Search results for: a method of problem solving.

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

Abstract:

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.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1917

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.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1489

Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

Abstract:

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2016

Authors: Melvin Ballera, Mosbah Mohamed Elssaedi, Ahmed Khalil Zohdy

Abstract:

Collaborative problem solving in e-learning can take in the form of discussion among learner, creating a highly social learning environment and characterized by participation and interactivity. This paper, designed a collaborative learning environment where agent act as co-learner, can play different roles during interaction. Since different roles have been assigned to the agent, learner will assume that multiple co-learner exists to help and guide him all throughout the collaborative problem solving process, but in fact, alone during the learning process. Specifically, it answers the questions what roles of the agent should be incorporated to contribute better learning outcomes, how agent will facilitate the communication process to provide social learning and interactivity and what are the specific instructional strategies that facilitate learner participation, increased skill acquisition and develop critical thinking.

Keywords: Collaborative e-learning, collaborative problem solving, , imaginary co-learner, social learning.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1604

Authors: S. Babaie-Kafaki, R. Ghanbari, S.H. Nasseri, E. Ardil

Abstract:

Bus networks design is an important problem in public transportation. The main step to this design, is determining the number of required terminals and their locations. This is an especial type of facility location problem, a large scale combinatorial optimization problem that requires a long time to be solved. The genetic algorithm (GA) is a search and optimization technique which works based on evolutionary principle of natural chromosomes. Specifically, the evolution of chromosomes due to the action of crossover, mutation and natural selection of chromosomes based on Darwin's survival-of-the-fittest principle, are all artificially simulated to constitute a robust search and optimization procedure. In this paper, we first state the problem as a mixed integer programming (MIP) problem. Then we design a new crossover and mutation for bus terminal location problem (BTLP). We tested the different parameters of genetic algorithm (for a sample problem) and obtained the optimal parameters for solving BTLP with numerical try and error.

Keywords: Bus networks, Genetic algorithm (GA), Locationproblem, Mixed integer programming (MIP).

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2305

Authors: Min Sun, Zhenyu Liu

Abstract:

In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.

Keywords: variational inequalities, monotone function, global convergence.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1292

Authors: Dariusz Barbucha, Piotr Jedrzejowicz

Abstract:

The paper proposes and validates a new method of solving instances of the vehicle routing problem (VRP). The approach is based on a multiple agent system paradigm. The paper contains the VRP formulation, an overview of the multiple agent environment used and a description of the proposed implementation. The approach is validated experimentally. The experiment plan and the discussion of experiment results follow.

Keywords: multi-agent systems, population-based methods, vehiclerouting problem.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2245

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

Abstract:

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

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1394

Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand

Abstract:

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.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1874

Authors: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.

Keywords: Close surfaces, high-order approach, numerical solutions, reaction-diffusion systems.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1267

Authors: Xueting Liu, Daojin Song, Chuandai Dong, Hongkui Li

Abstract:

From a set of shifted, blurred, and decimated image , super-resolution image reconstruction can get a high-resolution image. So it has become an active research branch in the field of image restoration. In general, super-resolution image restoration is an ill-posed problem. Prior knowledge about the image can be combined to make the problem well-posed, which contributes to some regularization methods. In the regularization methods at present, however, regularization parameter was selected by experience in some cases and other techniques have too heavy computation cost for computing the parameter. In this paper, we construct a new super-resolution algorithm by transforming the solving of the System stem Є=An into the solving of the equations X+A*X-1A=I , and propose an inverse iterative method.

Keywords: High-resolution MAP image, Reconstruction, Image interpolation, Motion Estimation, Hermitian positive definite solutions.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2156

Authors: N. M. Kamoh, M. C. Soomiyol

Abstract:

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 659

Authors: Lei Wang, Sizong Guo

Abstract:

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability.

Keywords: Fuzzy-valued function, fuzzy initial value problem, strongly generalized differentiability, adomian decomposition method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2535

Authors: J.S.C. Prentice

Abstract:

The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: RK1GL2X3, RK1GL2, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, local error, global error.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1318

Authors: Parvaneh Shabanzadeh, Malik Hj Abu Hassan, Leong Wah June, Maryam Mohagheghtabar

Abstract:

Clustering is one of an interesting data mining topics that can be applied in many fields. Recently, the problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on nonsmooth optimization techniques is developed. This optimization problem has a number of characteristics that make it challenging: it has many local minimum, the optimization variables can be either continuous or categorical, and there are no exact analytical derivatives. In this study we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods do not explicitly use derivatives, an important feature that has not been addressed in previous studies. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed method.

