Search results for: mathematical compromise programming

Authors: Ingu Kim, Shangmun Shin, Yongsun Choi, Nguyen Manh Thang, Edwin R. Ramos, Won-Joo Hwang

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Project selection problems on management information system (MIS) are often considered a multi-criteria decision-making (MCDM) for a solving method. These problems contain two aspects, such as interdependencies among criteria and candidate projects and qualitative and quantitative factors of projects. However, most existing methods reported in literature consider these aspects separately even though these two aspects are simultaneously incorporated. For this reason, we proposed a hybrid method using analytic network process (ANP) and fuzzy logic in order to represent both aspects. We then propose a goal programming model to conduct an optimization for the project selection problems interpreted by a hybrid concept. Finally, a numerical example is conducted as verification purposes.

Keywords: Analytic Network Process (ANP), Multi-Criteria Decision-Making (MCDM), Fuzzy Logic, Information System Project Selection, Goal Programming.

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Authors: Kristina Davoian, Wolfram-M. Lippe

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Evolutionary Programming (EP) represents a methodology of Evolutionary Algorithms (EA) in which mutation is considered as a main reproduction operator. This paper presents a novel EP approach for Artificial Neural Networks (ANN) learning. The proposed strategy consists of two components: the self-adaptive, which contains phenotype information and the dynamic, which is described by genotype. Self-adaptation is achieved by the addition of a value, called the network weight, which depends on a total number of hidden layers and an average number of neurons in hidden layers. The dynamic component changes its value depending on the fitness of a chromosome, exposed to mutation. Thus, the mutation step size is controlled by two components, encapsulated in the algorithm, which adjust it according to the characteristics of a predefined ANN architecture and the fitness of a particular chromosome. The comparative analysis of the proposed approach and the classical EP (Gaussian mutation) showed, that that the significant acceleration of the evolution process is achieved by using both phenotype and genotype information in the mutation strategy.

Keywords: Artificial Neural Networks (ANN), Learning Theory, Evolutionary Programming (EP), Mutation, Self-Adaptation.

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Authors: Adesoji T. Jaiyeola, Josiah Adeyemo

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This paper presents an extensive review of literature relevant to the modelling techniques adopted in sediment yield and hydrological modelling. Several studies relating to sediment yield are discussed. Many research areas of sedimentation in rivers, runoff and reservoirs are presented. Different types of hydrological models, different methods employed in selecting appropriate models for different case studies are analysed. Applications of evolutionary algorithms and artificial intelligence techniques are discussed and compared especially in water resources management and modelling. This review concentrates on Genetic Programming (GP) and fully discusses its theories and applications. The successful applications of GP as a soft computing technique were reviewed in sediment modelling. Some fundamental issues such as benchmark, generalization ability, bloat, over-fitting and other open issues relating to the working principles of GP are highlighted. This paper concludes with the identification of some research gaps in hydrological modelling and sediment yield.

Keywords: Artificial intelligence, evolutionary algorithm, genetic programming, sediment yield.

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Authors: Wennan Long, Yuhao Nie, Yunan Li, Adam Brandt

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To fight against climate change, California government issued the Senate Bill No. 100 (SB-100) in 2018 September, which aims at achieving a target of 100% renewable electricity by the end of 2045. A capacity expansion problem is solved in this case study using a binary quadratic programming model. The optimal locations and capacities of the potential renewable power plants (i.e., solar, wind, biomass, geothermal and hydropower), the phase-out schedule of existing fossil-based (nature gas) power plants and the transmission of electricity across the entire network are determined with the minimal total annualized cost measured by net present value (NPV). The results show that the renewable electricity contribution could increase to 85.9% by 2030 and reach 100% by 2035. Fossil-based power plants will be totally phased out around 2035 and solar and wind will finally become the most dominant renewable energy resource in California electricity mix.

Keywords: 100% renewable electricity, California, capacity expansion, binary quadratic programming.

