Search results for: Convergence order

Authors: Yusuke Onoue, Seiji Fujino, Norimasa Nakashima

Abstract:

The IDR(s) method based on an extended IDR theorem was proposed by Sonneveld and van Gijzen. The original IDR(s) method has excellent property compared with the conventional iterative methods in terms of efficiency and small amount of memory. IDR(s) method, however, has unexpected property that relative residual 2-norm stagnates at the level of less than 10-12. In this paper, an effective strategy for stagnation detection, stagnation avoidance using adaptively information of parameter s and improvement of convergence rate itself of IDR(s) method are proposed in order to gain high accuracy of the approximated solution of IDR(s) method. Through numerical experiments, effectiveness of adaptive tuning IDR(s) method is verified and demonstrated.

Keywords: Krylov subspace methods, IDR(s), adaptive tuning, stagnation of relative residual.

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Authors: V. Piscopo

Abstract:

In the classical buckling analysis of rectangular plates subjected to the concurrent action of shear and uniaxial forces, the Euler shear buckling stress is generally evaluated separately, so that no influence on the shear buckling coefficient, due to the in-plane tensile or compressive forces, is taken into account. In this paper the buckling problem of simply supported rectangular plates, under the combined action of shear and uniaxial forces, is discussed from the beginning, in order to obtain new project formulas for the shear buckling coefficient that take into account the presence of uniaxial forces. Furthermore, as the classical expression of the shear buckling coefficient for simply supported rectangular plates is considered only a “rough" approximation, as the exact one is defined by a system of intersecting curves, the convergence and the goodness of the classical solution are analyzed, too. Finally, as the problem of the Euler shear buckling stress evaluation is a very important topic for a variety of structures, (e.g. ship ones), two numerical applications are carried out, in order to highlight the role of the uniaxial stresses on the plating scantling procedures and the goodness of the proposed formulas.

Keywords: Buckling analysis, Shear, Uniaxial Stresses.

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Authors: Ze-Jun Hu, Ting-Zhu Huang, Ning-Bo Tan

Abstract:

To solve saddle point systems efficiently, several preconditioners have been published. There are many methods for constructing preconditioners for linear systems from saddle point problems, for instance, the relaxed dimensional factorization (RDF) preconditioner and the augmented Lagrangian (AL) preconditioner are used for both steady and unsteady Navier-Stokes equations. In this paper we compare the RDF preconditioner with the modified AL (MAL) preconditioner to show which is more effective to solve Navier-Stokes equations. Numerical experiments indicate that the MAL preconditioner is more efficient and robust, especially, for moderate viscosities and stretched grids in steady problems. For unsteady cases, the convergence rate of the RDF preconditioner is slightly faster than the MAL perconditioner in some circumstances, but the parameter of the RDF preconditioner is more sensitive than the MAL preconditioner. Moreover the convergence rate of the MAL preconditioner is still quite acceptable. Therefore we conclude that the MAL preconditioner is more competitive than the RDF preconditioner. These experiments are implemented with IFISS package. 

Keywords: Navier-Stokes equations, Krylov subspace method, preconditioner, dimensional splitting, augmented Lagrangian preconditioner.

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Authors: Zhenhuan Zhu, David Mulvaney, Vassilios Chouliaras

Abstract:

A new genetic algorithm, termed the 'optimum individual monogenetic genetic algorithm' (OIMGA), is presented whose properties have been deliberately designed to be well suited to hardware implementation. Specific design criteria were to ensure fast access to the individuals in the population, to keep the required silicon area for hardware implementation to a minimum and to incorporate flexibility in the structure for the targeting of a range of applications. The first two criteria are met by retaining only the current optimum individual, thereby guaranteeing a small memory requirement that can easily be stored in fast on-chip memory. Also, OIMGA can be easily reconfigured to allow the investigation of problems that normally warrant either large GA populations or individuals many genes in length. Local convergence is achieved in OIMGA by retaining elite individuals, while population diversity is ensured by continually searching for the best individuals in fresh regions of the search space. The results given in this paper demonstrate that both the performance of OIMGA and its convergence time are superior to those of a range of existing hardware GA implementations.

