Search results for: mathematical programming problems with equilibrium constraints

Authors: Zaid Jamal Saeed Almahmoud

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Smart Grid is the vision of the future power system that combines advanced monitoring and communication technologies to provide energy in a smart, efficient, and user-friendly manner. This proposal considers a demand response model in the Smart Grid based on utility maximization. Given a set of consumers with conflicting preferences in terms of consumption and a utility company that aims to minimize the peak demand and match demand to supply, we study the problem of aggregating these preferences while modelling the problem as a game. We also investigate whether an equilibrium can be reached to maximize the social benefit. Based on such equilibrium, we propose a dynamic pricing heuristic that computes the equilibrium and sets the prices accordingly. The developed approach was analysed theoretically and evaluated experimentally using real appliances data. The results show that our proposed approach achieves a substantial reduction in the overall energy consumption.

Keywords: heuristics, smart grid, aggregation, mechanism design, equilibrium

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Authors: Irena Smetackova

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The important part of school mathematics are word problems which represent the connection between school knowledge and life reality. To find the reasons why students consider word problems to be difficult, it is necessary to take into consideration the motivational settings, besides mathematical knowledge and reading skills. Our goal is to identify whether the familiar or unfamiliar context of math word problem influences solving success rate and if so, whether the reasons are motivational or cognitive. For this purpose, we conducted three steps study in group of fifty pupils 9-10 years old. In the first step, we asked pupils to create ‘the best’ word problems for entered numerical formula. The set of 19 word problems with different contexts were selected. In the second step, pupils were asked to evaluate (without solving) how they like each item and how easy it is for them. The 6 word problems with low preference and low estimated success rate were selected and combined with other 6 problems with high preference and success rate. In the third step, the same pupils were asked to solve the word problems. The analysis showed that pupils attitudes and solving toward word problems varied by the context. The strong gender patterns both in preferred contexts and in estimated success rates were identified however the real success rate did not differ so strongly. The success gap between word problems with and without preferred contexts were stronger than the gap between problems with and without real experience with the context. The hypothesis that motivational factors are more important than cognitive factors was confirmed.

Keywords: mathematics, context of reality, motivation, cognition, word problems

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Authors: Y. Smirlis, G. Koronakos, S. Plitsos

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Shipbrokers assist the ship companies in chartering or selling and buying vessels, acting as intermediates between them and the market. They facilitate deals, providing their expertise, negotiating skills, and knowledge about ship market bargains. Their role is very important as it affects the profitability and market position of a shipping company. Due to their significant contribution, the shipping companies have to employ systematic procedures to evaluate the shipbrokers’ services in order to select the best and, consequently, to achieve the best deals. Towards this, in this paper, we consider shipbrokers as financial service providers, and we formulate the problem of evaluating and selecting shipbrokers’ services as a multi-criteria decision making (MCDM) procedure. The proposed methodology comprises a first normalization step to adjust different scales and orientations of the criteria and a second step that includes the mathematical model to evaluate the performance of the shipbrokers’ services involved in the assessment. The criteria along which the shipbrokers are assessed may refer to their size and reputation, the potential efficiency of the services, the terms and conditions imposed, the expenses (e.g., commission – brokerage), the expected time to accomplish a chartering or selling/buying task, etc. and according to our modelling approach these criteria may be assigned different importance. The mathematical programming model performs a comparative assessment and estimates for the shipbrokers involved in the evaluation, a relative score that ranks the shipbrokers in terms of their potential performance. To illustrate the proposed methodology, we present a case study in which a shipping company evaluates and selects the most suitable among a number of sale and purchase (S&P) brokers. Acknowledgment: This study is supported by the OptiShip project, implemented within the framework of the National Recovery Plan and Resilience “Greece 2.0” and funded by the European Union – NextGenerationEU programme.