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Authors: Norziana Aminudin, Titik Khawa Abdul Rahman, Ismail Musirin

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One of the factors to maintain system survivability is the adequate reactive power support to the system. Lack of reactive power support may cause undesirable voltage decay leading to total system instability. Thus, appropriate reactive power support scheme should be arranged in order to maintain system stability. The strength of a system capacity is normally denoted as system loadability. This paper presents the enhancement of system loadability through optimal reactive power planning technique using a newly developed optimization technique, termed as Multiagent Immune Evolutionary Programming (MAIEP). The concept of MAIEP is developed based on the combination of Multiagent System (MAS), Artificial Immune System (AIS) and Evolutionary Programming (EP). In realizing the effectiveness of the proposed technique, validation is conducted on the IEEE-26-Bus Reliability Test System. The results obtained from pre-optimization and post-optimization process were compared which eventually revealed the merit of MAIEP.

Keywords: Load margin, MAIEP, Maximum loading point, ORPP.

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Authors: Md. Ashikur Rahman Khan, M. M. Rahman

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In electrical discharge machining (EDM), a complete and clear theory has not yet been established. The developed theory (physical models) yields results far from reality due to the complexity of the physics. It is difficult to select proper parameter settings in order to achieve better EDM performance. However, modelling can solve this critical problem concerning the parameter settings. Therefore, the purpose of the present work is to develop mathematical model to predict performance characteristics of EDM on Ti-5Al-2.5Sn titanium alloy. Response surface method (RSM) and artificial neural network (ANN) are employed to develop the mathematical models. The developed models are verified through analysis of variance (ANOVA). The ANN models are trained, tested, and validated utilizing a set of data. It is found that the developed ANN and mathematical model can predict performance of EDM effectively. Thus, the model has found a precise tool that turns EDM process cost-effective and more efficient.

Keywords: Analysis of variance, artificial neural network, material removal rate, modelling, response surface method, surface finish.

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Authors: Mahbub C. Mishu, Venketesh N. Dubey, Tamas Hickish, Jonathan Cole

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Pressure ulcer is a common problem for today’s healthcare industry. It occurs due to external load applied to the skin. Also when the subject is immobile for a longer period of time and there is continuous load applied to a particular area of human body, blood flow gets reduced and as a result pressure ulcer develops. Body support surface has a significant role in preventing ulceration so it is important to know the characteristics of support surface under loading conditions. In this paper we have presented mathematical models of different types of viscoelastic materials and also we have shown the validation of our simulation results with experiments.

Keywords: Pressure ulcer, viscoelastic material, mathematical model, experimental validation.

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Authors: Moustapha Bande, Hakima Ould-Slimane, Hanifa Boucheneb

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Software development for complex systems requires efficient and automatic tools that can be used to verify the satisfiability of some critical properties such as security ones. With the emergence of Aspect-Oriented Programming (AOP), considerable work has been done in order to better modularize the separation of concerns in the software design and implementation. The goal is to prevent the cross-cutting concerns to be scattered across the multiple modules of the program and tangled with other modules. One of the key challenges in the aspect-oriented programs is to be sure that all the pieces put together at the weaving time ensure the satisfiability of the overall system requirements. Our paper focuses on this problem and proposes a formal property verification approach for a given property from the woven program. The approach is based on the control flow graph (CFG) of the woven program, and the use of a satisfiability modulo theories (SMT) solver to check whether each property (represented par one aspect) is satisfied or not once the weaving is done.

Keywords: Aspect-oriented programming, control flow graph, satisfiability modulo theories, property verification.

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Authors: Ersen Yazıcı, Erhan Ertekin

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In this study, any possible differences between mathematics beliefs and anxiety of prospective elementary mathematics teachers have been investigated according to their gender. In this purpose, 1st, 2nd, 3rd and 4th grade students from a Government University in Turkey were selected as a sample. Mathematics Teaching Anxiety Scale (MATAS) and Beliefs About Mathematics Survey (BAMS) has been used as data collection tools. As a result of the study, it has been observed that prospective male teachers have more instrumentalist approach in learning mathematics than females according to their mathematical beliefs. On the other hand, females have more mathematics teaching anxiety than males especially, for subject knowledge in mathematics and selfconfidence.

Keywords: Mathematical beliefs, mathematics teaching anxiety, gender, prospective elementary mathematics teachers.

