Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 282

Search results for: programming

282 CScheme in Traditional Concurrency Problems

Authors: Nathar Shah, Visham Cheerkoot

Abstract:

CScheme, a concurrent programming paradigm based on scheme concept enables concurrency schemes to be constructed from smaller synchronization units through a GUI based composer and latter be reused on other concurrency problems of a similar nature. This paradigm is particularly important in the multi-core environment prevalent nowadays. In this paper, we demonstrate techniques to separate concurrency from functional code using the CScheme paradigm. Then we illustrate how the CScheme methodology can be used to solve some of the traditional concurrency problems – critical section problem, and readers-writers problem - using synchronization schemes such as Single Threaded Execution Scheme, and Readers Writers Scheme.

Keywords: Concurrent Programming, Object Oriented Programming, Environments for multiple-processor systems, Programming paradigms.

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281 Understanding the Programming Techniques Using a Complex Case Study to Teach Advanced Object-Oriented Programming

Authors: M. Al-Jepoori, D. Bennett

Abstract:

Teaching Object-Oriented Programming (OOP) as part of a Computing-related university degree is a very difficult task; the road to ensuring that students are actually learning object oriented concepts is unclear, as students often find it difficult to understand the concept of objects and their behavior. This problem is especially obvious in advanced programming modules where Design Pattern and advanced programming features such as Multi-threading and animated GUI are introduced. Looking at the students’ performance at their final year on a university course, it was obvious that the level of students’ understanding of OOP varies to a high degree from one student to another. Students who aim at the production of Games do very well in the advanced programming module. However, the students’ assessment results of the last few years were relatively low; for example, in 2016-2017, the first quartile of marks were as low as 24.5 and the third quartile was 63.5. It is obvious that many students were not confident or competent enough in their programming skills. In this paper, the reasons behind poor performance in Advanced OOP modules are investigated, and a suggested practice for teaching OOP based on a complex case study is described and evaluated.

Keywords: Complex programming case study, design pattern, learning advanced programming, object oriented programming.

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280 Programming Aid Tool for Detecting Common Mistakes of Novice Programmers in OpenMP Code

Authors: Jae Young Park, Seung Wook Lee, Jong Tae Kim

Abstract:

OpenMP is an API for parallel programming model of shared memory multiprocessors. Novice OpenMP programmers often produce the code that compiler cannot find human errors. It was investigated how compiler coped with the common mistakes that can occur in OpenMP code. The latest version(4.4.3) of GCC is used for this research. It was found that GCC compiled the codes without any errors or warnings. In this paper the programming aid tool is presented for OpenMP programs. It can check 12 common mistakes that novice programmer can commit during the programming of OpenMP. It was demonstrated that the programming aid tool can detect the various common mistakes that GCC failed to detect.

Keywords: Parallel programming, OpenMP, programming aid.

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279 Mathematical Programming Models for Portfolio Optimization Problem: A Review

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

Abstract:

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

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

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278 A Programming Assessment Software Artefact Enhanced with the Help of Learners

Authors: Romeo A. Botes, Imelda Smit

Abstract:

The demands of an ever changing and complex higher education environment, along with the profile of modern learners challenge current approaches to assessment and feedback. More learners enter the education system every year. The younger generation expects immediate feedback. At the same time, feedback should be meaningful. The assessment of practical activities in programming poses a particular problem, since both lecturers and learners in the information and computer science discipline acknowledge that paper-based assessment for programming subjects lacks meaningful real-life testing. At the same time, feedback lacks promptness, consistency, comprehensiveness and individualisation. Most of these aspects may be addressed by modern, technology-assisted assessment. The focus of this paper is the continuous development of an artefact that is used to assist the lecturer in the assessment and feedback of practical programming activities in a senior database programming class. The artefact was developed using three Design Science Research cycles. The first implementation allowed one programming activity submission per assessment intervention. This pilot provided valuable insight into the obstacles regarding the implementation of this type of assessment tool. A second implementation improved the initial version to allow multiple programming activity submissions per assessment. The focus of this version is on providing scaffold feedback to the learner – allowing improvement with each subsequent submission. It also has a built-in capability to provide the lecturer with information regarding the key problem areas of each assessment intervention.