Keywords: shipbrokers, multi-criteria decision making, mathematical programming, service-provider selection

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Authors: Ranadhir Roy

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Inverse problems arise in medical (molecular) imaging. These problems are characterized by large in three dimensions, and by the diffusion equation which models the physical phenomena within the media. The inverse problems are posed as a nonlinear optimization where the unknown parameters are found by minimizing the difference between the predicted data and the measured data. To obtain a unique and stable solution to an ill-posed inverse problem, a priori information must be used. Mathematical conditions to obtain stable solutions are established in Tikhonov’s regularization method, where the a priori information is introduced via a stabilizing functional, which may be designed to incorporate some relevant information of an inverse problem. Effective determination of the Tikhonov regularization parameter requires knowledge of the true solution, or in the case of optical imaging, the true image. Yet, in, clinically-based imaging, true image is not known. To alleviate these difficulties we have applied the penalty/modified barrier function (PMBF) method instead of Tikhonov regularization technique to make the inverse problems well-posed. Unlike the Tikhonov regularization method, the constrained optimization technique, which is based on simple bounds of the optical parameter properties of the tissue, can easily be implemented in the PMBF method. Imposing the constraints on the optical properties of the tissue explicitly restricts solution sets and can restore uniqueness. Like the Tikhonov regularization method, the PMBF method limits the size of the condition number of the Hessian matrix of the given objective function. The accuracy and the rapid convergence of the PMBF method require a good initial guess of the Lagrange multipliers. To obtain the initial guess of the multipliers, we use a least square unconstrained minimization problem. Three-dimensional images of fluorescence absorption coefficients and lifetimes were reconstructed from contact and noncontact experimentally measured data.

Keywords: constrained minimization, ill-conditioned inverse problems, Tikhonov regularization method, penalty modified barrier function method

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Authors: Rizky Oktaviana

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The main purpose of studying lies in improving students’ understanding. Teachers usually use written test to measure students’ understanding about learning material especially mathematical learning material. This common method actually has a lack point, such that in mathematics content, written test only show procedural steps to solve mathematical problems. Therefore, teachers unable to see whether students actually understand about mathematical concepts and the relation between concepts or not. One of the best tools to observe students’ understanding about the mathematical concepts is concept map. The goal of this research is to describe junior high school students understanding about mathematical concepts through Concept Maps based on the difference of mathematical ability. There were three steps in this research; the first step was choosing the research subjects by giving mathematical ability test to students. The subjects of this research are three students with difference mathematical ability, high, intermediate and low mathematical ability. The second step was giving concept mapping training to the chosen subjects. The last step was giving concept mapping task about the function to the subjects. Nodes which are the representation of concepts of function were provided in concept mapping task. The subjects had to use the nodes in concept mapping. Based on data analysis, the result of this research shows that subject with high mathematical ability has formal understanding, due to that subject could see the connection between concepts of function and arranged the concepts become concept map with valid hierarchy. Subject with intermediate mathematical ability has relational understanding, because subject could arranged all the given concepts and gave appropriate label between concepts though it did not represent the connection specifically yet. Whereas subject with low mathematical ability has poor understanding about function, it can be seen from the concept map which is only used few of the given concepts because subject could not see the connection between concepts. All subjects have instrumental understanding for the relation between linear function concept, quadratic function concept and domain, co domain, range.

Keywords: concept map, concept mapping, mathematical concepts, understanding

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Authors: Saeideh Salimpour, Sophie-Charlotte Viaux, Ahmed Azab, Mohammed Fazle Baki

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The Facility Layout Problem (FLP) is key to the efficient and cost-effective operation of a system. This paper presents a hybrid heuristic- and mathematical-programming-based approach that divides the problem conceptually into those of clustering and sequencing. First, clusters of vertically aligned facilities are formed, which are later on sequenced horizontally. The developed methodology provides promising results in comparison to its counterparts in the literature by minimizing the inter-distances for facilities which have more interactions amongst each other and aims at placing the facilities with more interactions at the centroid of the shop.

