Search results for: NP-Hard problems.
2368 Haar wavelet Method for Solving Initial and Boundary Value Problems of Bratu-type
Authors: S.G.Venkatesh, S.K.Ayyaswamy, G.Hariharan
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In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.
Keywords: Haar wavelet method, Bratu's problem, boundary value problems, initial value problems, adomain decomposition method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29642367 A New Design Partially Blind Signature Scheme Based on Two Hard Mathematical Problems
Authors: Nedal Tahat
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Recently, many existing partially blind signature scheme based on a single hard problem such as factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. However sooner or later these systems will become broken and vulnerable, if the factoring or discrete logarithms problems are cracked. This paper proposes a secured partially blind signature scheme based on factoring (FAC) problem and elliptic curve discrete logarithms (ECDL) problem. As the proposed scheme is focused on factoring and ECDLP hard problems, it has a solid structure and will totally leave the intruder bemused because it is very unlikely to solve the two hard problems simultaneously. In order to assess the security level of the proposed scheme a performance analysis has been conducted. Results have proved that the proposed scheme effectively deals with the partial blindness, randomization, unlinkability and unforgeability properties. Apart from this we have also investigated the computation cost of the proposed scheme. The new proposed scheme is robust and it is difficult for the malevolent attacks to break our scheme.
Keywords: Cryptography, Partially Blind Signature, Factoring, Elliptic Curve Discrete Logarithms.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17692366 The Basic Problems for the Realization of the Concept of Economic Policy
Authors: R. Gvelesiani, I. Gogorishvili
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The concept of economic policy and the practical economic policy diverge from each other at a certain stage of development. This is related to the concept of realization of the underlying problems. It comes with all the problems emerged in the market oriented economic order due to the political processes based on social welfare policy. The realization of the concept of economic policy is impeded by economic and political obstacles. If you want to fill the appeared between the concept and reality, it is necessary to identify and avoid these obstacles. It requires the following: increase of the level of the knowledge of prevention technology in understanding of economic relations, as well as political aspects of the formation of ideas; perfection of economic policy toolkit, and political methods. It is necessary to realize what is the main precondition of implementation and further development of the concept of economic policy, as well as the formation of opinions about economic and public safety. This is a broad consensus on the basic values of the content and the scale of action, which the general public wants to be realized.Keywords: Economic Policy, Basic Problems, Social Welfare Policy.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12712365 Problems Occurring in the Process of Audit by Taking into Consideration their Theoretic Aspects against the Background of Reforms Conducted in a Country: The Example of Georgia
Authors: Levan Sabauri
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The purpose of this article is an examination of the meaning of theoretic aspects of audit in the context of solving of specific problems of the audit. The audit’s aim is the estimation of financial statements by the auditor, i.e. if they are prepared according to the basic requirements of current financial statements. By examination of concrete examples, we can clearly see problems created in an audit and in often cases, those contradictions which can be caused by incompliance of matters regulated by legislation and by reality. An important part of this work is the analysis of reform in the direction of business accounting, statements and audit in Georgia and its comparison with EU countries. In the article, attention is concentrated on the analysis of specific problems of auditing practice and ways of their solving by taking into consideration theoretical aspects of the audit are proposed.