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Authors: Mohamed Amine Ouddan, Hassane Essafi

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Source code retrieval is of immense importance in the software engineering field. The complex tasks of retrieving and extracting information from source code documents is vital in the development cycle of the large software systems. The two main subtasks which result from these activities are code duplication prevention and plagiarism detection. In this paper, we propose a Mohamed Amine Ouddan, and Hassane Essafi source code retrieval system based on two-level fingerprint representation, respectively the structural and the semantic information within a source code. A sequence alignment technique is applied on these fingerprints in order to quantify the similarity between source code portions. The specific purpose of the system is to detect plagiarism and duplicated code between programs written in different programming languages belonging to the same class, such as C, Cµ, Java and CSharp. These four languages are supported by the actual version of the system which is designed such that it may be easily adapted for any programming language.

Keywords: Source code retrieval, plagiarism detection, clonedetection, sequence alignment.

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Authors: Hamed Rafiei, Masoud Rabbani

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This paper deals with the project selection problem. Project selection problem is one of the problems arose firstly in the field of operations research following some production concepts from primary product mix problem. Afterward, introduction of managerial considerations into the project selection problem have emerged qualitative factors and criteria to be regarded as well as quantitative ones. To overcome both kinds of criteria, an analytic network process is developed in this paper enhanced with fuzzy sets theory to tackle the vagueness of experts- comments to evaluate the alternatives. Additionally, a modified version of Least-Square method through a non-linear programming model is augmented to the developed group decision making structure in order to elicit the final weights from comparison matrices. Finally, a case study is considered by which developed structure in this paper is validated. Moreover, a sensitivity analysis is performed to validate the response of the model with respect to the condition alteration.

Keywords: Analytic network process, Fuzzy sets theory, Nonlinear programming, Project selection.

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Authors: Xiang Zhang, David Rey, S. Travis Waller

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Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate error term parameter value for the SUE model. First, the significance of the parameter is explored through a numerical example. Second, the parameter calibration method is developed based on the Logit-based route choice model. The calibration process is realized through multiple nonlinear regression, using sequential quadratic programming combined with least square method. Finally, case analysis is conducted to demonstrate the application of the calibration process and validate the better performance of the SUE model calibrated by the proposed method compared to the SUE models under other parameter values and the DUE model.

Keywords: Parameter calibration, sequential quadratic programming, Stochastic User Equilibrium, traffic assignment, transportation planning.

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Authors: S. Babaie-Kafaki, R. Ghanbari, S.H. Nasseri, E. Ardil

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Bus networks design is an important problem in public transportation. The main step to this design, is determining the number of required terminals and their locations. This is an especial type of facility location problem, a large scale combinatorial optimization problem that requires a long time to be solved. The genetic algorithm (GA) is a search and optimization technique which works based on evolutionary principle of natural chromosomes. Specifically, the evolution of chromosomes due to the action of crossover, mutation and natural selection of chromosomes based on Darwin's survival-of-the-fittest principle, are all artificially simulated to constitute a robust search and optimization procedure. In this paper, we first state the problem as a mixed integer programming (MIP) problem. Then we design a new crossover and mutation for bus terminal location problem (BTLP). We tested the different parameters of genetic algorithm (for a sample problem) and obtained the optimal parameters for solving BTLP with numerical try and error.

Keywords: Bus networks, Genetic algorithm (GA), Locationproblem, Mixed integer programming (MIP).

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Authors: Rafayel A. Azizyan, Aram E. Gevogyan, Valeri B. Arakelyan, Emil S. Gevorgyan

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The mathematical modeling of different biological processes is usually used to predict or assess behavior of systems in which these processes take place. This study deals with mathematical and computer modeling of bi-substrate enzymatic reactions with ping-pong mechanism, which play an important role in different biochemical pathways. Besides that, three models of competitive inhibition were designed using different software packages. The main objective of this study is to represent the results from in silico investigation of bi-substrate enzymatic reactions with ordered pingpong mechanism in the presence of competitive inhibitors, as well as to describe in details the inhibition effects. The simulation of the models with certain kinetic parameters allowed investigating the behavior of reactions as well as determined some interesting aspects concerning influence of different cases of competitive inhibition. Simultaneous presence of two inhibitors, competitive to the S1 and S2 substrates have been studied. Moreover, we have found the pattern of simultaneous influence of both inhibitors.