Keywords: clustering-sequencing approach, mathematical modeling, optimization, unequal facility layout problem

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Authors: Tao Zhang

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Job stress appears nearly everywhere especially in the hospitality industry because employees in this industry usually have to work long time and try to meet conflicting demands of their customers, managers, and company. To reduce job stress, employees of casino hotels try to perform leisure activities or tourism. However, casino employees often meet many obstacles or constraints when they plan to travel. Until now, there is little understanding as to why casino hotel employees often face many travel constraints or leisure barriers. What is more, few studies explore the relationship between travel constraints and job stress of casino employees. Therefore, this study is to explore the construct of casino hotel employees' travel constraints and the relationship among job stress, travel constraints, and job satisfaction. Using convenient sampling method, this study planned to investigate 500 front line employees and managers of ten casino hotels in Macau. A total of 500 questionnaires were distributed, and 414 valid questionnaires were received. The return rate of valid questionnaires is 82.8%. Several statistical techniques such as factor analysis, t-test, one-way ANOVA, and regression analysis were applied to analyze the collected data. The findings of this study are as follows. Firstly, by using factor analysis, this study found the travel constraints of casino employees include intrapersonal constraints, interpersonal constraints, and structural constraints. Secondly, by using regression analysis, the study found travel constraints are positively related with job stress while negatively related with job satisfaction. This means reducing travel constraints may create a chance for casino employees to travel so that they could reduce job stress, therefore raise their job satisfaction. Thirdly, this research divided the research samples into three groups by the degree of job stress. The three groups are low satisfaction group, medium satisfaction group, and high satisfaction group. The means values of these groups were compared by t-test. Results showed that there are significant differences of the means values of interpersonal constraints between low satisfaction group and high satisfaction group. This suggests positive interpersonal relationship especially good family member relationship reduce not only job stress but also travel constraints of casino employees. Interestingly, results of t-test showed there is not a significant difference of the means values of structural constraints between low satisfaction group and high satisfaction group. This suggests structural constraints are outside variables which may be related with tourism destination marketing. Destination marketing organizations (DMO) need use all kinds of tools and techniques to promote their tourism destinations so as to reduce structural constraints of casino employees. This research is significant for both theoretical and practical fields. From the theoretical perspective, the study found the internal relationship between travel constraints, job stress, and job satisfaction and the different roles of three dimensions of travel constraints. From the practical perspective, the study provides useful methods to reduce travel constraints and job stress, therefore, raise job satisfaction of casino employees.

Keywords: hotel, job satisfaction, job stress, travel constraints

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Authors: Bo Kampmann Walther

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This essay examines the narratives of the Book of Genesis through the lens of game theory, a mathematical framework for analyzing strategic interactions among rational actors. By treating key figures in Genesis as players in a game, this analysis sheds light on their decisions and the resulting consequences. Focusing primarily on the story of Adam and Eve, the essay utilizes concepts such as game state, saddle point, optimal strategy, and Nash equilibrium to explore the dynamics at play and scrutinize the existence of two kinds of game rules in Genesis: one being global and post-Fall oriented, the other being local and relegated to life in the Garden. The serpent's intervention and the subsequent actions of Adam and Eve are modeled as strategic moves, revealing the complexities and shifts in the game state from harmony in Eden to a world marked by toil and mortality post-Fall.

Keywords: game theory, Genesis, strategy, saddle point, nash equilibrium, New Game State

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Authors: Pratiksha Saxena, Dipti Singh, Neha Khanna

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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

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Authors: Elham Kiyani

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In this paper, we first introduce the concept of Q-efficient solutions in a real linear space not necessarily endowed with a topology, where Q is some nonempty (not necessarily convex) set. We also used the scalarization technique including the Gerstewitz function generated by a nonconvex set to characterize these Q-efficient solutions. The algebraic concepts of interior and closure are useful to study optimization problems without topology. Studying nonconvex vector optimization is valuable since topological interior is equal to algebraic interior for a convex cone. So, we use the algebraic concepts of interior and closure to define Q-weak efficient solutions and Q-Henig proper efficient solutions of set-valued optimization problems, where Q is not a convex cone. Optimization problems with set-valued maps have a wide range of applications, so it is expected that there will be a useful analytical tool in optimization theory for set-valued maps. These kind of optimization problems are closely related to stochastic programming, control theory, and economic theory. The paper focus on nonconvex problems, the results are obtained by assuming generalized non-convexity assumptions on the data of the problem. In convex problems, main mathematical tools are convex separation theorems, alternative theorems, and algebraic counterparts of some usual topological concepts, while in nonconvex problems, we need a nonconvex separation function. Thus, we consider the Gerstewitz function generated by a general set in a real linear space and re-examine its properties in the more general setting. A useful approach for solving a vector problem is to reduce it to a scalar problem. In general, scalarization means the replacement of a vector optimization problem by a suitable scalar problem which tends to be an optimization problem with a real valued objective function. The Gerstewitz function is well known and widely used in optimization as the basis of the scalarization. The essential properties of the Gerstewitz function, which are well known in the topological framework, are studied by using algebraic counterparts rather than the topological concepts of interior and closure. Therefore, properties of the Gerstewitz function, when it takes values just in a real linear space are studied, and we use it to characterize Q-efficient solutions of vector problems whose image space is not endowed with any particular topology. Therefore, we deal with a constrained vector optimization problem in a real linear space without assuming any topology, and also Q-weak efficient and Q-proper efficient solutions in the senses of Henig are defined. Moreover, by means of the Gerstewitz function, we provide some necessary and sufficient optimality conditions for set-valued vector optimization problems.