Keywords: Genetic algorithms, genetic hardware, machinelearning.

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Authors: Yiqiong Yuan, Jun Sun, Dongmei Zhou, Jianan Sun

Abstract:

In this paper, we presented a Multi-Objective Random Drift Particle Swarm Optimization algorithm (MORDPSO-CD) based on RDPSO and crowding distance sorting to improve the convergence and distribution with less computation cost. MORDPSO-CD makes the most of RDPSO to approach the true Pareto optimal solutions fast. We adopt the crowding distance sorting technique to update and maintain the archived optimal solutions. Introducing the crowding distance technique into MORDPSO can make the leader particles find the true Pareto solution ultimately. The simulation results reveal that the proposed algorithm has better convergence and distribution.

Keywords: Multi-objective optimization, random drift particle swarm optimization, crowding distance, Pareto optimal solution.

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Authors: Yongzhong Wu, Ping Ji

Abstract:

This paper proposes a genetic algorithm based on a new replacement strategy to solve the quadratic assignment problems, which are NP-hard. The new replacement strategy aims to improve the performance of the genetic algorithm through well balancing the convergence of the searching process and the diversity of the population. In order to test the performance of the algorithm, the instances in QAPLIB, a quadratic assignment problem library, are tried and the results are compared with those reported in the literature. The performance of the genetic algorithm is promising. The significance is that this genetic algorithm is generic. It does not rely on problem-specific genetic operators, and may be easily applied to various types of combinatorial problems.

Keywords: Quadratic assignment problem, Genetic algorithm, Replacement strategy, QAPLIB.

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Authors: Kiamran Radjabli

Abstract:

State Estimator became an intrinsic part of Energy Management Systems (EMS). The SCADA measurements received from the field are processed by the State Estimator in order to accurately determine the actual operating state of the power systems and provide that information to other real-time network applications. All EMS vendors offer a State Estimator functionality in their baseline products. However, setting up and ensuring that State Estimator consistently produces a reliable solution often consumes a substantial engineering effort. This paper provides generic recommendations and describes a simple practical approach to efficient tuning of State Estimator, based on the working experience with major EMS software platforms and consulting projects in many electrical utilities of the USA.

Keywords: Convergence, monitoring, performance, state estimator, troubleshooting, tuning, power systems.

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Authors: Zeyu Zhang, Guisheng Yin, Ziying Zhang, Liguo Zhang

Abstract:

This paper mainly studies the path planning method based on ant colony optimization (ACO), and proposes heuristic integration ant colony optimization (HIACO). This paper not only analyzes and optimizes the principle, but also simulates and analyzes the parameters related to the application of HIACO in path planning. Compared with the original algorithm, the improved algorithm optimizes probability formula, tabu table mechanism and updating mechanism, and introduces more reasonable heuristic factors. The optimized HIACO not only draws on the excellent ideas of the original algorithm, but also solves the problems of premature convergence, convergence to the sub optimal solution and improper exploration to some extent. HIACO can be used to achieve better simulation results and achieve the desired optimization. Combined with the probability formula and update formula, several parameters of HIACO are tested. This paper proves the principle of the HIACO and gives the best parameter range in the research of path planning.

Keywords: Ant colony optimization, heuristic integration, path planning

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Authors: Min Sun, Jing Liu

Abstract:

In this article, a new inexact alternating direction method(ADM) is proposed for solving a class of variational inequality problems. At each iteration, the new method firstly solves the resulting subproblems of ADM approximately to generate an temporal point ˜xk, and then the multiplier yk is updated to get the new iterate yk+1. In order to get xk+1, we adopt a new descent direction which is simple compared with the existing prediction-correction type ADMs. For the inexact ADM, the resulting proximal subproblem has closedform solution when the proximal parameter and inexact term are chosen appropriately. We show the efficiency of the inexact ADM numerically by some preliminary numerical experiments.

