Search results for: reliability constraints.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1239

Search results for: reliability constraints.

759 Static and Dynamic Complexity Analysis of Software Metrics

Authors: Kamaljit Kaur, Kirti Minhas, Neha Mehan, Namita Kakkar

Abstract:

Software complexity metrics are used to predict critical information about reliability and maintainability of software systems. Object oriented software development requires a different approach to software complexity metrics. Object Oriented Software Metrics can be broadly classified into static and dynamic metrics. Static Metrics give information at the code level whereas dynamic metrics provide information on the actual runtime. In this paper we will discuss the various complexity metrics, and the comparison between static and dynamic complexity.

Keywords: Static Complexity, Dynamic Complexity, Halstead Metric, Mc Cabe's Metric.

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758 Categorical Data Modeling: Logistic Regression Software

Authors: Abdellatif Tchantchane

Abstract:

A Matlab based software for logistic regression is developed to enhance the process of teaching quantitative topics and assist researchers with analyzing wide area of applications where categorical data is involved. The software offers an option of performing stepwise logistic regression to select the most significant predictors. The software includes a feature to detect influential observations in data, and investigates the effect of dropping or misclassifying an observation on a predictor variable. The input data may consist either as a set of individual responses (yes/no) with the predictor variables or as grouped records summarizing various categories for each unique set of predictor variables' values. Graphical displays are used to output various statistical results and to assess the goodness of fit of the logistic regression model. The software recognizes possible convergence constraints when present in data, and the user is notified accordingly.

Keywords: Logistic regression, Matlab, Categorical data, Influential observation.

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757 Neural Network Controller for Mobile Robot Motion Control

Authors: Jasmin Velagic, Nedim Osmic, Bakir Lacevic

Abstract:

In this paper the neural network-based controller is designed for motion control of a mobile robot. This paper treats the problems of trajectory following and posture stabilization of the mobile robot with nonholonomic constraints. For this purpose the recurrent neural network with one hidden layer is used. It learns relationship between linear velocities and error positions of the mobile robot. This neural network is trained on-line using the backpropagation optimization algorithm with an adaptive learning rate. The optimization algorithm is performed at each sample time to compute the optimal control inputs. The performance of the proposed system is investigated using a kinematic model of the mobile robot.

Keywords: Mobile robot, kinematic model, neural network, motion control, adaptive learning rate.

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756 Expert System for Chose Material used Gears

Authors: E.V. Butilă, F. Gîrbacia

Abstract:

In order to give high expertise the computer aided design of mechanical systems involves specific activities focused on processing two type of information: knowledge and data. Expert rule based knowledge is generally processing qualitative information and involves searching for proper solutions and their combination into synthetic variant. Data processing is based on computational models and it is supposed to be inter-related with reasoning in the knowledge processing. In this paper an Intelligent Integrated System is proposed, for the objective of choosing the adequate material. The software is developed in Prolog – Flex software and takes into account various constraints that appear in the accurate operation of gears.

Keywords: Expert System, computer aided design, gear boxdesign, chose material, Prolog, Flex

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755 Embodied Carbon Footprint of Existing Malaysian Green Homes

Authors: Fahanim Abdul Rashid, Muhammad Azzam Ismail

Abstract:

Part and parcel of building green homes (GHs) with favorable thermal comfort (TC) is to design and build with reduced carbon footprint (CF) from embodied energy in the building envelope and reduced operational CF overall. Together, the environmental impact of GHs can be reduced significantly. Nevertheless, there is still a need to identify the base CF value for Malaysian GHs and this can be done by assessing existing ones which can then be compared to conventional and vernacular houses which are built differently with different building materials. This paper underlines the research design and introduces the case studies. For now, the operational CF of the case studies is beyond the scope of this study. Findings from this research could identify the best building material and construction technique combination to build GHs depending on the available skills, financial constraints and the condition of the immediate environment.

Keywords: Embodied carbon footprint, Malaysian green homes.

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754 Integral Methods in the Determination of Temperature Fields of Cooled Blades of Gas Turbines

Authors: C. Ardil

Abstract:

A mathematical model and an effective numerical method for calculating the temperature field of the profile part of convection cooled blades have been developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli.The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations.The reliability of the developed methods is confirmed by the calculation-experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of a gas turbine.

Keywords: Integral methods, determination of temperature fields, cooled blades, gas turbines.

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753 Numerical Modeling of Temperature Fields in Aviation Gas Turbine Elements

Authors: A. M. Pashaev, R. A. Sadihov, A. S. Samedov, C. Ardil

Abstract:

A mathematical model and a numerical method for computing the temperature field of the profile part of convectionally cooled blades are developed. The theoretical substantiation of the method is proved by corresponding theorems. To this end, convergent quadrature processes were developed and error estimates were obtained in terms of the Zygmund continuity moduli. The boundary conditions for heat exchange are determined from the solution of the corresponding integral equations and empirical relations. The reliability of the developed methods is confirmed by calculation and experimental studies of the thermohydraulic characteristics of the nozzle apparatus of the first stage of the gas turbine.

Keywords: Aviation gas turbine, temperature field, cooled blades, numerical modeling.