Keywords: algebraic interior, Gerstewitz function, vector closure, vector optimization

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Authors: Jorge A. Ruiz-Vanoye, Ocotlán Díaz-Parra, Alejandro Fuentes-Penna, José J. Hernández-Flores, Edith Olaco Garcia

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The Project Scheduling Problem (PSP) is a generic name given to a whole class of problems in which the best form, time, resources and costs for project scheduling are necessary. The PSP is an application area related to the project management. This paper aims at being a guide to understand PSP by presenting a survey of the general parameters of PSP: the Resources (those elements that realize the activities of a project), and the Activities (set of operations or own tasks of a person or organization); the mathematical models of the main variants of PSP and the algorithms used to solve the variants of the PSP. The project scheduling is an important task in project management. This paper contains mathematical models, resources, activities, and algorithms of project scheduling problems. The project scheduling problem has attracted researchers of the automotive industry, steel manufacturer, medical research, pharmaceutical research, telecommunication, industry, aviation industry, development of the software, manufacturing management, innovation and technology management, construction industry, government project management, financial services, machine scheduling, transportation management, and others. The project managers need to finish a project with the minimum cost and the maximum quality.

Keywords: PSP, Combinatorial Optimization Problems, Project Management; Manufacturing Management, Technology Management.

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Authors: Aydin Sipahioglu, Gokhan Celik

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Helicopter routing problem (HRP) is finding good tours for helicopter so as to pick up and deliver personnel or material among specified nodes, mutually. It can be encountered in case of being lots of supply and demand points for different commodities and requiring delivering commodities with helicopter. For instance, to deliver personnel or material from shore to oil rig is a good example. In fact, HRP is a branch of vehicle routing problem with pickup and delivery (VRPPD). However, it has additional constraints such that fuel capacity, performance of helicopter in different altitude and temperature, and the number of maximum takeoff and landing allowed. This kind of pickup and delivery problems can be classified into 3 groups, basically. 1-1 (one to one), M-M (many to many) and 1-M-1 (one to many to one). 1-1 means each commodity has only one supply and one demand point. M-M means there can be more than one supply and demand points for each kind of commodity. 1-M-1 means commodities at depot are delivered to demand points and commodities at customers are delivered to depot. In this case helicopter takes off from its own base, complete its tour and return to its own base. In this study, we define 1-M-M-1 type HRP. That means helicopter takes off from its home base, deliver commodities among the nodes as well as between depot and customers and return to its home base. These problems have NP-hard nature. Therefore, obtaining a good solution in a reasonable time is not easy. In this study, a model is offered for 1-M-M-1 type HRP. It is shown on small scale test instances that the model can find the optimal solution.

Keywords: helicopter routing problem, vehicle routing with pickup and delivery, integer programming

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Authors: Asma Aid, Samira Amokrane, Djamel Nibou, Hadj Mekatel

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The marine Enteromorpha Compressa (L.) (ECL) biomass was used as a low-cost biological adsorbent for the removal of Cr⁶⁺, Co²⁺ and Ni²⁺ ions from artificially contaminated aqueous solutions. The operating variables pH, the initial concentration C₀, the solid/liquid ratio R and the temperature T were studied. A full factorial experimental design technique enabled us to obtain a mathematical model describing the adsorption of Cr⁶⁺, Co²⁺ and Ni²⁺ ions and to study the main effects and interactions among operational parameters. The equilibrium isotherm has been analyzed by Langmuir, Freundlich, and Dubinin-Radushkevich models; it has been found that the adsorption process follows the Langmuir model for the used ions. Kinetic studies showed that the pseudo-second-order model correlates our experimental data. Thermodynamic parameters showed the endothermic heat of adsorption and the spontaneity of the adsorption process for Cr⁶⁺ ions and exothermic heat of adsorption for Co²⁺ and Ni²⁺ ions.

