Search results for: bilevel programming
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 938

Search results for: bilevel programming

908 Improving Performance and Progression of Novice Programmers: Factors Considerations

Authors: Hala Shaari, Nuredin Ahmed

Abstract:

Teaching computer programming is recognized to be difficult and a real challenge. The biggest problem faced by novice programmers is their lack of understanding of basic programming concepts. A visualized learning tool was developed and used by volunteered first-year students for two semesters. The purposes of this paper are firstly, to emphasize factors which directly affect the performance of our students negatively. Secondly, to examine whether the proposed tool would improve their performance and learning progression. The results of adopting this tool were conducted using a pre-survey and post-survey questionnaire. As a result, students who used the learning tool showed better performance in their programming subject.

Keywords: factors, novice, programming, visualization

Procedia PDF Downloads 363
907 An Optimization Model for Maximum Clique Problem Based on Semidefinite Programming

Authors: Derkaoui Orkia, Lehireche Ahmed

Abstract:

The topic of this article is to exploring the potentialities of a powerful optimization technique, namely Semidefinite Programming, for solving NP-hard problems. This approach provides tight relaxations of combinatorial and quadratic problems. In this work, we solve the maximum clique problem using this relaxation. The clique problem is the computational problem of finding cliques in a graph. It is widely acknowledged for its many applications in real-world problems. The numerical results show that it is possible to find a maximum clique in polynomial time, using an algorithm based on semidefinite programming. We implement a primal-dual interior points algorithm to solve this problem based on semidefinite programming. The semidefinite relaxation of this problem can be solved in polynomial time.

Keywords: semidefinite programming, maximum clique problem, primal-dual interior point method, relaxation

Procedia PDF Downloads 223
906 Design Of An Arduino Shield For New Generation Microcontroller Training

Authors: Boubacar Niang, Denis Raulin

Abstract:

This paper presents the design of a dedicated board for learning and programming with ATMEL AVR new generation micro controller’s family. This board designed as a "shield" for the Arduino Uno allows us to focus on the design and programming of basic micro controller functionalities in high level language with a considerable time saving because of dealing with additional components is not required.

Keywords: Arduino, microcontroller, programming, language

Procedia PDF Downloads 584
905 Modeling Revolution Shell Structures by MATLAB Programming-Axisymmetric and Nonaxisymmetric Shells

Authors: Hamadi Djamal, Labiodh Bachir, Ounis Abdelhafid, Chaalane Mourad

Abstract:

The objective of this work is setting numerically operational finite element CAXI_L for the axisymmetric and nonaxisymmetric shells. This element is based on the Reissner-Mindlin theory and mixed model formulation. The MATLAB language is used for the programming. In order to test the elaborated program, some applications are carried out.

Keywords: axisymmetric shells, nonaxisymmetric behaviour, finite element, MATLAB programming

Procedia PDF Downloads 320
904 Learning Programming for Hearing Impaired Students via an Avatar

Authors: Nihal Esam Abuzinadah, Areej Abbas Malibari, Arwa Abdulaziz Allinjawi, Paul Krause

Abstract:

Deaf and hearing-impaired students face many obstacles throughout their education, especially with learning applied sciences such as computer programming. In addition, there is no clear signs in the Arabic Sign Language that can be used to identify programming logic terminologies such as while, for, case, switch etc. However, hearing disabilities should not be a barrier for studying purpose nowadays, especially with the rapid growth in educational technology. In this paper, we develop an Avatar based system to teach computer programming to deaf and hearing-impaired students using Arabic Signed language with new signs vocabulary that is been developed for computer programming education. The system is tested on a number of high school students and results showed the importance of visualization in increasing the comprehension or understanding of concepts for deaf students through the avatar.

Keywords: hearing-impaired students, isolation, self-esteem, learning difficulties

Procedia PDF Downloads 145
903 Solution of Nonlinear Fractional Programming Problem with Bounded Parameters

Authors: Mrinal Jana, Geetanjali Panda

Abstract:

In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example.

