Search results for: Problem Solving Skills

Authors: San Nah Sze, Wei King Tiong

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The multiple traveling salesman problem (mTSP) can be used to model many practical problems. The mTSP is more complicated than the traveling salesman problem (TSP) because it requires determining which cities to assign to each salesman, as well as the optimal ordering of the cities within each salesman's tour. Previous studies proposed that Genetic Algorithm (GA), Integer Programming (IP) and several neural network (NN) approaches could be used to solve mTSP. This paper compared the results for mTSP, solved with Genetic Algorithm (GA) and Nearest Neighbor Algorithm (NNA). The number of cities is clustered into a few groups using k-means clustering technique. The number of groups depends on the number of salesman. Then, each group is solved with NNA and GA as an independent TSP. It is found that k-means clustering and NNA are superior to GA in terms of performance (evaluated by fitness function) and computing time.

Keywords: Multiple Traveling Salesman Problem, GeneticAlgorithm, Nearest Neighbor Algorithm, k-Means Clustering.

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Authors: Omid Noroozi

Abstract:

Digital dialogue games have opened up opportunities for learning skills by engaging students in complex problem solving that mimic real world situations, without importing unwanted constraints and risks of the real world. Digital dialogue games can be motivating and engaging to students for fun, creative thinking, and learning. This study explored how undergraduate students engage with argumentative discourse activities which have been designed to intensify debate. A pre-test, post-test design was used with students who were assigned to groups of four and asked to debate a controversial topic with the aim of exploring various 'pros and cons' on the 'Genetically Modified Organisms (GMOs)'. Findings reveal that the Digital dialogue game can facilitate argumentation-based learning. The digital Dialogue game was also evaluated positively in terms of students’ satisfaction and learning experiences.

Keywords: Argumentation, dialogue, digital game, learning, motivation.

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Authors: Gunasekaran Raja, Ramkumar Jayaraman

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In this paper, we consider CCL-N (Cooperative Cross Layer Network) topology based on the cross layer (both centralized and distributed) environment to form network communities. Various performance metrics related to the IEEE 802.16 networks are discussed to design CCL-N Topology. In CCL-N topology, nodes are classified as master nodes (Master Base Station [MBS]) and serving nodes (Relay Station [RS]). Nodes communities are organized based on the networking terminologies. Based on CCL-N Topology, various simulation analyses for both transparent and non-transparent relays are tabulated and throughput efficiency is calculated. Weighted load balancing problem plays a challenging role in IEEE 802.16 network. CoTS (Concurrent Transmission Scheduling) Scheme is formulated in terms of three aspects – transmission mechanism based on identical communities, different communities and identical node communities. CoTS scheme helps in identifying the weighted load balancing problem. Based on the analytical results, modularity value is inversely proportional to that of the error value. The modularity value plays a key role in solving the CoTS problem based on hop count. The transmission mechanism for identical node community has no impact since modularity value is same for all the network groups. In this paper three aspects of communities based on the modularity value which helps in solving the problem of weighted load balancing and CoTS are discussed.

Keywords: Cross layer network topology, concurrent scheduling, modularity value, network communities and weighted load balancing.

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Authors: Manpreet Singh, Parvinder Singh Sandhu, Manjinder Singh Kahlon

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There are many classical algorithms for finding routing in FPGA. But Using DNA computing we can solve the routes efficiently and fast. The run time complexity of DNA algorithms is much less than other classical algorithms which are used for solving routing in FPGA. The research in DNA computing is in a primary level. High information density of DNA molecules and massive parallelism involved in the DNA reactions make DNA computing a powerful tool. It has been proved by many research accomplishments that any procedure that can be programmed in a silicon computer can be realized as a DNA computing procedure. In this paper we have proposed two tier approaches for the FPGA routing solution. First, geometric FPGA detailed routing task is solved by transforming it into a Boolean satisfiability equation with the property that any assignment of input variables that satisfies the equation specifies a valid routing. Satisfying assignment for particular route will result in a valid routing and absence of a satisfying assignment implies that the layout is un-routable. In second step, DNA search algorithm is applied on this Boolean equation for solving routing alternatives utilizing the properties of DNA computation. The simulated results are satisfactory and give the indication of applicability of DNA computing for solving the FPGA Routing problem.

Keywords: FPGA, Routing, DNA Computing.