Keywords: enteromorpha Compressa, adsorption process, Cr⁶⁺, Co²⁺ and Ni²⁺, equilibrium isotherm

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Authors: Joao Teotonio Manzi

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Reversibility, irreversibility, equilibrium and steady-state that play a central role in the thermodynamic analysis of processes arising in the context of reactive systems are discussed in this article. Such concepts have generated substantial doubts, even among the most experienced researchers, and engineers, because from the literature, conclusive or definitive statements cannot be extracted. Concepts such as the time-reversibility of irreversible processes seem paradoxical, requiring further analysis. Equilibrium and reversibility, which appear to be of the same nature, have also been re-examined in the light of maximum entropy. The goal of this paper is to revisit and explore these concepts based on classical thermodynamics in order to have a better understanding them due to their impacts on technological advances, as a result, to generate an optimal procedure for designing, monitoring, and engineering optimization. Furthermore, an effective graphic procedure for dimensioning a Plug Flow Reactor has been provided. Thus, to meet the needs of chemical engineering from a simple conceptual analysis but with significant practical effects, a macroscopic approach is taken so as to integrate the different parts of this paper.

Keywords: reversibility, equilibrium, steady-state, thermodynamics, reactive system

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Authors: Abdullahi Mohammed Auwal

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Formation and change or decamping from one political party to another have now become a common trend in Nigeria. Many of the parties’ members who could not secure positions and or win elections in their parties or are not very much satisfied with the trends occurring in the party’s internal democratic principles and mechanisms, change their respective parties. This paper developed/presented and analyzed the used of non linear mathematical model for defections between two political parties using epidemiological approach. The whole population was assumed to be a constant and homogeneously mixed. Equilibria have been analytically obtained and their local and global stability discussed. Conditions for the co-existence of both the political parties have been determined, in the study of defections between People Democratic Party (PDP) and All Progressive Congress (APC) in Nigeria using numerical simulations to support the analytical results.

Keywords: model, political parties, deffection, stability, equilibrium, epidemiology

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Authors: Vanessa Vasconcelos, Mariza A. S. Bigonha

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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

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Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda

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This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.

Keywords: adsorption, mathematical modeling, nanocarbons, numerical analysis

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Authors: Mai A. Ibrahim, Mohammed El-Beltagy, Motaz Khorshid

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Emerging Markets return distributions have shown significance departure from normality were they are characterized by fatter tails relative to the normal distribution and exhibit levels of skewness and kurtosis that constitute a significant departure from normality. Therefore, the classical Markowitz Mean-Variance is not applicable for emerging markets since it assumes normally-distributed returns (with zero skewness and kurtosis) and a quadratic utility function. Moreover, the Markowitz mean-variance analysis can be used in cases of moderate non-normality and it still provides a good approximation of the expected utility, but it may be ineffective under large departure from normality. Higher moments models and median models have been suggested in the literature for asset allocation in this case. Higher moments models have been introduced to account for the insufficiency of the description of a portfolio by only its first two moments while the median model has been introduced as a robust statistic which is less affected by outliers than the mean. Tail risk measures such as Value-at Risk (VaR) and Conditional Value-at-Risk (CVaR) have been introduced instead of Variance to capture the effect of risk. In this research, higher moment models including the Mean-Variance-Skewness (MVS) and Mean-Variance-Skewness-Kurtosis (MVSK) are formulated as single-objective non-linear programming problems (NLP) and median models including the Median-Value at Risk (MedVaR) and Median-Mean Absolute Deviation (MedMAD) are formulated as a single-objective mixed-integer linear programming (MILP) problems. The higher moment models and median models are compared to some benchmark portfolios and tested on real financial data in the Egyptian main Index EGX30. The results show that all the median models outperform the higher moment models were they provide higher final wealth for the investor over the entire period of study. In addition, the results have confirmed the inapplicability of the classical Markowitz Mean-Variance to the Egyptian stock market as it resulted in very low realized profits.