Keywords: Programming, computer-aided assessment, technology-assisted assessment, programming assessment software, design science research, mixed-method.

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277 On Pattern-Based Programming towards the Discovery of Frequent Patterns

Authors: Kittisak Kerdprasop, Nittaya Kerdprasop

Abstract:

The problem of frequent pattern discovery is defined as the process of searching for patterns such as sets of features or items that appear in data frequently. Finding such frequent patterns has become an important data mining task because it reveals associations, correlations, and many other interesting relationships hidden in a database. Most of the proposed frequent pattern mining algorithms have been implemented with imperative programming languages. Such paradigm is inefficient when set of patterns is large and the frequent pattern is long. We suggest a high-level declarative style of programming apply to the problem of frequent pattern discovery. We consider two languages: Haskell and Prolog. Our intuitive idea is that the problem of finding frequent patterns should be efficiently and concisely implemented via a declarative paradigm since pattern matching is a fundamental feature supported by most functional languages and Prolog. Our frequent pattern mining implementation using the Haskell and Prolog languages confirms our hypothesis about conciseness of the program. The comparative performance studies on line-of-code, speed and memory usage of declarative versus imperative programming have been reported in the paper.

Keywords: Frequent pattern mining, functional programming, pattern matching, logic programming.

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276 Evaluation of Introductory Programming Course for Non-Computer Science Majored Students

Authors: H. Varol

Abstract:

Although students’ interest level in pursuing Computer Science and related degrees are lower than previous decade, fundamentals of computers, specifically introductory level programming courses are either listed as core or elective courses for a number of non-computer science majors. Universities accommodate these non-computer science majored students either via creating separate sections of a class for them or simply offering mixed-body classroom solutions, in which both computer science and non-computer science students take the courses together. In this work, we demonstrated how we handle introductory level programming course at Sam Houston State University and also provide facts about our observations on students’ success during the coursework. Moreover, we provide suggestions and methodologies that are based on students’ major and skills to overcome the deficiencies of mix-body type of classes.

Keywords: Computer science, non-computer science major, programming, programming education.

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275 Making Data Structures and Algorithms more Understandable by Programming Sudoku the Human Way

Authors: Roelien Goede

Abstract:

Data Structures and Algorithms is a module in most Computer Science or Information Technology curricula. It is one of the modules most students identify as being difficult. This paper demonstrates how programming a solution for Sudoku can make abstract concepts more concrete. The paper relates concepts of a typical Data Structures and Algorithms module to a step by step solution for Sudoku in a human type as opposed to a computer oriented solution.

Keywords: Data Structures, Algorithms, Sudoku, ObjectOriented Programming, Programming Teaching, Education.

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274 Production Plan and Technological Variants Optimization by Goal Programming Methods

Authors: Tunjo Perić, Franjo Bratić

Abstract:

In this paper, the goal programming methodology for solving multiple objective problem of the technological variants and production plan optimization has been applied. The optimization criteria are determined and the multiple objective linear programming model for solving a problem of the technological variants and production plan optimization is formed and solved. Then the obtained results are analysed. The obtained results point out to the possibility of efficient application of the goal programming methodology in solving the problem of the technological variants and production plan optimization. The paper points out on the advantages of the application of the goal programming methodology compare to the Surrogat Worth Trade-off method in solving this problem.

Keywords: Goal programming, multi objective programming, production plan, SWT method, technological variants.

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273 Simulation and 40 Years of Object-Oriented Programming

Authors: Eugene Kindler

Abstract:

2007 is a jubilee year: in 1967, programming language SIMULA 67 was presented, which contained all aspects of what was later called object-oriented programming. The present paper contains a description of the development unto the objectoriented programming, the role of simulation in this development and other tools that appeared in SIMULA 67 and that are nowadays called super-object-oriented programming.

Keywords: Simulation, super-object-oriented programming, object-oriented programming, SIMULA.