Keywords: fractional programming, interval valued function, interval inequalities, partial order relation

Procedia PDF Downloads 520
902 Pedagogical Tools In The 21st Century

Authors: M. Aherrahrou

Abstract:

Moroccan education is currently facing many difficulties and problems due to traditional methods of teaching. Neuro -Linguistic Programming (NLP) appears to hold much potential for education at all levels. In this paper, the major aim is to explore the effect of certain Neuro -Linguistic Programming techniques in one educational institution in Morocco. Quantitative and Qualitative methods are used. The findings prove the effectiveness of this new approach regarding Moroccan education, and it is a promising tool to improve the quality of learning.

Keywords: learning and teaching environment, Neuro- Linguistic Programming, education, quality of learning

Procedia PDF Downloads 355
901 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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900 Review of Currently Adopted Intelligent Programming Tutors

Authors: Rita Garcia

Abstract:

Intelligent Programming Tutors, IPTs, are supplemental educational devices that assist in teaching software development. These systems provide customized learning allowing the user to select the presentation pace, pedagogical strategy, and to recall previous and additional teaching materials reinforcing learning objectives. In addition, IPTs automatically records individual’s progress, providing feedback to the instructor and student. These tutoring systems have an advantage over Tutoring Systems because Intelligent Programming Tutors are not limited to one teaching strategy and can adjust when it detects the user struggling with a concept. The Intelligent Programming Tutor is a category of Intelligent Tutoring Systems, ITS. ITS are available for many fields in education, supporting different learning objectives and integrate into other learning tools, improving the student's learning experience. This study provides a comparison of the IPTs currently adopted by the educational community and will focus on the different teaching methodologies and programming languages. The study also includes the ability to integrate the IPT into other educational technologies, such as massive open online courses, MOOCs. The intention of this evaluation is to determine one system that would best serve in a larger ongoing research project and provide findings for other institutions looking to adopt an Intelligent Programming Tutor.

Keywords: computer education tools, integrated software development assistance, intelligent programming tutors, tutoring systems

Procedia PDF Downloads 318
899 Multi-Criteria Goal Programming Model for Sustainable Development of India

Authors: Irfan Ali, Srikant Gupta, Aquil Ahmed

Abstract:

Every country needs a sustainable development (SD) for its economic growth by forming suitable policies and initiative programs for the development of different sectors of the country. This paper is comprised of modeling and optimization of different sectors of India that form a multi-criterion model. In this paper, we developed a fractional goal programming (FGP) model that helps in providing the efficient allocation of resources simultaneously by achieving the sustainable goals in gross domestic product (GDP), electricity consumption (EC) and greenhouse gasses (GHG) emission by the year 2030. Also, a weighted model of FGP is presented to obtain varying solution according to the priorities set by the policy maker for achieving future goals of GDP growth, EC, and GHG emission. The presented models provide a useful insight to the decision makers for implementing strategies in a different sector.

Keywords: sustainable and economic development, multi-objective fractional programming, fuzzy goal programming, weighted fuzzy goal programming

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898 Jointly Learning Python Programming and Analytic Geometry

Authors: Cristina-Maria Păcurar

Abstract:

The paper presents an original Python-based application that outlines the advantages of combining some elementary notions of mathematics with the study of a programming language. The application support refers to some of the first lessons of analytic geometry, meaning conics and quadrics and their reduction to a standard form, as well as some related notions. The chosen programming language is Python, not only for its closer to an everyday language syntax – and therefore, enhanced readability – but also for its highly reusable code, which is of utmost importance for a mathematician that is accustomed to exploit already known and used problems to solve new ones. The purpose of this paper is, on one hand, to support the idea that one of the most appropriate means to initiate one into programming is throughout mathematics, and reciprocal, one of the most facile and handy ways to assimilate some basic knowledge in the study of mathematics is to apply them in a personal project. On the other hand, besides being a mean of learning both programming and analytic geometry, the application subject to this paper is itself a useful tool for it can be seen as an independent original Python package for analytic geometry.