Keywords: Mathematical modeling, bi-substrate enzymatic reactions, ping-pong mechanism, competitive inhibition.

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Authors: Oscar Javier Herrera Ochoa, Ivan Dario Romero Fonseca

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This paper presents a design of a model for planning the distribution logistics operation. The significance of this work relies on the applicability of this fact to the analysis of small and medium enterprises (SMEs) of dry freight in Bogotá. Two stages constitute this implementation: the first one is the place where optimal planning is achieved through a hybrid model developed with mixed integer programming, which considers the transhipment operation based on a combined load allocation model as a classic transshipment model; the second one is the specific routing of that operation through the heuristics of Clark and Wright. As a result, an integral model is obtained to carry out the step by step planning of the distribution of dry freight for SMEs in Bogotá. In this manner, optimum assignments are established by utilizing transshipment centers with that purpose of determining the specific routing based on the shortest distance traveled.

Keywords: Transshipment model, mixed integer programming, saving algorithm, dry freight transportation.

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Authors: Danilo López, Nelson Vera, Luis Pedraza

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This paper analyzes fundamental ideas and concepts related to neural networks, which provide the reader a theoretical explanation of Long Short-Term Memory (LSTM) networks operation classified as Deep Learning Systems, and to explicitly present the mathematical development of Backward Pass equations of the LSTM network model. This mathematical modeling associated with software development will provide the necessary tools to develop an intelligent system capable of predicting the behavior of licensed users in wireless cognitive radio networks.

Keywords: Neural networks, multilayer perceptron, long short-term memory, recurrent neuronal network, mathematical analysis.

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Authors: Amin Hajizadeh, Ehsan Hajizadeh

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This paper presents a multi-objective formulation for optimal siting and sizing of distributed generation (DG) resources in distribution systems in order to minimize the cost of power losses and energy not supplied. The implemented technique is based on particle swarm optimization (PSO) and weight method that employed to obtain the best compromise between these costs. Simulation results on 33-bus distribution test system are presented to demonstrate the effectiveness of the proposed procedure.

Keywords: Distributed generation, distribution networks, particle swarm optimization, reliability, weight method

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Authors: Muh. Hisjam, Nancy Oktyajati, Wakhid A. Jauhari, Wahyudi Sutopo

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This research is intended to develop a raw material allocation model in timber processing industry in Perum Perhutani Unit I, Central Java, Indonesia. The model can be used to determine the quantity of allocation of timber between chain in the supply chain to select supplier considering factors that are log price and the distance. In determining the quantity of allocation of timber between chains in the supply chain, the model considers the optimal inventory in each chain. Whilst the optimal inventory is determined based on demand forecast, the capacity and safety stock. Problem solving allocation is conducted by developing linear programming model that aims to minimize the total cost of the purchase, transportation cost and storage costs at each chain. The results of numerical examples show that the proposed model can generate savings of the purchase cost of 20.84% and select suppliers with mileage closer.

Keywords: Allocation model, linear programming, purchase costs, storage costs, suppliers, transportation costs.

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Authors: Ahmed Mateen, Zhu Qingsheng, Faisal Shahzad

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Requirement Engineering (RE) is a part being created for programming structure during the software development lifecycle. Software product line development is a new topic area within the domain of software engineering. It also plays important role in decision making and it is ultimately helpful in rising business environment for productive programming headway. Decisions are central to engineering processes and they hold them together. It is argued that better decisions will lead to better engineering. To achieve better decisions requires that they are understood in detail. In order to address the issues, companies are moving towards Software Product Line Engineering (SPLE) which helps in providing large varieties of products with minimum development effort and cost. This paper proposed a new framework for software product line and compared with other models. The results can help to understand the needs in SPL testing, by identifying points that still require additional investigation. In our future scenario, we will combine this model in a controlled environment with industrial SPL projects which will be the new horizon for SPL process management testing strategies.

Keywords: Requirements engineering, software product lines, scoping, process structure, domain specific language.