Keywords: Egyptian stock exchange, emerging markets, higher moment models, median models, mixed-integer linear programming, non-linear programming

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Authors: Nicoly Coelho, Eduardo Vieira Vilas Boas, Paulo Orestes Formigoni

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Faced with the remarkable developments in the various segments of modern engineering, provided by the increasing technological development, professionals of all educational areas need to overcome the difficulties generated due to the good understanding of those who are starting their academic journey. Aiming to overcome these difficulties, this article aims at an introduction to the basic study of numerical methods applied to fluid mechanics and thermodynamics, demonstrating the modeling and simulations with its substance, and a detailed explanation of the fundamental numerical solution for the use of finite difference method, using SCILAB, a free software easily accessible as it is free and can be used for any research center or university, anywhere, both in developed and developing countries. It is known that the Computational Fluid Dynamics (CFD) is a necessary tool for engineers and professionals who study fluid mechanics, however, the teaching of this area of knowledge in undergraduate programs faced some difficulties due to software costs and the degree of difficulty of mathematical problems involved in this way the matter is treated only in postgraduate courses. This work aims to bring the use of DFC low cost in teaching Transport Phenomena for graduation analyzing a small classic case of fundamental thermodynamics with Scilab® program. The study starts from the basic theory involving the equation the partial differential equation governing heat transfer problem, implies the need for mastery of students, discretization processes that include the basic principles of series expansion Taylor responsible for generating a system capable of convergence check equations using the concepts of Sassenfeld, finally coming to be solved by Gauss-Seidel method. In this work we demonstrated processes involving both simple problems solved manually, as well as the complex problems that required computer implementation, for which we use a small algorithm with less than 200 lines in Scilab® in heat transfer study of a heated plate in rectangular shape on four sides with different temperatures on either side, producing a two-dimensional transport with colored graphic simulation. With the spread of computer technology, numerous programs have emerged requiring great researcher programming skills. Thinking that this ability to program DFC is the main problem to be overcome, both by students and by researchers, we present in this article a hint of use of programs with less complex interface, thus enabling less difficulty in producing graphical modeling and simulation for DFC with an extension of the programming area of experience for undergraduates.

Keywords: numerical methods, finite difference method, heat transfer, Scilab

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Authors: A. A. Ahmadi, A. R. Pishevar, M. Nili

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As the test gas in a gun tunnel is non-isentropically compressed and heated by a light weight piston. Here, first consideration is the optimum piston weight. Although various aspects of the influence of piston weight on gun tunnel performance have been studied, it is not possible to decide from the existing literature what piston weight is required for optimum performance in various conditions. The technique whereby the piston is rapidly brought to rest at the end of the gun tunnel barrel, and the resulted peak pressure is equal in magnitude to the final equilibrium pressure, is called the equilibrium piston technique. The equilibrium piston technique was developed to estimate the equilibrium piston mass; but this technique cannot give an appropriate estimate for the optimum piston weight. In the present work, a gun tunnel with diameter of 3 in. is described and its performance is investigated numerically to obtain the effect of piston and its weight. Numerical results in the present work are in very good agreement with experimental results. Significant influence of the existence of a piston is shown by comparing the gun tunnel results with results of a conventional shock tunnel in the same dimension and same initial condition. In gun tunnel, an increase of around 250% in running time is gained relative to shock tunnel. Also, Numerical results show that equilibrium piston technique is not a good way to estimate suitable piston weight and there will be a lighter piston which can increase running time of the gun tunnel around 60%.