Keywords: analytic geometry, conics, python, quadrics

Procedia PDF Downloads 296
897 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 is skewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB is formulated 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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896 A Survey on Constraint Solving Approaches Using Parallel Architectures

Authors: Nebras Gharbi, Itebeddine Ghorbel

Abstract:

In the latest years and with the advancements of the multicore computing world, the constraint programming community tried to benefit from the capacity of new machines and make the best use of them through several parallel schemes for constraint solving. In this paper, we propose a survey of the different proposed approaches to solve Constraint Satisfaction Problems using parallel architectures. These approaches use in a different way a parallel architecture: the problem itself could be solved differently by several solvers or could be split over solvers.

Keywords: constraint programming, parallel programming, constraint satisfaction problem, speed-up

Procedia PDF Downloads 320
895 Use the Null Space to Create Starting Point for Stochastic Programming

Authors: Ghussoun Al-Jeiroudi

Abstract:

Stochastic programming is one of the powerful technique which is used to solve real-life problems. Hence, the data of real-life problems is subject to significant uncertainty. Uncertainty is well studied and modeled by stochastic programming. Each day, problems become bigger and bigger and the need for a tool, which does deal with large scale problems, increase. Interior point method is a perfect tool to solve such problems. Interior point method is widely employed to solve the programs, which arise from stochastic programming. It is an iterative technique, so it is required a starting point. Well design starting point plays an important role in improving the convergence speed. In this paper, we propose a starting point for interior point method for multistage stochastic programming. Usually, the optimal solution of stage k+1 is used as starting point for the stage k. This point has the advantage of being close to the solution of the current program. However, it has a disadvantage; it is not in the feasible region of the current program. So, we suggest to take this point and modifying it. That is by adding to it a vector in the null space of the matrix of the unchanged constraints because the solution will change only in the null space of this matrix.

Keywords: interior point methods, stochastic programming, null space, starting points

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894 Stochastic Programming and C-Somga: Animal Ration Formulation

Authors: Pratiksha Saxena, Dipti Singh, Neha Khanna

Abstract:

A self-organizing migrating genetic algorithm(C-SOMGA) is developed for animal diet formulation. This paper presents animal diet formulation using stochastic and genetic algorithm. Tri-objective models for cost minimization and shelf life maximization are developed. These objectives are achieved by combination of stochastic programming and C-SOMGA. Stochastic programming is used to introduce nutrient variability for animal diet. Self-organizing migrating genetic algorithm provides exact and quick solution and presents an innovative approach towards successful application of soft computing technique in the area of animal diet formulation.

Keywords: animal feed ration, feed formulation, linear programming, stochastic programming, self-migrating genetic algorithm, C-SOMGA technique, shelf life maximization, cost minimization, nutrient maximization

Procedia PDF Downloads 443
893 Detecting Logical Errors in Haskell

Authors: Vanessa Vasconcelos, Mariza A. S. Bigonha

Abstract:

In order to facilitate both processes, this paper presents HaskellFL, a tool that uses fault localization techniques to locate a logical error in Haskell code. The Haskell subset used in this work is sufficiently expressive for those studying functional programming to get immediate help debugging their code and to answer questions about key concepts associated with the functional paradigm. HaskellFL was tested against functional programming assignments submitted by students enrolled at the functional programming class at the Federal University of Minas Gerais and against exercises from the Exercism Haskell track that are publicly available on GitHub. Furthermore, the EXAM score was chosen to evaluate the tool’s effectiveness, and results showed that HaskellFL reduced the effort needed to locate an error for all tested scenarios. Results also showed that the Ochiai method was more effective than Tarantula.