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272 Comparative Survey of Object Serialization Techniques and the Programming Supports

Authors: Kazuaki Maeda

Abstract:

This paper compares six approaches of object serialization from qualitative and quantitative aspects. Those are object serialization in Java, IDL, XStream, Protocol Buffers, Apache Avro, and MessagePack. Using each approach, a common example is serialized to a file and the size of the file is measured. The qualitative comparison works are investigated in the way of checking whether schema definition is required or not, whether schema compiler is required or not, whether serialization is based on ascii or binary, and which programming languages are supported. It is clear that there is no best solution. Each solution makes good in the context it was developed.

Keywords: structured data, serialization, programming

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271 Modern Method for Solving Pure Integer Programming Models

Authors: G. Shojatalab

Abstract:

In this paper, all variables are supposed to be integer and positive. In this modern method, objective function is assumed to be maximized or minimized but constraints are always explained like less or equal to. In this method, choosing a dual combination of ideal nonequivalent and omitting one of variables. With continuing this act, finally, having one nonequivalent with (n-m+1) unknown quantities in which final nonequivalent, m is counter for constraints, n is counter for variables of decision.

Keywords: Integer, Programming, Operation Research, Variables of decision.

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270 Using Genetic Programming to Evolve a Team of Data Classifiers

Authors: Gregor A. Morrison, Dominic P. Searson, Mark J. Willis

Abstract:

The purpose of this paper is to demonstrate the ability of a genetic programming (GP) algorithm to evolve a team of data classification models. The GP algorithm used in this work is “multigene" in nature, i.e. there are multiple tree structures (genes) that are used to represent team members. Each team member assigns a data sample to one of a fixed set of output classes. A majority vote, determined using the mode (highest occurrence) of classes predicted by the individual genes, is used to determine the final class prediction. The algorithm is tested on a binary classification problem. For the case study investigated, compact classification models are obtained with comparable accuracy to alternative approaches.

Keywords: classification, genetic programming.

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269 Robot Task-Level Programming Language and Simulation

Authors: M. Samaka

Abstract:

This paper presents the development of a software application for Off-line robot task programming and simulation. Such application is designed to assist in robot task planning and to direct manipulator motion on sensor based programmed motion. The concept of the designed programming application is to use the power of the knowledge base for task accumulation. In support of the programming means, an interactive graphical simulation for manipulator kinematics was also developed and integrated into the application as the complimentary factor to the robot programming media. The simulation provides the designer with useful, inexpensive, off-line tools for retain and testing robotics work cells and automated assembly lines for various industrial applications.

Keywords: Robot programming, task-level programming, robot languages, robot simulation, robotics software.

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268 Algorithmic Method for Efficient Cruise Program

Authors: Pelaez Verdet, Antonio, Loscertales Sanchez, Pilar

Abstract:

One of the mayor problems of programming a cruise circuit is to decide which destinations to include and which don-t. Thus a decision problem emerges, that might be solved using a linear and goal programming approach. The problem becomes more complex if several boats in the fleet must be programmed in a limited schedule, trying their capacity matches best a seasonal demand and also attempting to minimize the operation costs. Moreover, the programmer of the company should consider the time of the passenger as a limited asset, and would like to maximize its usage. The aim of this work is to design a method in which, using linear and goal programming techniques, a model to design circuits for the cruise company decision maker can achieve an optimal solution within the fleet schedule.

Keywords: Itinerary design, cruise programming, goalprogramming, linear programming

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267 Using Non-Linear Programming Techniques in Determination of the Most Probable Slip Surface in 3D Slopes

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

Abstract:

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

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

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266 Application of De Novo Programming Approach for Optimizing the Business Process

Authors: Z. Babic, I. Veza, A. Balic, M. Crnjac

Abstract:

The linear programming model is sometimes difficult to apply in real business situations due to its assumption of proportionality. This paper shows an example of how to use De Novo programming approach instead of linear programming. In the De Novo programming, resources are not fixed like in linear programming but resource quantities depend only on available budget. Budget is a new, important element of the De Novo approach. Two different production situations are presented: increasing costs and quantity discounts of raw materials. The focus of this paper is on advantages of the De Novo approach in the optimization of production plan for production company which produces souvenirs made from famous stone from the island of Brac, one of the greatest islands from Croatia.

Keywords: De Novo Programming, production plan, stone souvenirs, variable prices.