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Authors: Watchara Songserm, Teeradej Wuttipornpun

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This paper presents a genetic algorithm based permutation and non-permutation scheduling heuristics (GAPNP) to solve a multi-stage finite capacity material requirement planning (FCMRP) problem in automotive assembly flow shop with unrelated parallel machines. In the algorithm, the sequences of orders are iteratively improved by the GA characteristics, whereas the required operations are scheduled based on the presented permutation and non-permutation heuristics. Finally, a linear programming is applied to minimize the total cost. The presented GAPNP algorithm is evaluated by using real datasets from automotive companies. The required parameters for GAPNP are intently tuned to obtain a common parameter setting for all case studies. The results show that GAPNP significantly outperforms the benchmark algorithm about 30% on average.

Keywords: Finite capacity MRP, genetic algorithm, linear programming, flow shop, unrelated parallel machines, application in industries.

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Authors: A. Pashayev, R. Sadiqov, C. Ardil, F. Ildiz , H. Karabork

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The new technology of fuzzy neural networks for identification of parameters for mathematical models of geofields is proposed and checked. The effectiveness of that soft computing technology is demonstrated, especially in the early stage of modeling, when the information is uncertain and limited.

Keywords: Identification, interpolation methods, neuro-fuzzy networks, geofield.

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Authors: Dong-Joong Kim, Sangho Choi, Woong Lim

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This paper discusses Sfard’s commognitive approach and provides an empirical study as an example to illustrate the theory as method. Traditionally, research in mathematics education focused on the acquisition of mathematical knowledge and the didactic process of knowledge transfer. Through attending to a distinctive form of language in mathematics, as well as mathematics as a discursive subject, alternative views of making meaning in mathematics have emerged; these views are therefore “critical,” as in critical discourse analysis. The commognitive discourse analysis method has the potential to bring more clarity to our understanding of students’ mathematical thinking and the process through which students are socialized into school mathematics.

Keywords: Commognitive framework, discourse analysis, mathematical discourse, mathematics education.

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Authors: Yiming Nie, Tao Wu, Xiangjing An, Hangen He

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Fast depth estimation from binocular vision is often desired for autonomous vehicles, but, most algorithms could not easily be put into practice because of the much time cost. We present an image-processing technique that can fast estimate depth image from binocular vision images. By finding out the lines which present the best matched area in the disparity space image, the depth can be estimated. When detecting these lines, an edge-emphasizing filter is used. The final depth estimation will be presented after the smooth filter. Our method is a compromise between local methods and global optimization.

Keywords: Depth estimation, image filters, stereo match.

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Authors: Edikan E. Akpanibah, Ogunmodimu Dupe Catherine

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The relevance of geometric Brownian motion (GBM) in modelling the behaviour of stock market prices (SMP) cannot be over emphasized taking into consideration the volatility of the SMP. Consequently, there is need to investigate how GBM models are being estimated and used in financial market to predict SMP. To achieve this, the GBM estimation and its application to the SMP of some selected companies are studied. The normal and log-normal distributions were used to determine the expected value, variance and co-variance. Furthermore, the GBM model was used to predict the SMP of some selected companies over a period of time and the mean absolute percentage error (MAPE) were calculated and used to determine the accuracy of the GBM model in predicting the SMP of the four companies under consideration. It was observed that for all the four companies, their MAPE values were within the region of acceptance. Also, the MAPE values of our data were compared to an existing literature to test the accuracy of our prediction with respect to time of investment. Finally, some numerical simulations of the graphs of the SMP, expectations and variance of the four companies over a period of time were presented using MATLAB programming software.

Keywords: Stock Market, Geometric Brownian Motion, normal and log-normal distribution, mean absolute percentage error.

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Authors: M. Ravindra, R. Srinivasa Rao, V. Shanmukha Naga Raju

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This paper presents state estimation with Phasor Measurement Unit (PMU) allocation to obtain complete observability of network. A matrix is designed with modeling of zero injection constraints to minimize PMU allocations. State estimation algorithm is developed with optimal allocation of PMUs to find accurate states of network. The incorporation of PMU into traditional state estimation process improves accuracy and computational performance for large power systems. The nonlinearity integrated with zero injection (ZI) constraints is remodeled to linear frame to optimize number of PMUs. The problem of optimal PMU allocation is regarded with modeling of ZI constraints, PMU loss or line outage, cost factor and redundant measurements. The proposed state estimation with optimal PMU allocation has been compared with traditional state estimation process to show its importance. MATLAB programming on IEEE 14, 30, 57, and 118 bus networks is implemented out by Binary Integer Programming (BIP) method and compared with other methods to show its effectiveness.