Keywords: Clustering functions, Non-smooth Optimization, Nonconvex Optimization, Pattern Search Method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1640

Authors: Yasser F. Hassan, Marwa Abdeen, Mustafa Fahmy

Abstract:

In recent years multi-agent systems have emerged as one of the interesting architectures facilitating distributed collaboration and distributed problem solving. Each node (agent) of the network might pursue its own agenda, exploit its environment, develop its own problem solving strategy and establish required communication strategies. Within each node of the network, one could encounter a diversity of problem-solving approaches. Quite commonly the agents can realize their processing at the level of information granules that is the most suitable from their local points of view. Information granules can come at various levels of granularity. Each agent could exploit a certain formalism of information granulation engaging a machinery of fuzzy sets, interval analysis, rough sets, just to name a few dominant technologies of granular computing. Having this in mind, arises a fundamental issue of forming effective interaction linkages between the agents so that they fully broadcast their findings and benefit from interacting with others.

Keywords: Granular computing, rough sets, agents, traffic system.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1728

Authors: Jafar Biazar, Behzad Ghanbari

Abstract:

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

Keywords: System of nonlinear equations.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1593

Authors: Linda Mei Sui Khoo, Dorit Maor, Renato Schibeci

Abstract:

Graduate attributes have received increasing attention over recent years as universities incorporate these attributes into the curriculum. Graduates who have adequate technical knowledge only are not sufficiently equipped to compete effectively in the work place; they also need non disciplinary skills ie, graduate attributes. The purpose of this paper is to investigate the impact of an eportfolio in a technical communication course to enhance engineering students- graduate attributes: namely, learning of communication, critical thinking and problem solving and teamwork skills. Two questionnaires were used to elicit information from the students: one on their preferred and the other on the actual learning process. In addition, student perceptions of the use of eportfolio as a learning tool were investigated. Preliminary findings showed that most of the students- expectations have been met with their actual learning. This indicated that eportfolio has the potential as a tool to enhance students- graduate attributes.

Keywords: Eportfolio, Communication Skills, Critical Thinking and Problem Solving Skills and Teamwork Skills

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1794

Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou

Abstract:

In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.

Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1826

Authors: S. H. Borghei, E. Teymourian, M. Mobin, G. M. Komaki, S. Sheikh

Abstract:

Imperialist Competitive Algorithm (ICA) is a recent meta-heuristic method that is inspired by the social evolutions for solving NP-Hard problems. The ICA is a population-based algorithm which has achieved a great performance in comparison to other metaheuristics. This study is about developing enhanced ICA approach to solve the Cell Formation Problem (CFP) using sequence data. In addition to the conventional ICA, an enhanced version of ICA, namely EICA, applies local search techniques to add more intensification aptitude and embed the features of exploration and intensification more successfully. Suitable performance measures are used to compare the proposed algorithms with some other powerful solution approaches in the literature. In the same way, for checking the proficiency of algorithms, forty test problems are presented. Five benchmark problems have sequence data, and other ones are based on 0-1 matrices modified to sequence based problems. Computational results elucidate the efficiency of the EICA in solving CFP problems.

Keywords: Cell formation problem, Group technology, Imperialist competitive algorithm, Sequence data.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1588

Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1211

Authors: Halizah Awang, Ishak Ramly

Abstract:

Problem-based learning (PBL) is one of the student centered approaches and has been considered by a number of higher educational institutions in many parts of the world as a method of delivery. This paper presents a creative thinking approach for implementing Problem-based Learning in Mechanics of Structure within a Malaysian Polytechnics environment. In the learning process, students learn how to analyze the problem given among the students and sharing classroom knowledge into practice. Further, through this course-s emphasis on problem-based learning, students acquire creative thinking skills and professional skills as they tackle complex, interdisciplinary and real-situation problems. Once the creative ideas are generated, there are useful additional techniques for tender ideas that will grow into a productive concept or solution. The combination of creative skills and technical abilities will enable the students to be ready to “hit-the-ground-running" and produce in industry when they graduate.