Keywords: variational inequality problems, alternating direction method, global convergence

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Authors: Shibly Abdullah

Abstract:

This paper provides an overview of fundamental philosophical and functional differences in conventional and Islamic accounting. The aim of this research is to undertake a detailed analysis focus on specific illustrations drawn from both these systems and highlight how these differences implicate in recording financial transactions and preparation of financial reports for a range of stakeholders. Accounting as being universally considered as a platform for providing a ‘true and fair’ view of corporate entities can be challenged in the current world view, as the business environment has evolved and transformed significantly. Growth of the non-traditional corporate entity such as Islamic financial institutions, fundamentally questions the applicability of conventional accounting standards in preparation of Shariah-compliant financial reporting. Coupled with this, there are significant concerns about the wider applicability of Islamic accounting standards and framework in order to achieve reporting practices satisfying the information needs generally. Against the backdrop of such a context, this paper raises fundamental question as to how potential convergence could be achieved between these two systems in order to provide users’ a transparent and comparable state of financial information resulting in an alternative framework of financial reporting.

Keywords: Accounting, Islamic accounting, conventional accounting, corporate reporting.

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Authors: Yingjie Zhang

Abstract:

This paper is concerned with an improved algorithm based on the piecewise-smooth Mumford and Shah (MS) functional for an efficient and reliable segmentation. In order to speed up convergence, an additional force, at each time step, is introduced further to drive the evolution of the curves instead of only driven by the extensions of the complementary functions u + and u - . In our scheme, furthermore, the piecewise-constant MS functional is integrated to generate the extra force based on a temporary image that is dynamically created by computing the union of u + and u - during segmenting. Therefore, some drawbacks of the original algorithm, such as smaller objects generated by noise and local minimal problem also are eliminated or improved. The resulting algorithm has been implemented in Matlab and Visual Cµ, and demonstrated efficiently by several cases.

Keywords: Active contours, energy minimization, image segmentation, level sets.

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Authors: Maria C. Mariani, Md Al Masum Bhuiyan, Osei K. Tweneboah, Hector G. Huizar

Abstract:

This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.

Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model.

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Authors: Z. Zainuddin, W. D. Wan Rosli, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulping problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified odified problem M-1 Ax= M-1b where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, pulping modeling, neural networks, preconditioned conjugate gradient.

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Authors: Gilberto Gonzalez-A, Gerardo Jaimes-A

Abstract:

A methodology to design a nonlinear observer in a bond graph approach is proposed. The class of nonlinear observer with multivariable nonlinearities is considered. A junction structure of the bond graph observer is proposed. The proposed methodology to an electrical transformer and a DC motor including the nonlinear saturation is applied. Nonlinear observers for the transformer and DC motor based on multivariable circle criterion in the physical domain are proposed. In order to show the saturation effects on the transformer and DC motor, simulation results are obtained. Finally, the paper describes that convergence of the estimates to the true states is achieved.

Keywords: Bond graph, nonlinear observer, electrical transformer, nonlinear saturation

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Authors: W. D. Wan Rosli, Z. Zainuddin, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, Modeling, Neural Networks, Preconditioned Conjugate Gradient.

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Authors: R. Haoui

Abstract:

The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.

Keywords: Launchers, supersonic flow, finite volume, nozzles, shock wave.

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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.

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Authors: Mazidah Tajjudin, Norhashim Mohd Arshad, Ramli Adnan

Abstract:

Fractional-order controller was proven to perform better than the integer-order controller. However, the absence of a pole at origin produced marginal error in fractional-order control system. This study demonstrated the enhancement of the fractionalorder PI over the integer-order PI in a steam temperature control. The fractional-order controller was cascaded with an error compensator comprised of a very small zero and a pole at origin to produce a zero steady-state error for the closed-loop system. Some modification on the error compensator was suggested for different order fractional integrator that can improve the overall phase margin.