Keywords: gun tunnel, hypersonic flow, piston, shock tunnel

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Authors: Aliasghar Arab

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Autonomous robots interacting with humans, as safety-critical nonlinear control systems, are complex closed-loop cyber-physical dynamical machines. Keeping these intelligent yet complicated systems safe and smooth during their operations is challenging. The aim of the safe predictive output feedback linearization control synthesis is to design a novel controller for smooth trajectory following while unsafe situations must be avoided. The controller design should obtain a linearized output for smoothness and invariance to a safety subset. Inspired by finite-horizon nonlinear model predictive control, the problem is formulated as constrained nonlinear dynamic programming. The safety constraints can be defined as control barrier functions. Avoiding unsafe maneuvers and performing smooth motions increases the predictability of the robot’s movement for humans when robots and people are working together. Our results demonstrate the proposed output linearization method obeys the safety constraints and, compared to existing safety-guaranteed methods, is smoother and performs better.

Keywords: robotics, collaborative robots, safety, autonomous robots

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Authors: Arindam Chaudhuri

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The research presents epsilon- hierarchical fuzzy twin support vector regression (epsilon-HFTSVR) based on epsilon-fuzzy twin support vector regression (epsilon-FTSVR) and epsilon-twin support vector regression (epsilon-TSVR). Epsilon-FTSVR is achieved by incorporating trapezoidal fuzzy numbers to epsilon-TSVR which takes care of uncertainty existing in forecasting problems. Epsilon-FTSVR determines a pair of epsilon-insensitive proximal functions by solving two related quadratic programming problems. The structural risk minimization principle is implemented by introducing regularization term in primal problems of epsilon-FTSVR. This yields dual stable positive definite problems which improves regression performance. Epsilon-FTSVR is then reformulated as epsilon-HFTSVR consisting of a set of hierarchical layers each containing epsilon-FTSVR. Experimental results on both synthetic and real datasets reveal that epsilon-HFTSVR has remarkable generalization performance with minimum training time.

Keywords: regression, epsilon-TSVR, epsilon-FTSVR, epsilon-HFTSVR

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Authors: Fahad Alsharari, Mohd Salmi Md. Noorani

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A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron-Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift AZ, x is in M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, we find a new method of calculating the topological entropy of the Motzkin shift M(M,N) without any measure theoretical discussion.

Keywords: entropy, Motzkin shift, mathematical model, theory

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Authors: Seok Hong Min, Tae Kwon Ha

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High strength Fe-36Ni-base Invar alloys containing Al contents up to 0.3 weight percent were cast into ingots and thermodynamic equilibrium during solidification has been investigated in this study. From the thermodynamic simulation using Thermo-Calc®, it has been revealed that equilibrium phases which can be formed are two kinds of MC-type precipitates, MoC, and M2C carbides. The mu phase was also expected to form by addition of aluminum. Microstructure observation revealed the coarse precipitates in the as-cast ingots, which was non-equilibrium phase and could be resolved by the successive heat treatment. With increasing Al contents up to 0.3 wt.%, tensile strength of Invar alloy increased as 1400MPa after cold rolling and thermal expansion coefficient increased significantly. Cold rolling appeared to dramatically decrease thermal expansion coefficient.

Keywords: invar alloy, aluminum, phase equilibrium, thermal expansion coefficient, microstructure, tensile properties

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Authors: Anvar Atayev, Karl Steinborn, Aleksander Lovric, Saif Al-Ibadi, Jorg Fliege

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In this paper, we present results obtained from optimising the aerodynamic performance of aerostructures in external ow. The optimisation method used was developed to efficiently handle multi-variable problems with numerous black-box objective functions and constraints. To demonstrate these capabilities, a series of CFD problems were considered; (1) a two-dimensional NACA aerofoil with three variables, (2) a two-dimensional morphing aerofoil with 17 variables, and (3) a three-dimensional morphing aeroplane tail with 33 variables. The objective functions considered were related to combinations of the mean aerodynamic coefficients, as well as their relative variations/oscillations. It was observed that for each CFD problem, an improved objective value was found. Notably, the scale-up in variables for the latter problems did not greatly hinder optimisation performance. This makes the method promising for scaled-up CFD problems, which require considerable computational resources.

Keywords: computational fluid dynamics, optimisation algorithms, aerodynamic design, engineering design

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Authors: Song Ni, Junxiang Xu

Abstract:

This paper concerns quasi-periodic perturbations with parameters of 2-dimensional degenerate systems. If the equilibrium point of the unperturbed system is elliptic-type degenerate. Assume that the perturbation is real analytic quasi-periodic with diophantine frequency. Without imposing any assumption on the perturbation, we can use a path of equilibrium points to tackle with the Melnikov non-resonance condition, then by the Leray-Schauder Continuation Theorem and the Kolmogorov-Arnold-Moser technique, it is proved that the equation has a small response solution for many sufficiently small parameters.