Keywords: Observability, phasor measurement units, synchrophasors, SCADA measurements, zero injection bus.

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Authors: Ririn Dewi Cahyani, Muh. Hisjam, Wahyudi Sutopo, Kuncoro Harto Widodo

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Availability of raw materials is important for Indonesia as a furniture exporting country. Teak log as raw materials is supplied to the furniture industry by Perum Perhutani (PP). PP needs to involve carbon trading for nature conservation. PP also has an obligation in the Corporate Social Responsibility program. PP and furniture industry also must prosecute the regulations related to ecological issues and labor rights. This study has the objective to create the relationship model between supplier and manufacturer to fulfill teak log demand that involving teak forest carbon sequestration. A model is formulated as Goal Programming to get the favorable solution for teak log procurement and support carbon sequestration that considering economical, ecological, and social aspects of both supplier and manufacturer. The results show that the proposed model can be used to determine the teak log quantity involving carbon trading to achieve the seven goals to be satisfied the sustainability considerations.

Keywords: Availability of teak log, support carbon sequestration, goal programming, sustainability consideration.

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Authors: Oluwaseun K. Oyebode, Josiah A. Adeyemo

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Hydrological modelling plays a crucial role in the planning and management of water resources, most especially in water stressed regions where the need to effectively manage the available water resources is of critical importance. However, due to the complex, nonlinear and dynamic behaviour of hydro-climatic interactions, achieving reliable modelling of water resource systems and accurate projection of hydrological parameters are extremely challenging. Although a significant number of modelling techniques (process-based and data-driven) have been developed and adopted in that regard, the field of hydrological modelling is still considered as one that has sluggishly progressed over the past decades. This is majorly as a result of the identification of some degree of uncertainty in the methodologies and results of techniques adopted. In recent times, evolutionary computation (EC) techniques have been developed and introduced in response to the search for efficient and reliable means of providing accurate solutions to hydrological related problems. This paper presents a comprehensive review of the underlying principles, methodological needs and applications of a promising evolutionary computation modelling technique – genetic programming (GP). It examines the specific characteristics of the technique which makes it suitable to solving hydrological modelling problems. It discusses the opportunities inherent in the application of GP in water related-studies such as rainfall estimation, rainfall-runoff modelling, streamflow forecasting, sediment transport modelling, water quality modelling and groundwater modelling among others. Furthermore, the means by which such opportunities could be harnessed in the near future are discussed. In all, a case for total embracement of GP and its variants in hydrological modelling studies is made so as to put in place strategies that would translate into achieving meaningful progress as it relates to modelling of water resource systems, and also positively influence decision-making by relevant stakeholders.

Keywords: Computational modelling, evolutionary algorithms, genetic programming, hydrological modelling.

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Authors: Robert L. Burdett, Bayan Bevrani

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Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways, these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

Keywords: Capacity analysis, capacity expansion, railways.

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Authors: Evgeniy Burlutskiy

Abstract:

The paper presents a one-dimensional transient mathematical model of thermal oil-water two-phase emulsion flows in pipes. The set of the mass, momentum and enthalpy conservation equations for the continuous fluid and droplet phases are solved. Two friction correlations for the continuous fluid phase to wall friction are accounted for in the model and tested. The aerodynamic drag force between the continuous fluid phase and droplets is modeled, too. The density and viscosity of both phases are assumed to be constant due to adiabatic experimental conditions. The proposed mathematical model is validated on the experimental measurements of oil-water emulsion flows in horizontal pipe [1,2]. Numerical analysis on single- and two-phase oil-water flows in a pipe is presented in the paper. The continuous oil flow having water droplets is simulated. Predictions, which are performed by using the presented model, show excellent agreement with the experimental data if the water fraction is equal or less than 10%. Disagreement between simulations and measurements is increased if the water fraction is larger than 10%.

Keywords: Mathematical model, Oil-Water, Pipe flows.

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Authors: S. Bennoud, M. Zergoug

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The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models.

The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces.

The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations.

In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: Eddy current, Finite element method, Non destructive testing, Numerical simulations.

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