Keywords: Audit, auditor, auditor’s ethic code, auditor’s risk, financial statement, objectivity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8122364 On a New Inverse Polynomial Numerical Scheme for the Solution of Initial Value Problems in Ordinary Differential Equations
Authors: R. B. Ogunrinde
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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.Keywords: Differential equations, Numerical, Initial value problem, Polynomials.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17712363 Adaptation of Iterative Methods to Solve Fuzzy Mathematical Programming Problems
Authors: Ricardo C. Silva, Luiza A. P. Cantao, Akebo Yamakami
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Based on the fuzzy set theory this work develops two adaptations of iterative methods that solve mathematical programming problems with uncertainties in the objective function and in the set of constraints. The first one uses the approach proposed by Zimmermann to fuzzy linear programming problems as a basis and the second one obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. We outline similarities between the two iterative methods studied. Selected examples from the literature are presented to validate the efficiency of the methods addressed.Keywords: Fuzzy Theory, Nonlinear Optimization, Fuzzy Mathematics Programming.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16222362 Positive Solutions for a Class of Semipositone Discrete Boundary Value Problems with Two Parameters
Authors: Benshi Zhu
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In this paper, the existence, multiplicity and noexistence of positive solutions for a class of semipositone discrete boundary value problems with two parameters is studied by applying nonsmooth critical point theory and sub-super solutions method.Keywords: Discrete boundary value problems, nonsmoothcritical point theory, positive solutions, semipositone, sub-super solutions method
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13422361 A Family of Distributions on Learnable Problems without Uniform Convergence
Authors: César Garza
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In supervised binary classification and regression problems, it is well-known that learnability is equivalent to uniform convergence of the hypothesis class, and if a problem is learnable, it is learnable by empirical risk minimization. For the general learning setting of unsupervised learning tasks, there are non-trivial learning problems where uniform convergence does not hold. We present here the task of learning centers of mass with an extra feature that “activates” some of the coordinates over the unit ball in a Hilbert space. We show that the learning problem is learnable under a stable RLM rule. We introduce a family of distributions over the domain space with some mild restrictions for which the sample complexity of uniform convergence for these problems must grow logarithmically with the dimension of the Hilbert space. If we take this dimension to infinity, we obtain a learnable problem for which the uniform convergence property fails for a vast family of distributions.
Keywords: Statistical learning theory, learnability, uniform convergence, stability, regularized loss minimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3522360 AGENTMAP: A Conceptual Meta-Model of Interacting Simulations
Authors: Thomas M. Prinz Wilhelm R. Rossak, Kai Gebhardt
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A straightforward and intuitive combination of single simulations into an aggregated master-simulation is not trivial. There are lots of problems, which trigger-specific difficulties during the modeling and execution of such a simulation. In this paper we identify these problems and aim to solve them by mapping the task to the field of multi agent systems. The solution is a new meta-model named AGENTMAP, which is able to mitigate most of the problems and to support intuitive modeling at the same time. This meta-model will be introduced and explained on basis of an example from the e-commerce domain.
Keywords: Multi Agent System, Agent-based Simulation, Distributed Systems, Meta-models.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18772359 Multi-Criteria Based Robust Markowitz Model under Box Uncertainty
Authors: Pulak Swain, A. K. Ojha
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Portfolio optimization is based on dealing with the problems of efficient asset allocation. Risk and Expected return are two conflicting criteria in such problems, where the investor prefers the return to be high and the risk to be low. Using multi-objective approach we can solve those type of problems. However the information which we have for the input parameters are generally ambiguous and the input values can fluctuate around some nominal values. We can not ignore the uncertainty in input values, as they can affect the asset allocation drastically. So we use Robust Optimization approach to the problems where the input parameters comes under box uncertainty. In this paper, we solve the multi criteria robust problem with the help of E- constraint method.Keywords: Portfolio optimization, multi-objective optimization, E-constraint method, box uncertainty, robust optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6162358 Positive Solutions for Semipositone Discrete Eigenvalue Problems via Three Critical Points Theorem
Authors: Benshi Zhu
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In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional.Keywords: Discrete eigenvalue problems, positive solutions, semipositone, three critical points theorem