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752 STATISTICA Software: A State of the Art Review

Authors: S. Sarumathi, N. Shanthi, S. Vidhya, P. Ranjetha

Abstract:

Data mining idea is mounting rapidly in admiration and also in their popularity. The foremost aspire of data mining method is to extract data from a huge data set into several forms that could be comprehended for additional use. The data mining is a technology that contains with rich potential resources which could be supportive for industries and businesses that pay attention to collect the necessary information of the data to discover their customer’s performances. For extracting data there are several methods are available such as Classification, Clustering, Association, Discovering, and Visualization… etc., which has its individual and diverse algorithms towards the effort to fit an appropriate model to the data. STATISTICA mostly deals with excessive groups of data that imposes vast rigorous computational constraints. These results trials challenge cause the emergence of powerful STATISTICA Data Mining technologies. In this survey an overview of the STATISTICA software is illustrated along with their significant features.

Keywords: Data Mining, STATISTICA Data Miner, Text Miner, Enterprise Server, Classification, Association, Clustering, Regression.

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751 Reconfiguration of Deregulated Distribution Network for Minimizing Energy Supply Cost by using Multi-Objective BGA

Authors: H. Kazemi Karegar, S. Jalilzadeh, V. Nabaei, A. Shabani

Abstract:

In this paper, the problem of finding the optimal topological configuration of a deregulated distribution network is considered. The new features of this paper are proposing a multiobjective function and its application on deregulated distribution networks for finding the optimal configuration. The multi-objective function will be defined for minimizing total Energy Supply Costs (ESC) and energy losses subject to load flow constraints. The optimal configuration will be obtained by using Binary Genetic Algorithm (BGA).The proposed method has been tested to analyze a sample and a practical distribution networks.

Keywords: Binary Genetic Algorithm, Deregulated Distribution Network, Minimizing Cost, Reconfiguration.

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750 The Study on Mechanical Properties of Graphene Using Molecular Mechanics

Authors: I-Ling Chang, Jer-An Chen

Abstract:

The elastic properties and fracture of two-dimensional graphene were calculated purely from the atomic bonding (stretching and bending) based on molecular mechanics method. Considering the representative unit cell of graphene under various loading conditions, the deformations of carbon bonds and the variations of the interlayer distance could be realized numerically under the geometry constraints and minimum energy assumption. In elastic region, it was found that graphene was in-plane isotropic. Meanwhile, the in-plane deformation of the representative unit cell is not uniform along armchair direction due to the discrete and non-uniform distributions of the atoms. The fracture of graphene could be predicted using fracture criteria based on the critical bond length, over which the bond would break. It was noticed that the fracture behavior were directional dependent, which was consistent with molecular dynamics simulation results.

Keywords: Energy minimization, fracture, graphene, molecular mechanics.

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749 The Development of Decision Support System for Waste Management; a Review

Authors: M. S. Bani, Z. A. Rashid, K. H. K. Hamid, M. E. Harbawi, A.B.Alias, M. J. Aris

Abstract:

Most Decision Support Systems (DSS) for waste management (WM) constructed are not widely marketed and lack practical applications. This is due to the number of variables and complexity of the mathematical models which include the assumptions and constraints required in decision making. The approach made by many researchers in DSS modelling is to isolate a few key factors that have a significant influence to the DSS. This segmented approach does not provide a thorough understanding of the complex relationships of the many elements involved. The various elements in constructing the DSS must be integrated and optimized in order to produce a viable model that is marketable and has practical application. The DSS model used in assisting decision makers should be integrated with GIS, able to give robust prediction despite the inherent uncertainties of waste generation and the plethora of waste characteristics, and gives optimal allocation of waste stream for recycling, incineration, landfill and composting.

Keywords: Review, decision support system, GIS and waste management.

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748 Stability of Electrical Drives Supplied by a Three Level Inverter

Authors: M. S. Kelaiaia, H. Labar, S. Kelaiaia, T. Mesbah

Abstract:

The development of the power electronics has allowed increasing the precision and reliability of the electrical devices, thanks to the adjustable inverters, as the Pulse Wide Modulation (PWM) applied to the three level inverters, which is the object of this study. The authors treat the relation between the law order adopted for a given system and the oscillations of the electrical and mechanical parameters of which the tolerance depends on the process with which they are integrated (paper factory, lifting of the heavy loads, etc.).Thus, the best choice of the regulation indexes allows us to achieve stability and safety training without investment (management of existing equipment). The optimal behavior of any electric device can be achieved by the minimization of the stored electrical and mechanical energy.

Keywords: Multi level inverter, PWM, Harmonics, oscillation, control.

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747 Design and Implementation of Rule-based Expert System for Fault Management

Authors: Su Myat Marlar Soe, May Paing Paing Zaw

Abstract:

It has been defined that the “network is the system". This implies providing levels of service, reliability, predictability and availability that are commensurate with or better than those that individual computers provide today. To provide this requires integrated network management for interconnected networks of heterogeneous devices covering both the local campus. In this paper we are addressing a framework to effectively deal with this issue. It consists of components and interactions between them which are required to perform the service fault management. A real-world scenario is used to derive the requirements which have been applied to the component identification. An analysis of existing frameworks and approaches with respect to their applicability to the framework is also carried out.