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265 Prioritization Method in the Fuzzy Analytic Network Process by Fuzzy Preferences Programming Method

Authors: Tarifa S. Almulhim, Ludmil Mikhailov, Dong-Ling Xu

Abstract:

In this paper, a method for deriving a group priority vector in the Fuzzy Analytic Network Process (FANP) is proposed. By introducing importance weights of multiple decision makers (DMs) based on their experiences, the Fuzzy Preferences Programming Method (FPP) is extended to a fuzzy group prioritization problem in the FANP. Additionally, fuzzy pair-wise comparison judgments are presented rather than exact numerical assessments in order to model the uncertainty and imprecision in the DMs- judgments and then transform the fuzzy group prioritization problem into a fuzzy non-linear programming optimization problem which maximize the group satisfaction. Unlike the known fuzzy prioritization techniques, the new method proposed in this paper can easily derive crisp weights from incomplete and inconsistency fuzzy set of comparison judgments and does not require additional aggregation producers. Detailed numerical examples are used to illustrate the implement of our approach and compare with the latest fuzzy prioritization method.

Keywords: Fuzzy Analytic Network Process (FANP), Fuzzy Non-linear Programming, Fuzzy Preferences Programming Method (FPP), Multiple Criteria Decision-Making (MCDM), Triangular Fuzzy Number.

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264 A Consideration of the Achievement of Productive Level Parallel Programming Skills

Authors: Tadayoshi Horita, Masakazu Akiba, Mina Terauchi, Tsuneo Kanno

Abstract:

This paper gives a consideration of the achievement of productive level parallel programming skills, based on the data of the graduation studies in the Polytechnic University of Japan. The data show that most students can achieve only parallel programming skills during the graduation study (about 600 to 700 hours), if the programming environment is limited to GPGPUs. However, the data also show that it is a very high level task that a student achieves productive level parallel programming skills during only the graduation study. In addition, it shows that the parallel programming environments for GPGPU, such as CUDA and OpenCL, may be more suitable for parallel computing education than other environments such as MPI on a cluster system and Cell.B.E. These results must be useful for the areas of not only software developments, but also hardware product developments using computer technologies.

Keywords: Parallel computing, programming education, GPU, GPGPU, CUDA, OpenCL, MPI, Cell.B.E.

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263 Adaptation of Iterative Methods to Solve Fuzzy Mathematical Programming Problems

Authors: Ricardo C. Silva, Luiza A. P. Cantao, Akebo Yamakami

Abstract:

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.

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262 On Optimum Stratification

Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

Abstract:

In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: Auxiliary variable, Dynamic programming technique, Nonlinear programming problem, Optimum stratification, Uniform distribution.

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261 Stochastic Programming Model for Power Generation

Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

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260 Optimum Stratification of a Skewed Population

Authors: D.K. Rao, M.G.M. Khan, K.G. Reddy

Abstract:

The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries(OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy isskewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB isformulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: Stratified sampling, Optimum strata boundaries, Optimum sample size, Pareto distribution, Mathematical programming problem, Dynamic programming technique.

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259 Use of Linear Programming for Optimal Production in a Production Line in Saudi Food Co.

Authors: Qasim M. Kriri

Abstract:

Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

Keywords: Parameter linear programming, objective function, sensitivity analysis, optimize profit.

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258 Genetic Programming Approach to Hierarchical Production Rule Discovery

Authors: Basheer M. Al-Maqaleh, Kamal K. Bharadwaj

Abstract:

Automated discovery of hierarchical structures in large data sets has been an active research area in the recent past. This paper focuses on the issue of mining generalized rules with crisp hierarchical structure using Genetic Programming (GP) approach to knowledge discovery. The post-processing scheme presented in this work uses flat rules as initial individuals of GP and discovers hierarchical structure. Suitable genetic operators are proposed for the suggested encoding. Based on the Subsumption Matrix(SM), an appropriate fitness function is suggested. Finally, Hierarchical Production Rules (HPRs) are generated from the discovered hierarchy. Experimental results are presented to demonstrate the performance of the proposed algorithm.

Keywords: Genetic Programming, Hierarchy, Knowledge Discovery in Database, Subsumption Matrix.