Keywords: debug, fault localization, functional programming, Haskell

Procedia PDF Downloads 298
892 The Impact of Using Microlearning to Enhance Students' Programming Skills and Learning Motivation

Authors: Ali Alqarni

Abstract:

This study aims to explore the impact of microlearning on the development of the programming skills as well as on the motivation for learning of first-year high schoolers in Jeddah. The sample consists of 78 students, distributed as 40 students in the control group, and 38 students in the treatment group. The quasi-experimental method, which is a type of quantitative method, was used in this study. In addition to the technological tools used to create and deliver the digital content, the study utilized two tools to collect the data: first, an observation card containing a list of programming skills, and second, a tool to measure the student's motivation for learning. The findings indicate that microlearning positively impacts programming skills and learning motivation for students. The study, then, recommends implementing and expanding the use of microlearning in educational contexts both in the general education level and the higher education level.

Keywords: educational technology, teaching strategies, online learning, microlearning

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891 Optimal Performance of Plastic Extrusion Process Using Fuzzy Goal Programming

Authors: Abbas Al-Refaie

Abstract:

This study optimized the performance of plastic extrusion process of drip irrigation pipes using fuzzy goal programming. Two main responses were of main interest; roll thickness and hardness. Four main process factors were studied. The L18 array was then used for experimental design. The individual-moving range control charts were used to assess the stability of the process, while the process capability index was used to assess process performance. Confirmation experiments were conducted at the obtained combination of optimal factor setting by fuzzy goal programming. The results revealed that process capability was improved significantly from -1.129 to 0.8148 for roll thickness and from 0.0965 to 0.714 and hardness. Such improvement results in considerable savings in production and quality costs.

Keywords: fuzzy goal programming, extrusion process, process capability, irrigation plastic pipes

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890 Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problems with Equilibrium Constraints, Using Convexificators

Authors: Shashi Kant Mishra

Abstract:

In this paper, we consider semi-infinite mathematical programming problems with equilibrium constraints (SIMPEC). We establish necessary and sufficient optimality conditions for the SIMPEC, using convexificators. We study the Wolfe type dual problem for the SIMPEC under the ∂∗convexity assumptions. A Mond-Weir type dual problem is also formulated and studied for the SIMPEC under the ∂∗-convexity, ∂∗-pseudoconvexity and ∂∗quasiconvexity assumptions. Weak duality theorems are established to relate the SIMPEC and two dual programs in the framework of convexificators. Further, strong duality theorems are obtained under generalized standard Abadie constraint qualification (GS-ACQ).

Keywords: mathematical programming problems with equilibrium constraints, optimality conditions, semi-infinite programming, convexificators

Procedia PDF Downloads 329
889 Towards Expanding the Use of the Online Judge UnitJudge for Java Programming Exercises and Web Development Practices in Computer Science Education

Authors: Iván García-Magariño, Javier Bravo-Agapito, Marta López-Fernández

Abstract:

Online judges have proven their utility in partial auto-evaluation of programming short exercises in the last decades. UnitJudge online judge has the advantage of facilitating the evaluation of separate units to provide more segregate and meaningful feedback to students in complex exercises and practices. This paper discusses the use of UnitUdge in advanced Java object-oriented programming exercises and web development practices. This later usage has been proposed by means of the Selenium Java library and classes to provide the web address. Consequently, UnitJudge is an online judge system that can be applied in several subjects, and therefore, many other students would take advantage of self-testing their exercises. This paper presents the experiments with a Java programming exercise for learning Java object-oriented classes with a generic type. Considering 10 students who voluntarily used UnitJudge, 80% successfully learned this concept, passing the judge exercise with correct results.

Keywords: online judges, programming skills, computer science education, auto-evaluation

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888 Multi-Period Supply Chain Design under Uncertainty

Authors: Amir Azaron

Abstract:

In this research, a stochastic programming approach is developed for designing supply chains with uncertain parameters. Demands and selling prices of products at markets are considered as the uncertain parameters. The proposed mathematical model will be multi-period two-stage stochastic programming, which takes into account the selection of retailer sites, suppliers, production levels, inventory levels, transportation modes to be used for shipping goods, and shipping quantities among the entities of the supply chain network. The objective function is to maximize the chain’s net present value. In order to maximize the chain’s NPV, the sum of first-stage investment costs on retailers, and the expected second-stage processing, inventory-holding and transportation costs should be kept as low as possible over multiple periods. The effects of supply uncertainty where suppliers are unreliable will also be investigated on the efficiency of the supply chain.