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12532357 Computational Networks for Knowledge Representation
Authors: Nhon Van Do
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In the artificial intelligence field, knowledge representation and reasoning are important areas for intelligent systems, especially knowledge base systems and expert systems. Knowledge representation Methods has an important role in designing the systems. There have been many models for knowledge such as semantic networks, conceptual graphs, and neural networks. These models are useful tools to design intelligent systems. However, they are not suitable to represent knowledge in the domains of reality applications. In this paper, new models for knowledge representation called computational networks will be presented. They have been used in designing some knowledge base systems in education for solving problems such as the system that supports studying knowledge and solving analytic geometry problems, the program for studying and solving problems in Plane Geometry, the program for solving problems about alternating current in physics.Keywords: Artificial intelligence, artificial intelligence and education, knowledge engineering, knowledge representation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22172356 Security Analysis on Anonymous Mutual Authentication Protocol for RFID Tag without Back-End Database and its Improvement
Authors: Songyi Kim, Kwangwoo Lee, Seungjoo Kim, Dongho Won
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RFID (Radio Frequency IDentification) system has been widely used in our life, such as transport systems, passports, automotive, animal tracking, human implants, library, and so on. However, the RFID authentication protocols between RF (Radio Frequency) tags and the RF readers have been bring about various privacy problems that anonymity of the tags, tracking, eavesdropping, and so on. Many researchers have proposed the solution of the problems. However, they still have the problem, such as location privacy, mutual authentication. In this paper, we show the problems of the previous protocols, and then we propose a more secure and efficient RFID authentication protocol.Keywords: RFID, mutual authentication, serverless, anonymity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19312355 An Ontology for Knowledge Representation and Applications
Authors: Nhon Do
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Ontology is a terminology which is used in artificial intelligence with different meanings. Ontology researching has an important role in computer science and practical applications, especially distributed knowledge systems. In this paper we present an ontology which is called Computational Object Knowledge Base Ontology. It has been used in designing some knowledge base systems for solving problems such as the system that supports studying knowledge and solving analytic geometry problems, the program for studying and solving problems in Plane Geometry, the knowledge system in linear algebra.Keywords: Artificial intelligence, knowledge representation, knowledge base system, ontology.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21582354 Work Structuring and the Feasibility of Application to Construction Projects in Vietnam
Authors: Viet-Hung Nguyen, Luh-Maan Chang
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Design should be viewed concurrently by three ways as transformation, flow and value generation. An innovative approach to solve design – related problems is described as the integrated product - process design. As a foundation for a formal framework consisting of organizing principles and techniques, Work Structuring has been developed to guide efforts in the integration that enhances the development of operation and process design in alignment with product design. Vietnam construction projects are facing many delays, and cost overruns caused mostly by design related problems. A better design management that integrates product and process design could resolve these problems. A questionnaire survey and in – depth interviews were used to investigate the feasibility of applying Work Structuring to construction projects in Vietnam. The purpose of this paper is to present the research results and to illustrate the possible problems and potential solutions when Work Structuring is implemented to construction projects in Vietnam.Keywords: integrated product – process design, Work Structuring, construction projects, Vietnam
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16902353 A Modified Decoupled Semi-Analytical Approach Based On SBFEM for Solving 2D Elastodynamic Problems
Authors: M. Fakharian, M. I. Khodakarami
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In this paper, a new trend for improvement in semianalytical method based on scale boundaries in order to solve the 2D elastodynamic problems is provided. In this regard, only the boundaries of the problem domain discretization are by specific subparametric elements. Mapping functions are uses as a class of higherorder Lagrange polynomials, special shape functions, Gauss-Lobatto- Legendre numerical integration, and the integral form of the weighted residual method, the matrix is diagonal coefficients in the equations of elastodynamic issues. Differences between study conducted and prior research in this paper is in geometry production procedure of the interpolation function and integration of the different is selected. Validity and accuracy of the present method are fully demonstrated through two benchmark problems which are successfully modeled using a few numbers of DOFs. The numerical results agree very well with the analytical solutions and the results from other numerical methods.