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Authors: Anneke Harmse, Roelien Goede

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Information and communication technology (ICT) is essential to the operation of business, and create many employment opportunities. High volumes of students graduate in ICT however students struggle to find job placement. A discrepancy exists between graduate skills and industry skill requirements. To address the need for ICT skills required, universities must create programs to meet the demands of a changing ICT industry. This requires a partnership between industry, universities and other stakeholders. This situation may be viewed as a critical systems thinking problem situation as there are various role players each with their own needs and requirements. Jackson states a typical critical systems methods has a pluralistic nature. This paper explores the applicability and suitability of Maslow and Dooyeweerd to guide understanding and make recommendations for change in ICT WIL, to foster an all-inclusive understanding of the situation by stakeholders. The above methods provide tools for understanding softer issues beyond the skills required. The study findings suggest that besides skills requirements, a deeper understanding and empowering students from being a student to a professional need to be understood and addressed.

Keywords: Dooyeweerd, Maslow, Work Integrated Learning.

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Authors: D.Venkatesan, K.Kannan, S. Raja Balachandar

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In this paper a new Genetic Algorithm based on a heuristic operator and Centre of Mass selection operator (CMGA) is designed for the unbounded knapsack problem(UKP), which is NP-Hard combinatorial optimization problem. The proposed genetic algorithm is based on a heuristic operator, which utilizes problem specific knowledge. This center of mass operator when combined with other Genetic Operators forms a competitive algorithm to the existing ones. Computational results show that the proposed algorithm is capable of obtaining high quality solutions for problems of standard randomly generated knapsack instances. Comparative study of CMGA with simple GA in terms of results for unbounded knapsack instances of size up to 200 show the superiority of CMGA. Thus CMGA is an efficient tool of solving UKP and this algorithm is competitive with other Genetic Algorithms also.

Keywords: Genetic Algorithm, Unbounded Knapsack Problem, Combinatorial Optimization, Meta-Heuristic, Center of Mass

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Authors: M. Rodionov, Z. Dedovets

Abstract:

This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.

Keywords: Mathematics, motivation, secondary school, student, practical problem.

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Authors: Jayendra Krishna, Laxmi Srivastava

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Power flow (PF) study, which is performed to determine the power system static states (voltage magnitudes and voltage angles) at each bus to find the steady state operating condition of a system, is very important and is the most frequently carried out study by power utilities for power system planning, operation and control. In this paper, a counterpropagation neural network (CPNN) is proposed to solve power flow problem under different loading/contingency conditions for computing bus voltage magnitudes and angles of the power system. The counterpropagation network uses a different mapping strategy namely counterpropagation and provides a practical approach for implementing a pattern mapping task, since learning is fast in this network. The composition of the input variables for the proposed neural network has been selected to emulate the solution process of a conventional power flow program. The effectiveness of the proposed CPNN based approach for solving power flow is demonstrated by computation of bus voltage magnitudes and voltage angles for different loading conditions and single line-outage contingencies in IEEE 14-bus system.

Keywords: Admittance matrix, counterpropagation neural network, line outage contingency, power flow

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Authors: P. Shunmugapriya, S. Kanmani, P. Jude Fredieric, U. Vignesh, J. Reman Justin, K. Vivek

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Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem and it is quite difficult to find an optimal solution consisting of a set of routes for vehicles whose total cost is minimum. Evolutionary and swarm intelligent (SI) algorithms play a vital role in solving optimization problems. While the SI algorithms perform search, the diversity between the solutions they exploit is very important. This is because of the need to avoid early convergence and to get an appropriate balance between the exploration and exploitation. Therefore, it is important to check how far the solutions are diverse. In this paper, we measure the similarity between solutions, which ABC exploits while optimizing VRP. The similar solutions found are discarded at the end of the iteration and only unique solutions are passed on to the next iteration. The bees of discarded solutions become scouts and they start searching for new solutions. This process is continued and results show that the solution is optimized at lesser number of iterations but with the overhead of computing similarity in all the iterations. The problem instance from Solomon benchmarked dataset has been used for evaluating the presented methodology.

Keywords: ABC algorithm, vehicle routing problem, optimization, Jaccard’s similarity measure.

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Authors: Nai-Chieh Wei, I-Ming Chao, Chin-Jung Liuand, Hong Long Chen

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This paper combines the branch-and-bound method and the petri net to solve the two-sided assembly line balancing problem, thus facilitating effective branching and pruning of tasks. By integrating features of the petri net, such as reachability graph and incidence matrix, the propose method can support the branch-and-bound to effectively reduce poor branches with systematic graphs. Test results suggest that using petri net in the branching process can effectively guide the system trigger process, and thus, lead to consistent results.

 

Keywords: Branch-and-Bound Method, Petri Net, Two-Sided Assembly Line Balancing Problem.

