP), optimization, solid waste management (SWM), Waste-to-energy (WTE).

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Authors: Uday Hameed Farhan, Majid Tolouei-Rad, Simona O'Brien

Abstract:

Modular fixtures (MFs) are very important tools in manufacturing processes in terms of reduction the cost and the production time. This paper introduces an automated approach for assembling MFs elements by employing SolidWorks as a powerful 3D CAD software. Visual Basic (VB) programming language was applied integrating with SolidWorks API (Application programming interface) functions. This integration allowed creating plug-in file and generating new menus in the SolidWorks environment. The menus allow the user to select, insert, and assemble MFs elements.

Keywords: Assembly automation, modular fixtures, SolidWorks, Visual Basic.

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Authors: Noraziah Ahmad, Roslina Mohd Sidek, Mohd Affendy Omardin

Abstract:

E-Appointment Scheduling (EAS) has been developed to handle appointment for UMP students, lecturers in Faculty of Computer Systems & Software Engineering (FCSSE) and Student Medical Center. The schedules are based on the timetable and university activities. Constraints Logic Programming (CLP) has been implemented to solve the scheduling problems by giving recommendation to the users in part of determining any available slots from the lecturers and doctors- timetable. By using this system, we can avoid wasting time and cost because this application will set an appointment by auto-generated. In addition, this system can be an alternative to the lecturers and doctors to make decisions whether to approve or reject the appointments.

Keywords: EAS, Constraint Logic Programming, PHP, Apache.

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Authors: Siliang Wang, Minghui Wang, Jun Hu

Abstract:

A novel path planning approach is presented to solve optimal path in stochastic, time-varying networks under priori traffic information. Most existing studies make use of dynamic programming to find optimal path. However, those methods are proved to be unable to obtain global optimal value, moreover, how to design efficient algorithms is also another challenge. This paper employs a decision theoretic framework for defining optimal path: for a given source S and destination D in urban transit network, we seek an S - D path of lowest expected travel time where its link travel times are discrete random variables. To solve deficiency caused by the methods of dynamic programming, such as curse of dimensionality and violation of optimal principle, an integer programming model is built to realize assignment of discrete travel time variables to arcs. Simultaneously, pruning techniques are also applied to reduce computation complexity in the algorithm. The final experiments show the feasibility of the novel approach.

Keywords: pruning method, stochastic, time-varying networks, optimal path planning.

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Authors: Siyuan Jing, Kun She

Abstract:

Virtualization-based server consolidation has been proven to be an ideal technique to solve the server sprawl problem by consolidating multiple virtualized servers onto a few physical servers leading to improved resource utilization and return on investment. In this paper, we solve this problem by using existing servers, which are heterogeneous and diversely preferred by IT managers. Five practical consolidation rules are introduced, and a decision model is proposed to optimally allocate source services to physical target servers while maximizing the average resource utilization and preference value. Our model can be regarded as a multi-objective multi-dimension bin-packing (MOMDBP) problem with constraints, which is strongly NP-hard. An improved grouping generic algorithm (GGA) is introduced for the problem. Extensive simulations were performed and the results are given.

Keywords: GGA-based Heuristics, Preference, Real-worldConstraints, Resource Utilization, Server Consolidation

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Authors: M. Boudjerda, B. Touaibia, M. K. Mihoubi

Abstract:

In Algeria agricultural irrigation is the primary water consuming sector followed by the domestic and industrial sectors. Economic development in the last decade has weighed heavily on water resources which are relatively limited and gradually decreasing to the detriment of agriculture. The research presented in this paper focuses on the optimization of irrigation water demand. Dynamic Programming-Neural Network (DPNN) method is applied to investigate reservoir optimization. The optimal operation rule is formulated to minimize the gap between water release and water irrigation demand. As a case study, Foum El-Gherza dam’s reservoir system in south of Algeria has been selected to examine our proposed optimization model. The application of DPNN method allowed increasing the satisfaction rate (SR) from 12.32% to 55%. In addition, the operation rule generated showed more reliable and resilience operation for the examined case study.

Keywords: ater management, agricultural demand, dam and reservoir operation, Foum el-Gherza dam, dynamic programming, artificial neural network.

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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents established 3ⁿ enumeration procedure for mixed integer optimization problems for solving multi-objective reliability and redundancy allocation problem subject to design constraints. The formulated problem is to find the optimum level of unit reliability and the number of units for each subsystem. A number of illustrative examples are provided and compared to indicate the application of the superiority of the proposed method.

Keywords: Integer programming, mixed integer programming, multi-objective optimization, reliability redundancy allocation.

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Authors: Phruksaphanrat B.

Abstract:

This research presents a fuzzy multi-objective model for a machine selection problem in a flexible manufacturing system of a tire company. Two main objectives are minimization of an average machine error and minimization of the total setup time. Conventionally, the working team uses trial and error in selecting a pressing machine for each task due to the complexity and constraints of the problem. So, both objectives may not satisfy. Moreover, trial and error takes a lot of time to get the final decision. Therefore, in this research preemptive fuzzy goal programming model is developed for solving this multi-objective problem. The proposed model can obtain the appropriate results that the Decision Making (DM) is satisfied for both objectives. Besides, alternative choice can be easily generated by varying the satisfaction level. Additionally, decision time can be reduced by using the model, which includes all constraints of the system to generate the solutions. A numerical example is also illustrated to show the effectiveness of the proposed model.

Keywords: Machine Selection, Preemptive Fuzzy Goal Programming, Mixed Integer Programming, Application of Tire Industry.