Keywords: quasi-periodic systems, KAM-iteration, degenerate equilibrium point, response solution

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Authors: Khashayar Kazemzadeh, Mohammad Hanif Dasoomi

Abstract:

According to the increasing travel demand in cities, bridges and tunnels are viewed as one of the fundamental components of cities transportation systems. Normally, due to geometric constraints forms in the tunnels, the considered speed in the tunnels is lower than the speed in connected highways. Therefore, drivers tend to reduce the speed near the entrance of the tunnels. In this paper, the effect of speed reduction on accident happened in the entrance of the tunnels has been discussed. The relation between accidents frequency and the parameters of speed, traffic volume and time of the accident in the mentioned tunnel has been analyzed and the mathematical model has been proposed.

Keywords: urban highway, accident, tunnel, mathematical model

Procedia PDF Downloads 462

Authors: Hicham Benamirouche, Oum Elkheir Moussi

Abstract:

The purpose of the study is to examine the dynamics of Algeria’s natural gas exports through the Autoregressive Distributed Lag (ARDL) bounds testing approach with break points. The analysis was carried out for the period from 1967 to 2015. Based on imperfect substitution specification, the ARDL approach reveals a long-run equilibrium relationship between Algeria’s Natural gas exports and their determinant factors (Algeria’s gas reserves, Domestic gas consumption, Europe’s GDP per capita, relative prices, the European gas production and the market share of competitors). All the long-run elasticities estimated are statistically significant with a large impact of domestic factors, which constitute the supply constraints. In short term, the elasticities are statistically significant, and almost comparable to those of the long term. Furthermore, the speed of adjustment towards long-run equilibrium is less than one year because of the little flexibility of the long term export contracts. Two break points have been estimated when we employ the domestic gas consumption as a break variable; 1984 and 2010, which reflect the arbitration policy between the domestic gas market and gas exports.

Keywords: natural gas exports, elasticity, ARDL bounds testing, break points, Algeria

Procedia PDF Downloads 183

Authors: Alaa Sheta

Abstract:

Economic Load Dispatch (ELD) is one of the vital optimization problems in power system planning. Solving the ELD problems mean finding the best mixture of power unit outputs of all members of the power system network such that the total fuel cost is minimized while sustaining operation requirements limits satisfied across the entire dispatch phases. Many optimization techniques were proposed to solve this problem. A famous one is the Quadratic Programming (QP). QP is a very simple and fast method but it still suffer many problem as gradient methods that might trapped at local minimum solutions and cannot handle complex nonlinear functions. Numbers of metaheuristic algorithms were used to solve this problem such as Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO). In this paper, another meta-heuristic search algorithm named Differential Evolution (DE) is used to solve the ELD problem in power systems planning. The practicality of the proposed DE based algorithm is verified for three and six power generator system test cases. The gained results are compared to existing results based on QP, GAs and PSO. The developed results show that differential evolution is superior in obtaining a combination of power loads that fulfill the problem constraints and minimize the total fuel cost. DE found to be fast in converging to the optimal power generation loads and capable of handling the non-linearity of ELD problem. The proposed DE solution is able to minimize the cost of generated power, minimize the total power loss in the transmission and maximize the reliability of the power provided to the customers.

Keywords: economic load dispatch, power systems, optimization, differential evolution

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Authors: Chakib Jerry, Mounir Jerry

Abstract:

In this paper, a mathematical model of infested honey bees colonies is formulated in order to investigate Colony Collapse Disorder in a honeybee colony. CCD, as it is known, is a major problem on honeybee farms because of the massive decline in colony numbers. We introduce to the model a control variable which represents forager protection. We study the controlled model to derive conditions under which the bee colony can fight off epidemic. Secondly we study the problem of minimizing prevention cost under model’s dynamics constraints.

Keywords: honey bee, disease transmission model, disease control honeybees, optimal control

Procedia PDF Downloads 411