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Authors: Oon-Seng Tan

Abstract:

Human Computer Interaction (HCI) has been an emerging field that draws in the experts from various fields to enhance the application of computer programs and the ease of computer users. HCI has much to do with learning and cognition and an emerging approach to learning and problem-solving is problembased learning (PBL). The processes of PBL involve important cognitive functions in the various stages. This paper will illustrate how closely related fields to HCI, PBL and cognitive psychology can benefit from informing each other through analysing various cognitive functions. Several cognitive functions from cognitive function disc (CFD) would be presented and discussed in relation to human-computer interface. This paper concludes with the implications of bridging the gaps amongst these disciplines.

Keywords: problem-based learning, human computerinteraction, cognitive psychology, Cognitive Function Disc (CFD)

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Authors: George Cristian Gruia, Michal Kavan

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The article describes a case study on one of Czech Republic-s manufacturing middle size enterprises (ME), where due to the European financial crisis, production lines had to be redesigned and optimized in order to minimize the total costs of the production of goods. It is considered an optimization problem of minimizing the total cost of the work load, according to the costs of the possible locations of the workplaces, with an application of the Greedy algorithm and a partial analogy to a Set Packing Problem. The displacement of working tables in a company should be as a one-toone monotone increasing function in order for the total costs of production of the goods to be at minimum. We use a heuristic approach with greedy algorithm for solving this linear optimization problem, regardless the possible greediness which may appear and we apply it in a Czech ME.

Keywords: Czech, greedy algorithm, minimize, total costs.

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Authors: Halil Snopce, Ilir Spahiu, Lavdrim Elmazi

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A lot of Scientific and Engineering problems require the solution of large systems of linear equations of the form bAx in an effective manner. LU-Decomposition offers good choices for solving this problem. Our approach is to find the lower bound of processing elements needed for this purpose. Here is used the so called Omega calculus, as a computational method for solving problems via their corresponding Diophantine relation. From the corresponding algorithm is formed a system of linear diophantine equalities using the domain of computation which is given by the set of lattice points inside the polyhedron. Then is run the Mathematica program DiophantineGF.m. This program calculates the generating function from which is possible to find the number of solutions to the system of Diophantine equalities, which in fact gives the lower bound for the number of processors needed for the corresponding algorithm. There is given a mathematical explanation of the problem as well. Keywordsgenerating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equationsand : calculus.

Keywords: generating function, lattice points in polyhedron, lower bound of processor elements, system of Diophantine equations and calculus.

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Authors: Tarek M. Mahmoud

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Selecting the routes and the assignment of link flow in a computer communication networks are extremely complex combinatorial optimization problems. Metaheuristics, such as genetic or simulated annealing algorithms, are widely applicable heuristic optimization strategies that have shown encouraging results for a large number of difficult combinatorial optimization problems. This paper considers the route selection and hence the flow assignment problem. A genetic algorithm and simulated annealing algorithm are used to solve this problem. A new hybrid algorithm combining the genetic with the simulated annealing algorithm is introduced. A modification of the genetic algorithm is also introduced. Computational experiments with sample networks are reported. The results show that the proposed modified genetic algorithm is efficient in finding good solutions of the flow assignment problem compared with other techniques.

Keywords: Genetic Algorithms, Flow Assignment, Routing, Computer network, Simulated Annealing.

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Authors: G.Mehdiyeva, V.Ibrahimov, M.Imanova

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As is known, one of the priority directions of research works of natural sciences is introduction of applied section of contemporary mathematics as approximate and numerical methods to solving integral equation into practice. We fare with the solving of integral equation while studying many phenomena of nature to whose numerically solving by the methods of quadrature are mainly applied. Taking into account some deficiency of methods of quadrature for finding the solution of integral equation some sciences suggested of the multistep methods with constant coefficients. Unlike these papers, here we consider application of hybrid methods to the numerical solution of Volterra integral equation. The efficiency of the suggested method is proved and a concrete method with accuracy order p = 4 is constructed. This method in more precise than the corresponding known methods.

Keywords: Volterra integral equation, hybrid methods, stability and degree, methods of quadrature

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Authors: Hoong C. Chin, Soon H. Chew, Zhaoxia Wang

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Work on sustainable developments and the call for action in education for sustainable development have been ongoing for a number of years. Training engineering students with the relevant competencies, particularly in sustainable development literacy, has been identified as an urgent task in universities. This requires not only a holistic, multi-disciplinary approach to education but also a suitable training environment to develop the needed skills and to inculcate the appropriate attitudes in students towards sustainable development. To demonstrate how this can be done, a module involving an overseas field trip was introduced in 2013 at the National University of Singapore. This paper provides details of the module and describes its training philosophy and methods. Measured against the student learning outcomes, stipulated by the Engineering Accreditation Board, the module scored well on all of them, particularly those related to complex problem solving, environmental and sustainability awareness, multi-disciplinary team work and varied-level communications.