Keywords: supply chain management, stochastic programming, multiobjective programming, inventory control

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887 Performance Analysis of MATLAB Solvers in the Case of a Quadratic Programming Generation Scheduling Optimization Problem

Authors: Dávid Csercsik, Péter Kádár

Abstract:

In the case of the proposed method, the problem is parallelized by considering multiple possible mode of operation profiles, which determine the range in which the generators operate in each period. For each of these profiles, the optimization is carried out independently, and the best resulting dispatch is chosen. For each such profile, the resulting problem is a quadratic programming (QP) problem with a potentially negative definite Q quadratic term, and constraints depending on the actual operation profile. In this paper we analyze the performance of available MATLAB optimization methods and solvers for the corresponding QP.

Keywords: optimization, MATLAB, quadratic programming, economic dispatch

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886 An Empirical Study of the Effect of Robot Programming Education on the Computational Thinking of Young Children: The Role of Flowcharts

Authors: Wei Sun, Yan Dong

Abstract:

There is an increasing interest in introducing computational thinking at an early age. Computational thinking, like mathematical thinking, engineering thinking, and scientific thinking, is a kind of analytical thinking. Learning computational thinking skills is not only to improve technological literacy, but also allows learners to equip with practicable skills such as problem-solving skills. As people realize the importance of computational thinking, the field of educational technology faces a problem: how to choose appropriate tools and activities to help students develop computational thinking skills. Robots are gradually becoming a popular teaching tool, as robots provide a tangible way for young children to access to technology, and controlling a robot through programming offers them opportunities to engage in developing computational thinking. This study explores whether the introduction of flowcharts into the robotics programming courses can help children convert natural language into a programming language more easily, and then to better cultivate their computational thinking skills. An experimental study was adopted with a sample of children ages six to seven (N = 16) participated, and a one-meter-tall humanoid robot was used as the teaching tool. Results show that children can master basic programming concepts through robotic courses. Children's computational thinking has been significantly improved. Besides, results suggest that flowcharts do have an impact on young children’s computational thinking skills development, but it only has a significant effect on the "sequencing" and "correspondence" skills. Overall, the study demonstrates that the humanoid robot and flowcharts have qualities that foster young children to learn programming and develop computational thinking skills.

Keywords: robotics, computational thinking, programming, young children, flow chart

Procedia PDF Downloads 147
885 Optimizing Human Diet Problem Using Linear Programming Approach: A Case Study

Authors: P. Priyanka, S. Shruthi, N. Guruprasad

Abstract:

Health is a common theme in most cultures. In fact all communities have their concepts of health, as part of their culture. Health continues to be a neglected entity. Planning of Human diet should be done very careful by selecting the food items or groups of food items also the composition involved. Low price and good taste of foods are regarded as two major factors for optimal human nutrition. Linear programming techniques have been extensively used for human diet formulation for quiet good number of years. Through the process, we mainly apply “The Simplex Method” which is a very useful statistical tool based on the theorem of Elementary Row Operation from Linear Algebra and also incorporate some other necessary rules set by the Simplex Method to help solve the problem. The study done by us is an attempt to develop a programming model for optimal planning and best use of nutrient ingredients.

Keywords: diet formulation, linear programming, nutrient ingredients, optimization, simplex method

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884 Importance of Human Capital Development and Management in Industries

Authors: Birce Boga Bakirli

Abstract:

In this paper, we investigate ideas on human capital development and management in industries. We structured a model to be able to gather the data from the interviews conducted with worker, specialists and owners of companies. Different aspects of the situation are found in these interviews, and we used the information to model the benefit of the business owners and workers perspectives. These are modelled as a bi-level programming problem. Several instances of the generic cases are solved. The results show the importance of education within and out of the company for workers, and it returns for the company.