Keywords: Fractional-order PI, Ziegler-Nichols tuning, Oustaloup's Recursive Approximation, steam temperature control.

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Authors: Wen Zhang

Abstract:

The smartphone plays a significant role in media convergence, and smartphone photography is reconstructing the way we communicate and think. This article aims to explore the smartphone photography practices of urban Chinese smartphone users and images produced by smartphones from a techno-cultural perspective. The analysis consists of two types of data: One is a semi-structured interview of 21 participants, and the other consists of the images created by the participants. The findings are organised in two parts. The first part summarises the current tendencies of capturing, editing, sharing and archiving digital images via smartphones. The second part shows that food and selfie/anti-selfie are the preferred subjects of smartphone photographic images from a technical and multi-purpose perspective and demonstrates that screenshots and image texts are new genres of non-photographic images that are frequently made by smartphones, which contributes to improving operational efficiency, disseminating information and sharing knowledge. The analyses illustrate the positive impacts between smartphones and photography enthusiasm and practices based on the diffusion of innovation theory, which also makes us rethink the value of photographs and the practice of ‘photographic seeing’ from the screen itself.

Keywords: Digital photography, photographic-seeing, media convergence, technological innovation, smartphone, selfie/anti-selfie, image-text.

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Authors: M. A. Talha, M. Osman Gani, M. Ferdows

Abstract:

This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number P_r, magnetic field parameter M, Peclet number P_e, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

Keywords: Convection flow, internal heat generation, similarity, spectral method, numerical analysis, Williamson nanofluid.

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Authors: K. Vijayalakshmi, S. Radhakrishnan

Abstract:

In this paper we have proposed a novel dynamic least cost multicast routing protocol using hybrid genetic algorithm for IP networks. Our protocol finds the multicast tree with minimum cost subject to delay, degree, and bandwidth constraints. The proposed protocol has the following features: i. Heuristic local search function has been devised and embedded with normal genetic operation to increase the speed and to get the optimized tree, ii. It is efficient to handle the dynamic situation arises due to either change in the multicast group membership or node / link failure, iii. Two different crossover and mutation probabilities have been used for maintaining the diversity of solution and quick convergence. The simulation results have shown that our proposed protocol generates dynamic multicast tree with lower cost. Results have also shown that the proposed algorithm has better convergence rate, better dynamic request success rate and less execution time than other existing algorithms. Effects of degree and delay constraints have also been analyzed for the multicast tree interns of search success rate.

Keywords: Dynamic Group membership change, Hybrid Genetic Algorithm, Link / node failure, QoS Parameters.

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Authors: Dylan M. Copeland

Abstract:

We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: Sanjay Kumar Parjapati, Ajai Jain

Abstract:

This paper presents optimization of makespan for ‘n’ jobs and ‘m’ machines flexible job shop scheduling problem with sequence dependent setup time using genetic algorithm (GA) approach. A restart scheme has also been applied to prevent the premature convergence. Two case studies are taken into consideration. Results are obtained by considering crossover probability (pc = 0.85) and mutation probability (pm = 0.15). Five simulation runs for each case study are taken and minimum value among them is taken as optimal makespan. Results indicate that optimal makespan can be achieved with more than one sequence of jobs in a production order.

Keywords: Flexible Job Shop, Genetic Algorithm, Makespan, Sequence Dependent Setup Times.

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Authors: U. C. Amadi, N. A. Udoh

Abstract:

One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.

Keywords: Ying Buzu Shu, nonlinear boundary problem, Taylor series algorithm, infinite series.

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Authors: Aissam Belghiat, Mustapha Bourahla

Abstract:

Models are placed by modeling paradigm at the center of development process. These models are represented by languages, like UML the language standardized by the OMG which became necessary for development. Moreover the ontology engineering paradigm places ontologies at the center of development process; in this paradigm we find OWL the principal language for knowledge representation. Building ontologies from scratch is generally a difficult task. The bridging between UML and OWL appeared on several regards such as the classes and associations. In this paper, we have to profit from convergence between UML and OWL to propose an approach based on Meta-Modelling and Graph Grammars and registered in the MDA architecture for the automatic generation of OWL ontologies from UML class diagrams. The transformation is based on transformation rules; the level of abstraction in these rules is close to the application in order to have usable ontologies. We illustrate this approach by an example.