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Authors: M. M. Toufigh, A. R. Ahangarasr, A. Ouria

Abstract:

Among many different methods that are used for optimizing different engineering problems mathematical (numerical) optimization techniques are very important because they can easily be used and are consistent with most of engineering problems. Many studies and researches are done on stability analysis of three dimensional (3D) slopes and the relating probable slip surfaces and determination of factors of safety, but in most of them force equilibrium equations, as in simplified 2D methods, are considered only in two directions. In other words for decreasing mathematical calculations and also for simplifying purposes the force equilibrium equation in 3rd direction is omitted. This point is considered in just a few numbers of previous studies and most of them have only given a factor of safety and they haven-t made enough effort to find the most probable slip surface. In this study shapes of the slip surfaces are modeled, and safety factors are calculated considering the force equilibrium equations in all three directions, and also the moment equilibrium equation is satisfied in the slip direction, and using nonlinear programming techniques the shape of the most probable slip surface is determined. The model which is used in this study is a 3D model that is composed of three upper surfaces which can cover all defined and probable slip surfaces. In this research the meshing process is done in a way that all elements are prismatic with quadrilateral cross sections, and the safety factor is defined on this quadrilateral surface in the base of the element which is a part of the whole slip surface. The method that is used in this study to find the most probable slip surface is the non-linear programming method in which the objective function that must get optimized is the factor of safety that is a function of the soil properties and the coordinates of the nodes on the probable slip surface. The main reason for using non-linear programming method in this research is its quick convergence to the desired responses. The final results show a good compatibility with the previously used classical and 2D methods and also show a reasonable convergence speed.

Keywords: Non-linear programming, numerical optimization, slope stability, 3D analysis.

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Authors: Tayeb Lardjane, Rabah Messaci

Abstract:

We consider a network of two M/M/1 parallel queues having the same poisonnian arrival stream with rate λ. Upon his arrival to the system a customer heads to the shortest queue and stays until being served. If the two queues have the same length, an arriving customer chooses one of the two queues with the same probability. Each duration of service in the two queues is an exponential random variable with rate μ and no jockeying is permitted between the two queues. A new numerical method, based on linear programming and convex optimization, is performed for the computation of the steady state solution of the system.

Keywords: Steady state solution, matrix formulation, convex set, shortest queue, linear programming.

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Authors: J. H. Ahn, J. W. Moon, K. H. Kim, H. K. Kim

Abstract:

As the ecology of Lake Shihwa has been restored significantly nowadays, the urban development is in progress around Lake Shihwa areas. Each development project includes a plan on utilizing waterfront areas, but there exist a difference on waterfront design criteria between experts and users. Therefore, it is significant to analyze preferences in design elements of existing waterfront parks around Lake Shihwa (Ansan Waterfront Park, Shihwa Reed Wetland Park, and T-Light Park) based on users’ perspectives and to reflect the result on upcoming waterfront developments. This study derives design elements on waterfront parks from literature reviews. The survey questionnaires are created based on these classified elements and the surveys are conducted to experts and users with in-depth interviews. For all three parks, several park facilities appear to be not recognized by users. Therefore the circulation path should be introduced in guide maps and information activities and furthermore in disposition of park facilities.

Keywords: Design Elements, Lake Shihwa, Preference, Waterfront Park.

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Authors: Walid S. Abd El-hamid, Sherif S. El-etriby, Mohiy M. Hadhoud

Abstract:

This paper presents a new methodology to select test cases from regression test suites. The selection strategy is based on analyzing the dynamic behavior of the applications that written in any programming language. Methods based on dynamic analysis are more safe and efficient. We design a technique that combine the code based technique and model based technique, to allow comparing the object oriented of an application that written in any programming language. We have developed a prototype tool that detect changes and select test cases from test suite.

Keywords: Regression testing, Model based testing, Dynamicbehavior.

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Authors: P. N. Korde, P. P. Bedekar

Abstract:

The time coordination of overcurrent relays (OCR) in a power distribution network is of great importance, as it reduces the power outages by avoiding the mal-operation of the backup relays. For this, the optimum value of the time multiplier setting (TMS) of OCRs should be chosen. The problem of determining the optimum value of TMS of OCRs in power distribution networks is formulated as a constrained optimization problem. The objective is to find the optimum value of TMS of OCRs to minimize the time of operation of relays under the constraint of maintaining the coordination of relays. A power distribution network can have a combination of numerical and electromechanical relays. The TMS of numerical relays can be set to any real value (which satisfies the constraints of the problem), whereas the TMS of electromechanical relays can be set in fixed step (0 to 1 in steps of 0.05). The main contribution of this paper is a formulation of the problem as a mixed-integer linear programming (MILP) problem and application of Gomory's cutting plane method to find the optimum value of TMS of OCRs. The TMS of electromechanical relays are taken as integers in the range 1 to 20 in the step of 1, and these values are mapped to 0.05 to 1 in the step of 0.05. The results obtained are compared with those obtained using a simplex method and its variants. It has been shown that the mixed-integer linear programming method outperforms the simplex method (and its variants) in the case of a system having a combination of numerical and electromechanical relays.

Keywords: Backup protection, constrained optimization, Gomory's cutting plane method, mixed-integer linear programming, overcurrent relay coordination, simplex method.

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Authors: Mohd Kamir Yusof, Suhailan Dato' Safei

Abstract:

Images are important in disease research, education, and clinical medicine. This paper presents a Web Service Platform (WSP) for support multiple programming languages to access image from biomedical databases. The main function WSP is to allow web users access image from biomedical databases. The WSP will receive web user-s queries. After that, it will send to Querying Server (QS) and the QS will search and retrieve data from biomedical databases. Finally, the information will display to the web users. Simple application is developed and tested for experiment purpose. Result from experiment indicated WSP can be used in biomedical environment.

Keywords: Biomedical, Image, Web Service Platform

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