Keywords: bi-level programming, corporate strategy, cost tradeoffs, human capital, mixed integer programming, Stackelberg game, supplier relations, strategic planning

Procedia PDF Downloads 355
883 An Efficient Approach to Optimize the Cost and Profit of a Tea Garden by Using Branch and Bound Method

Authors: Abu Hashan Md Mashud, M. Sharif Uddin, Aminur Rahman Khan

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In this paper, we formulate a new problem as a linear programming and Integer Programming problem and maximize profit within the limited budget and limited resources based on the construction of a tea garden problem. It describes a new idea about how to optimize profit and focuses on the practical aspects of modeling and the challenges of providing a solution to a complex real life problem. Finally, a comparative study is carried out among Graphical method, Simplex method and Branch and bound method.

Keywords: integer programming, tea garden, graphical method, simplex method, branch and bound method

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882 Multi-Objective Multi-Mode Resource-Constrained Project Scheduling Problem by Preemptive Fuzzy Goal Programming

Authors: Busaba Phurksaphanrat

Abstract:

This research proposes a pre-emptive fuzzy goal programming model for multi-objective multi-mode resource constrained project scheduling problem. The objectives of the problem are minimization of the total time and the total cost of the project. Objective in a multi-mode resource-constrained project scheduling problem is often a minimization of make-span. However, both time and cost should be considered at the same time with different level of important priorities. Moreover, all elements of cost functions in a project are not included in the conventional cost objective function. Incomplete total project cost causes an error in finding the project scheduling time. In this research, pre-emptive fuzzy goal programming is presented to solve the multi-objective multi-mode resource constrained project scheduling problem. It can find the compromise solution of the problem. Moreover, it is also flexible in adjusting to find a variety of alternative solutions.

Keywords: multi-mode resource constrained project scheduling problem, fuzzy set, goal programming, pre-emptive fuzzy goal programming

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881 Collaborative Platform for Learning Basic Programming (Algorinfo)

Authors: Edgar Mauricio Ruiz Osuna, Claudia Yaneth Herrera Bolivar, Sandra Liliana Gomez Vasquez

Abstract:

The increasing needs of professionals with skills in software development in industry are incremental, therefore, the relevance of an educational process in line with the strengthening of these competencies, are part of the responsibilities of universities with careers related to the area of Informatics and Systems. In this sense, it is important to consider that in the National Science, Technology and Innovation Plan for the development of the Electronics, Information Technologies and Communications (2013) sectors, it is established as a weakness in the SWOT Analysis of the Software sector and Services, Deficiencies in training and professional training. Accordingly, UNIMINUTO's Computer Technology Program has addressed the analysis of students' performance in software development, identifying various problems such as dropout in programming subjects, academic averages, as well as deficiencies in strategies and competencies developed in the area of programming. As a result of this analysis, it was determined to design a collaborative learning platform in basic programming using heat maps as a tool to support didactic feedback. The pilot phase allows to evaluate in a programming course the ALGORINFO platform as a didactic resource, through an interactive and collaborative environment where students can develop basic programming practices and in turn, are fed back through the analysis of time patterns and difficulties frequent in certain segments or program cycles, by means of heat maps. The result allows the teacher to have tools to reinforce and advise critical points generated on the map, so that students and graduates improve their skills as software developers.

Keywords: collaborative platform, learning, feedback, programming, heat maps

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880 Solving Fuzzy Multi-Objective Linear Programming Problems with Fuzzy Decision Variables

Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

Abstract:

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

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879 Solving Linear Systems Involved in Convex Programming Problems

Authors: Yixun Shi

Abstract:

Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed.

Keywords: convex programming, interior point method, linear systems, vector division

Procedia PDF Downloads 402