Keywords: Civil engineering education, student learning outcomes, sustainable development.

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Authors: R. Goede, E. Taylor

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This paper demonstrates how the soft systems methodology can be used to improve the delivery of a module in data warehousing for fourth year information technology students. Graduates in information technology needs to have academic skills but also needs to have good practical skills to meet the skills requirements of the information technology industry. In developing and improving current data warehousing education modules one has to find a balance in meeting the expectations of various role players such as the students themselves, industry and academia. The soft systems methodology, developed by Peter Checkland, provides a methodology for facilitating problem understanding from different world views. In this paper it is demonstrated how the soft systems methodology can be used to plan the improvement of data warehousing education for fourth year information technology students.

Keywords: Data warehousing, education, soft systems methodology, stakeholders, systems thinking.

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Authors: Jagabondhu Hazra, Avinash Sinha

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Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimization, ant colony optimization and particle swarm optimization for solving the economic dispatch problem. All the methods are tested on IEEE 30 bus test system. Simulation results are presented to show the comparative performance of these methods.

Keywords: Ant colony optimization, bacteria foraging optimization, economic dispatch, evolutionary algorithm, genetic algorithm, particle swarm optimization.

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Authors: Khairil Iskandar Othman, Zarina Bibi Ibrahim, Mohamed Suleiman

Abstract:

A parallel block method based on Backward Differentiation Formulas (BDF) is developed for the parallel solution of stiff Ordinary Differential Equations (ODEs). Most common methods for solving stiff systems of ODEs are based on implicit formulae and solved using Newton iteration which requires repeated solution of systems of linear equations with coefficient matrix, I - hβJ . Here, J is the Jacobian matrix of the problem. In this paper, the matrix operations is paralleled in order to reduce the cost of the iterations. Numerical results are given to compare the speedup and efficiency of parallel algorithm and that of sequential algorithm.

Keywords: Backward Differentiation Formula, block, ordinarydifferential equations.

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Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand

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In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

Keywords: Quasilinearization method, Barycentric lagrange interpolation, nonlinear ODE, fin problem, heat transfer.

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Authors: M. Khaing, A. V. Tkacheva

Abstract:

The work is devoted to solving the problem of temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the Prandtl-Reis model is used. A piecewise-linear condition of the Ishlinsky-Ivlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewise-linear conditions (Treska or Ishlinsky-Ivlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow Ishlinsky-Ivlev allows one to solve the problem. At the same time, there are also no solutions on the edge of the Ishlinsky-Ivlev hexagon in the plane-stressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the Ishlinsky-Ivlev hexagon in a plane stressed state; therefore, in this paper, the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young's modulus, Poisson's ratio) which depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.

Keywords: Temperature stresses, elasticity, plasticity, Ishlinsky-Ivlev condition, plate, annular heating, elastic moduli.

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Authors: Charlie Y. Shim, Mina Choi, Jung Y. Kim

Abstract:

Software engineering education not only embraces technical skills of software development but also necessitates communication and interaction among learners. In this paper, it is proposed to adapt the PBL methodology that is especially designed to be integrated into software engineering classroom in order to promote collaborative learning environment. This approach helps students better understand the significance of social aspects and provides a systematic framework to enhance teamwork skills. The adaptation of PBL facilitates the transition to an innovative software development environment where cooperative learning can be actualized.

Keywords: problem-based learning, software engineering, software process models, teamwork.

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Authors: Mohamed Chabi, Mohammad Shahid Jamil, Mahmoud I Syam

Abstract:

The purpose of this study is to determine whether paper assessment especially in the subject mathematics will ever be completely replaced by online assessment using Learning Management System and Content Management System such as blackboard. Testing students has moved from the traditional scribbling and sketching on paper towards working online on a screen and keyboard. It is found that online assessment by using selective types of questions like multiple choices, true or false and final answer questions don’t reflect the actual understanding of students in solving the problems and teachers can’t determine the weakness points of students. In addition, it is showed that OBMCQs are a very good tool for self-assessment and when teachers are testing for knowledge and facts. But when it comes to the skills, OBMCQs are poor tools for measuring the ability to apply knowledge to complex math problem. 