Keywords: ATOM3, MDA, Ontology, OWL, UML

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Authors: Houda Abadlia, Nadia Smairi, Khaled Ghedira

Abstract:

Multiobjective Particle Swarm Optimization (MOPSO) has shown an effective performance for solving test functions and real-world optimization problems. However, this method has a premature convergence problem, which may lead to lack of diversity. In order to improve its performance, this paper presents a hybrid approach which embedded the MOPSO into the island model and integrated a local search technique, Variable Neighborhood Search, to enhance the diversity into the swarm. Experiments on two series of test functions have shown the effectiveness of the proposed approach. A comparison with other evolutionary algorithms shows that the proposed approach presented a good performance in solving multiobjective optimization problems.

Keywords: Particle swarm optimization, migration, variable neighborhood search, multiobjective optimization.

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Authors: Ghada Badr, Manar Hosny, Nuha Bintayyash, Eman Albilali, Souad Larabi Marie-Sainte

Abstract:

The median problem is significantly applied to derive the most reasonable rearrangement phylogenetic tree for many species. More specifically, the problem is concerned with finding a permutation that minimizes the sum of distances between itself and a set of three signed permutations. Genomes with equal number of genes but different order can be represented as permutations. In this paper, an algorithm, namely BeamGA median, is proposed that combines a heuristic search approach (local beam) as an initialization step to generate a number of solutions, and then a Genetic Algorithm (GA) is applied in order to refine the solutions, aiming to achieve a better median with the smallest possible reversal distance from the three original permutations. In this approach, any genome rearrangement distance can be applied. In this paper, we use the reversal distance. To the best of our knowledge, the proposed approach was not applied before for solving the median problem. Our approach considers true biological evolution scenario by applying the concept of common intervals during the GA optimization process. This allows us to imitate a true biological behavior and enhance genetic approach time convergence. We were able to handle permutations with a large number of genes, within an acceptable time performance and with same or better accuracy as compared to existing algorithms.

Keywords: Median problem, phylogenetic tree, permutation, genetic algorithm, beam search, genome rearrangement distance.

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Authors: Juhee Lee, Yongjun Lee

Abstract:

In designing a low-energy-consuming buildings, the heat transfer through a large glass or wall becomes critical. Multiple layers of the window glasses and walls are employed for the high insulation. The gravity driven air flow between window glasses or wall layers is a natural heat convection phenomenon being a key of the heat transfer. For the first step of the natural heat transfer analysis, in this study the development and application of a finite volume method for the numerical computation of viscous incompressible flows is presented. It will become a part of the natural convection analysis with high-order scheme, multi-grid method, and dual-time step in the future. A finite volume method based on a fully-implicit second-order is used to discretize and solve the fluid flow on unstructured grids composed of arbitrary-shaped cells. The integrations of the governing equation are discretised in the finite volume manner using a collocated arrangement of variables. The convergence of the SIMPLE segregated algorithm for the solution of the coupled nonlinear algebraic equations is accelerated by using a sparse matrix solver such as BiCGSTAB. The method used in the present study is verified by applying it to some flows for which either the numerical solution is known or the solution can be obtained using another numerical technique available in the other researches. The accuracy of the method is assessed through the grid refinement.

Keywords: Finite volume method, fluid flow, laminar flow, unstructured grid.

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Authors: Xin Luo, Jin Huang, Pan Cheng

Abstract:

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

Keywords: Stokes problem, boundary integral equation, mechanical quadrature methods, asymptotic expansions.

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Authors: Santosh Kr. Choudhary

Abstract:

In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.

Keywords: Fractional order calculus, fractional order controller, fractional order system, ball and beam system, PIλDμ controller, modelling, simulation.

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