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257 Determining Optimal Demand Rate and Production Decisions: A Geometric Programming Approach

Authors: Farnaz G. Nezami, Mir B. Aryanezhad, Seyed J. Sadjadi

Abstract:

In this paper a nonlinear model is presented to demonstrate the relation between production and marketing departments. By introducing some functions such as pricing cost and market share loss functions it will be tried to show some aspects of market modelling which has not been regarded before. The proposed model will be a constrained signomial geometric programming model. For model solving, after variables- modifications an iterative technique based on the concept of geometric mean will be introduced to solve the resulting non-standard posynomial model which can be applied to a wide variety of models in non-standard posynomial geometric programming form. At the end a numerical analysis will be presented to accredit the validity of the mentioned model.

Keywords: Geometric programming, marketing, nonlinear optimization, production.

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256 Distortion Estimation in Digital Image Watermarking using Genetic Programming

Authors: Labiba Gilani, Asifullah Khan, Anwar M. Mirza

Abstract:

This paper introduces a technique of distortion estimation in image watermarking using Genetic Programming (GP). The distortion is estimated by considering the problem of obtaining a distorted watermarked signal from the original watermarked signal as a function regression problem. This function regression problem is solved using GP, where the original watermarked signal is considered as an independent variable. GP-based distortion estimation scheme is checked for Gaussian attack and Jpeg compression attack. We have used Gaussian attacks of different strengths by changing the standard deviation. JPEG compression attack is also varied by adding various distortions. Experimental results demonstrate that the proposed technique is able to detect the watermark even in the case of strong distortions and is more robust against attacks.

Keywords: Blind Watermarking, Genetic Programming (GP), Fitness Function, Discrete Cosine Transform (DCT).

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255 Rule-Based Message Passing for Collaborative Application in Distributed Environments

Authors: Wataru Yamazaki, Hironori Hiraishi, Fumio Mizoguchi

Abstract:

In this paper, we describe a rule-based message passing method to support developing collaborative applications, in which multiple users share resources in distributed environments. Message communications of applications in collaborative environments tend to be very complex because of the necessity to manage context situations such as sharing events, access controlling of users, and network places. In this paper, we propose a message communications method based on unification of artificial intelligence and logic programming for defining rules of such context information in a procedural object-oriented programming language. We also present an implementation of the method as java classes.

Keywords: agent programming, logic programming, multi-media application, collaborative application.

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254 Genetic Programming Approach for Multi-Category Pattern Classification Appliedto Network Intrusions Detection

Authors: K.M. Faraoun, A. Boukelif

Abstract:

This paper describes a new approach of classification using genetic programming. The proposed technique consists of genetically coevolving a population of non-linear transformations on the input data to be classified, and map them to a new space with a reduced dimension, in order to get a maximum inter-classes discrimination. The classification of new samples is then performed on the transformed data, and so become much easier. Contrary to the existing GP-classification techniques, the proposed one use a dynamic repartition of the transformed data in separated intervals, the efficacy of a given intervals repartition is handled by the fitness criterion, with a maximum classes discrimination. Experiments were first performed using the Fisher-s Iris dataset, and then, the KDD-99 Cup dataset was used to study the intrusion detection and classification problem. Obtained results demonstrate that the proposed genetic approach outperform the existing GP-classification methods [1],[2] and [3], and give a very accepted results compared to other existing techniques proposed in [4],[5],[6],[7] and [8].

Keywords: Genetic programming, patterns classification, intrusion detection

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253 Stochastic Mixed 0-1 Integer Programming Applied to International Transportation Problems under Uncertainty

Authors: Y. Wu

Abstract:

Today-s business has inevitably been set in the global supply chain management environment. International transportation has never played such an important role in the global supply chain network, because movement of shipments from one country to another tends to be more frequent than ever before. This paper studies international transportation problems experienced by an international transportation company. Because of the limited fleet capacity, the transportation company has to hire additional trucks from two countries in advance. However, customer-s shipment information is uncertain, and decisions have to be made before accurate information can be obtained. This paper proposes a stochastic mixed 0-1 programming model to solve the international transportation problems under uncertain demand. A series of experiments demonstrate the effectiveness of the proposed stochastic model.

Keywords: Global supply chain management, international transportation, stochastic programming.

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