Keywords: Paper assessment, online assessment, learning management system, content management system.

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Authors: Janak Raj Sharma, Rajni Sharma

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Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations.

Keywords: Nonlinear equations and systems, Newton's method, fixed point iteration, order of convergence.

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Authors: M. Mokhtar, A. Shuib, D. Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: Portfolio optimization, Mathematical programming, Multi-objective programming, Solution approaches.

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Authors: Sirimanee Banjong

Abstract:

This study aimed to 1) develop pre-service teachers’ leadership skills through camp-based learning, and 2) develop preservice teachers’ teamwork skills through camp-based learning. An applied research methodology was used. The target group was derived from a purposive selection. It involved 32 fourth-year students in Early Childhood Education Program enrolling a course entitled Seminar in Early Childhood Education provided during second semester of academic year 2013. The treatment was camp-based learning activities which applied a PDCA process including four stages: 1) plan, 2) do, 3) check, and 4) act. Research instruments were a learning camp program, a camp-based learning management plan, a 5-level assessment form for leadership skills and a 5-level assessment form for assessing teamwork skills. Data were analyzed using descriptive statistics. Results were: 1) pre-service teachers’ leadership skills yielded the before treatment average score at x= 3.4, S.D.=0.6 2and the after-treatment average score at x 4.29 , S.D.=0.66 pre-service teachers’ teamwork skills yielded the before-treatment average score at x=3.31, S.D.=0.60 and the after-treatment average score at x=4.42, S.D.=0.66 Both differences were statistically significant at the .05 level. Thus, the pre-service teachers’ leadership and teamwork skills were significantly improved through the camp-based learning approach.

Keywords: Learning camp, leadership skills, teamwork skills.

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Authors: N. Paparisteidi, D. Rodamitou

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This article focuses on the skills development and path planning of students studying computer science at EPITECH: French private institute of higher education. We examine students’ points of view and experience in a blended learning model based on a skills development curriculum. The study is based on the collection of four main categories of data: semi-participant observation, distribution of questionnaires, interviews, and analysis of internal school databases. The findings seem to indicate that a skills-based program on active learning enables students to develop their learning strategies as well as their personal skills and to actively engage in the creation of their career path and contribute to providing additional information to curricula planners and decision-makers about learning design in higher education.

Keywords: Active learning, blended learning, higher education, skills development.

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Authors: Shrawan Kumar, D. K. Lobiyal

Abstract:

In this paper, we propose improved versions of DVHop algorithm as QDV-Hop algorithm and UDV-Hop algorithm for better localization without the need for additional range measurement hardware. The proposed algorithm focuses on third step of DV-Hop, first error terms from estimated distances between unknown node and anchor nodes is separated and then minimized. In the QDV-Hop algorithm, quadratic programming is used to minimize the error to obtain better localization. However, quadratic programming requires a special optimization tool box that increases computational complexity. On the other hand, UDV-Hop algorithm achieves localization accuracy similar to that of QDV-Hop by solving unconstrained optimization problem that results in solving a system of linear equations without much increase in computational complexity. Simulation results show that the performance of our proposed schemes (QDV-Hop and UDV-Hop) is superior to DV-Hop and DV-Hop based algorithms in all considered scenarios.

Keywords: Wireless sensor networks, Error term, DV-Hop algorithm, Localization.

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Authors: Minghui Wang

Abstract:

Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

Keywords: Matrix equation, bisymmetric matrix, least squares problem, like-minimum norm, iterative algorithm.

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Authors: Gaurav Kumar, Rakesh Kumar Bajaj

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The primary objective of the paper is to propose a new method for solving assignment problem under uncertain situation. In the classical assignment problem (AP), z_pqdenotes the cost for assigning the qth job to the pth person which is deterministic in nature. Here in some uncertain situation, we have assigned a cost in the form of composite relative degree F_pq instead of  and this replaced cost is in the maximization form. In this paper, it has been solved and validated by the two proposed algorithms, a new mathematical formulation of IVIF assignment problem has been presented where the cost has been considered to be an IVIFN and the membership of elements in the set can be explained by positive and negative evidences. To determine the composite relative degree of similarity of IVIFS the concept of similarity measure and the score function is used for validating the solution which is obtained by Composite relative similarity degree method. Further, hypothetical numeric illusion is conducted to clarify the method’s effectiveness and feasibility developed in the study. Finally, conclusion and suggestion for future work are also proposed.

Keywords: Assignment problem, Interval-valued Intuitionistic Fuzzy Sets, Similarity Measures, score function.

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