Keywords: 2D Elastodynamic Problems, Lagrange Polynomials, G-L-Lquadrature, Decoupled SBFEM.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19832352 The Design of Self-evolving Artificial Immune System II for Permutation Flow-shop Problem
Authors: Meng-Hui Chen, Pei-Chann Chang, Wei-Hsiu Huang
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Artificial Immune System is adopted as a Heuristic Algorithm to solve the combinatorial problems for decades. Nevertheless, many of these applications took advantage of the benefit for applications but seldom proposed approaches for enhancing the efficiency. In this paper, we continue the previous research to develop a Self-evolving Artificial Immune System II via coordinating the T and B cell in Immune System and built a block-based artificial chromosome for speeding up the computation time and better performance for different complexities of problems. Through the design of Plasma cell and clonal selection which are relative the function of the Immune Response. The Immune Response will help the AIS have the global and local searching ability and preventing trapped in local optima. From the experimental result, the significant performance validates the SEAIS II is effective when solving the permutation flows-hop problems.Keywords: Artificial Immune System, Clonal Selection, Immune Response, Permutation Flow-shop Scheduling Problems
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16062351 Numerical Computation of Sturm-Liouville Problem with Robin Boundary Condition
Authors: Theddeus T. Akano, Omotayo A. Fakinlede
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The modelling of physical phenomena, such as the earth’s free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm- Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solution of classical Sturm–Liouville problem is presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.Keywords: Sturm-Liouville problem, Robin boundary condition, finite element method, eigenvalue problems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29942350 Method for Solving Fully Fuzzy Assignment Problems Using Triangular Fuzzy Numbers
Authors: Amit Kumar, Anila Gupta, Amarpreet Kaur
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In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.
Keywords: Fuzzy assignment problem, Ranking function, Triangular fuzzy numbers.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16952349 Solving Fuzzy Multi-Objective Linear Programming Problems with Fuzzy Decision Variables
Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi
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In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.Keywords: Fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14132348 Solution Approaches for Some Scheduling Problems with Learning Effect and Job Dependent Delivery Times
Authors: M. Duran Toksarı, B. Uçarkuş
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In this paper, we propose two algorithms to optimally solve makespan and total completion time scheduling problems with learning effect and job dependent delivery times in a single machine environment. The delivery time is the extra time to eliminate adverse effect between the main processing and delivery to the customer. In this paper, we introduce the job dependent delivery times for some single machine scheduling problems with position dependent learning effect, which are makespan are total completion. The results with respect to two algorithms proposed for solving of the each problem are compared with LINGO solutions for 50-jobs, 100-jobs and 150- jobs problems. The proposed algorithms can find the same results in shorter time.Keywords: Delivery times, learning effect, makespan, scheduling, total completion time.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15502347 Research on Laws and Regulations of Sustainable Construction in China
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This paper introduced the status quo of laws and regulations of sustainable construction in China and investigated the existing problems of current laws and regulations through person-interviews in Beijing, Shanghai, Chongqing and Shenzhen in China. The problems include incomplete legal system, lack of guidance of higher-level laws, backward in some laws and regulations, unclear legal liability and poor law enforcement. Aimed at these problems, this paper also put forward some improvement approaches, such as filling the legal gap, revising laws and regulations, establishing incentive system and keeping pace with level of development.Keywords: Improvement, laws and regulations, status quo, sustainable construction
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23362346 Recognition-based Segmentation in Persian Character Recognition
Authors: Mohsen Zand, Ahmadreza Naghsh Nilchi, S. Amirhassan Monadjemi
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Optical character recognition of cursive scripts presents a number of challenging problems in both segmentation and recognition processes in different languages, including Persian. In order to overcome these problems, we use a newly developed Persian word segmentation method and a recognition-based segmentation technique to overcome its segmentation problems. This method is robust as well as flexible. It also increases the system-s tolerances to font variations. The implementation results of this method on a comprehensive database show a high degree of accuracy which meets the requirements for commercial use. Extended with a suitable pre and post-processing, the method offers a simple and fast framework to develop a full OCR system.Keywords: OCR, Persian, Recognition, Segmentation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18392345 Potential of GIS to Find Solutions to Space Related Problems in Construction Industry
Authors: V. K. Bansal