Keywords: Creative Thinking Skills, Problem-based Learning, Problem Solving.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7323

Authors: Mohammad J. Heydari, Farnaz Derakhshan

Abstract:

In this paper, we focus on the problem of driving and herding a collection of autonomous actors to a given area. Then, a new method based on multi-agent coordination is proposed for solving the problem. In our proposed method, we assume that the environment is covered by sensors. When an event is occurred, sensors forward information to a sink node. Based on received information, the sink node will estimate the direction and the speed of movement of actors and announce the obtained value to the actors. The actors coordinate to reach the target location.

Keywords: Coordination, Environmental Inspection, Multiagent systems, Wireless Sensor and Actor Networks (WSANs)

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1432

Authors: S. Khamsawang, S. Jiriwibhakorn

Abstract:

This paper proposes an improved approach based on conventional particle swarm optimization (PSO) for solving an economic dispatch(ED) problem with considering the generator constraints. The mutation operators of the differential evolution (DE) are used for improving diversity exploration of PSO, which called particle swarm optimization with mutation operators (PSOM). The mutation operators are activated if velocity values of PSO nearly to zero or violated from the boundaries. Four scenarios of mutation operators are implemented for PSOM. The simulation results of all scenarios of the PSOM outperform over the PSO and other existing approaches which appeared in literatures.

Keywords: Novel particle swarm optimization, Economic dispatch problem, Mutation operator, Prohibited operating zones, Differential Evolution.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2318

Authors: Reza Mollapourasl, Majid Haghi

Abstract:

In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: Radial basis functions, Hermite finite difference, Helmholtz equation, stability.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 129

Authors: Ibrahim Abu-Alshaikh

Abstract:

In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.

Keywords: Iterative method, root-finding method, sine-polynomial equations, nonlinear equations.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1693

Authors: Chinwendu. B. Eleje, Udechukwu P. Egbuhuzor

Abstract:

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

Keywords: Newton Raphson method, non-linear boundary value problem, Taylor series approximation, Michaelis-Menten equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 325

Authors: Yasunori Sugita, Toshinori Yoshikawa

Abstract:

The design problem of Infinite Impulse Response (IIR) digital filters is usually expressed as the minimization problem of the complex magnitude error that includes both the magnitude and phase information. However, the group delay of the filter obtained by solving such design problem may be far from the desired group delay. In this paper, we propose a design method of stable IIR digital filters with prespecified maximum group delay errors. In the proposed method, the approximation problems of the magnitude-phase and group delay are separately defined, and these two approximation problems are alternately solved using successive projections. As a result, the proposed method can design the IIR filters that satisfy the prespecified allowable errors for not only the complex magnitude but also the group delay by alternately executing the coefficient update for the magnitude-phase and the group delay approximation. The usefulness of the proposed method is verified through some examples.

Keywords: Filter design, Group delay approximation, Stable IIRfilters, Successive projection method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1561

Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: Dissipation, Oscillatory solutions, Phase-lag, Runge- Kutta methods.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1905

Authors: A. R. Seifi

Abstract:

This work presents a new algorithm based on a combination of fuzzy (FUZ), Dynamic Programming (DP), and Genetic Algorithm (GA) approach for capacitor allocation in distribution feeders. The problem formulation considers two distinct objectives related to total cost of power loss and total cost of capacitors including the purchase and installation costs. The novel formulation is a multi-objective and non-differentiable optimization problem. The proposed method of this article uses fuzzy reasoning for sitting of capacitors in radial distribution feeders, DP for sizing and finally GA for finding the optimum shape of membership functions which are used in fuzzy reasoning stage. The proposed method has been implemented in a software package and its effectiveness has been verified through a 9-bus radial distribution feeder for the sake of conclusions supports. A comparison has been done among the proposed method of this paper and similar methods in other research works that shows the effectiveness of the proposed method of this paper for solving optimum capacitor planning problem.

Keywords: Capacitor planning, Fuzzy logic method, Genetic Algorithm, Dynamic programming, Radial Distribution feeder

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1610