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Geographic Information System (GIS) is a computerbased tool used extensively to solve various engineering problems related to spatial data. In spite of growing popularity of GIS, its complete potential to construction industry has not been realized. In this paper, the summary of up-to-date work on spatial applications of GIS technologies in construction industry is presented. GIS technologies have the potential to solve space related problems of construction industry involving complex visualization, integration of information, route planning, E-commerce, cost estimation, etc. GISbased methodology to handle time and space issues of construction projects scheduling is developed and discussed in this paper.Keywords: Construction, GIS in construction, Scheduling, Project Management.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26632344 The Effect of Smartphones on Human Health Relative to User’s Addiction: A Study on a Wide Range of Audiences in Jordan
Authors: T. Qasim, M. Obeidat, S. Al-Sharairi
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The objective of this study is to investigate the effect of the excessive use of smartphones. Smartphones have enormous effects on the human body in that some musculoskeletal disorders (MSDs) and health problems might evolve. These days, there is a wide use of the smartphones among all age groups of society, thus, the focus on smartphone effects on human behavior and health, especially on the young and elderly people, becomes a crucial issue. This study was conducted in Jordan on smartphone users for different genders and ages, by conducting a survey to collect data related to the symptoms and MSDs that are resulted from the excessive use of smartphones. A total of 357 responses were used in the analysis. The main related symptoms were numbness, fingers pain, and pain in arm, all linked to age and gender for comparative reasons. A statistical analysis was performed to find the effects of extensive usage of a smartphone for long periods of time on the human body. Results show that the significant variables were the vision problems and the time spent when using the smartphone that cause vision problems. Other variables including age of user and ear problems due to the use of the headsets were found to be a border line significant.Keywords: Smartphone, age group, musculoskeletal disorders (MSDs), health problems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20482343 Solving the Quadratic Assignment Problems by a Genetic Algorithm with a New Replacement Strategy
Authors: Yongzhong Wu, Ping Ji
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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.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 27452342 Universal Method for Timetable Construction based on Evolutionary Approach
Authors: Maciej Norberciak
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Timetabling problems are often hard and timeconsuming to solve. Most of the methods of solving them concern only one problem instance or class. This paper describes a universal method for solving large, highly constrained timetabling problems from different domains. The solution is based on evolutionary algorithm-s framework and operates on two levels – first-level evolutionary algorithm tries to find a solution basing on given set of operating parameters, second-level algorithm is used to establish those parameters. Tabu search is employed to speed up the solution finding process on first level. The method has been used to solve three different timetabling problems with promising results.Keywords: Evolutionary algorithms, tabu search, timetabling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18402341 Generalized Stokes’ Problems for an Incompressible Couple Stress Fluid
Authors: M.Devakar, T.K.V.Iyengar
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In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest.
Keywords: Couple stress fluid, Generalized Stokes’ problems, Laplace transform, Numerical inversion
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 32372340 Problems and Possible Solutions with the Development of a Computer Model of Quantum Theory
Authors: Hans H. Diel
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A computer model of Quantum Theory (QT) has been developed by the author. Major goal of the computer model was support and demonstration of an as large as possible scope of QT. This includes simulations for the major QT (Gedanken-) experiments such as, for example, the famous double-slit experiment. Besides the anticipated difficulties with (1) transforming exacting mathematics into a computer program, two further types of problems showed up, namely (2) areas where QT provides a complete mathematical formalism, but when it comes to concrete applications the equations are not solvable at all, or only with extremely high effort; (3) QT rules which are formulated in natural language and which do not seem to be translatable to precise mathematical expressions, nor to a computer program. The paper lists problems in all three categories and describes also the possible solutions or circumventions developed for the computer model.Keywords: Computability, Foundation of Quantum Mechanics, Measurement Process, Modeling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17012339 Embedded Singly Diagonally Implicit Runge-Kutta –Nystrom Method Order 5(4) for the Integration of Special Second Order ODEs
Authors: Fudziah Ismail
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In this paper a new embedded Singly Diagonally Implicit Runge-Kutta Nystrom fourth order in fifth order method for solving special second order initial value problems is derived. A standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first order systems and solved using the existing embedded diagonally implicit Runge-Kutta method. The results suggests the superiority of the new method.Keywords: Runge-Kutta Nystrom, Special second orderproblems.
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