Keywords: To diagnose the possible network faults by using thepredetermined rules.

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746 Generation Scheduling Optimization of Multi-Hydroplants: A Case Study

Authors: Shuangquan Liu, Jinwen Wang, Dada Wang

Abstract:

A case study of the generation scheduling optimization of the multi-hydroplants on the Yuan River Basin in China is reported in this paper. Concerning the uncertainty of the inflows, the long/mid-term generation scheduling (LMTGS) problem is solved by a stochastic model in which the inflows are considered as stochastic variables. For the short-term generation scheduling (STGS) problem, a constraint violation priority is defined in case not all constraints are satisfied. Provided the stage-wise separable condition and low dimensions, the hydroplant-based operational region schedules (HBORS) problem is solved by dynamic programming (DP). The coordination of LMTGS and STGS is presented as well. The feasibility and the effectiveness of the models and solution methods are verified by the numerical results.

Keywords: generation scheduling, multi-hydroplants, optimization.

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745 Mathematical Model and Solution Algorithm for Containership Operation/Maintenance Scheduling

Authors: Hun Go, Ji-Su Kim, Dong-Ho Lee

Abstract:

This study considers the problem of determining operation and maintenance schedules for a containership equipped with components during its sailing according to a pre-determined navigation schedule. The operation schedule, which specifies work time of each component, determines the due-date of each maintenance activity, and the maintenance schedule specifies the actual start time of each maintenance activity. The main constraints are component requirements, workforce availability, working time limitation, and inter-maintenance time. To represent the problem mathematically, a mixed integer programming model is developed. Then, due to the problem complexity, we suggest a heuristic for the objective of minimizing the sum of earliness and tardiness between the due-date and the starting time of each maintenance activity. Computational experiments were done on various test instances and the results are reported.

Keywords: Containerships, operation and preventive maintenance schedules, integer programming, heuristic

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744 Modeling the Vapor Pressure of Biodiesel Fuels

Authors: O. Castellanos Díaz, F. Schoeggl, H. W. Yarranton, M. A. Satyro, T. M. Lovestead, T. J. Bruno

Abstract:

The composition, vapour pressure, and heat capacity of nine biodiesel fuels from different sources were measured. The vapour pressure of the biodiesel fuels is modeled assuming an ideal liquid phase of the fatty acid methyl esters constituting the fuel. New methodologies to calculate the vapour pressure and ideal gas and liquid heat capacities of the biodiesel fuel constituents are proposed. Two alternative optimization scenarios are evaluated: 1) vapour pressure only; 2) vapour pressure constrained with liquid heat capacity. Without physical constraints, significant errors in liquid heat capacity predictions were found whereas the constrained correlation accurately fit both vapour pressure and liquid heat capacity.

Keywords: Biodiesel fuels, Fatty acid methyl ester, Heat capacity, Modeling, Vapour pressure

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743 An Aggregate Production Planning Model for Brass Casting Industry in Fuzzy Environment

Authors: Ömer Faruk Baykoç, Ümit Sami Sakalli

Abstract:

In this paper, we propose a fuzzy aggregate production planning (APP) model for blending problem in a brass factory which is the problem of computing optimal amounts of raw materials for the total production of several types of brass in a period. The model has deterministic and imprecise parameters which follows triangular possibility distributions. The brass casting APP model can not always be solved by using common approaches used in the literature. Therefore a mathematical model is presented for solving this problem. In the proposed model, the Lai and Hwang-s fuzzy ranking concept is relaxed by using one constraint instead of three constraints. An application of the brass casting APP model in a brass factory shows that the proposed model successfully solves the multi-blend problem in casting process and determines the optimal raw material purchasing policies.

Keywords: Aggregate production planning, Blending, brasscasting, possibilistic programming.

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742 Forces Association-Based Active Contour

Authors: Aicha Baya Goumeidane, Nafaa. Nacereddine

Abstract:

A welded structure must be inspected to guarantee that the weld quality meets the design requirements to assure safety and reliability. However, X-ray image analyses and defect recognition with the computer vision techniques are very complex. Most difficulties lie in finding the small, irregular defects in poor contrast images which requires pre processing to image, extract, and classify features from strong background noise. This paper addresses the issue of designing methodology to extract defect from noisy background radiograph with image processing. Based on the use of actives contours this methodology seems to give good results

Keywords: Welding, Radiography, Computer vision, Active contour.

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741 Survival of Neutrino Mass Models in Nonthermal Leptogenesis

Authors: Amal Kr Sarma, H Zeen Devi, N Nimai Singh

Abstract:

The Constraints imposed by non-thermal leptogenesis on the survival of the neutrino mass models describing the presently available neutrino mass patterns, are studied numerically. We consider the Majorana CP violating phases coming from right-handed Majorana mass matrices to estimate the baryon asymmetry of the universe, for different neutrino mass models namely quasi-degenerate, inverted hierarchical and normal hierarchical models, with tribimaximal mixings. Considering two possible diagonal forms of Dirac neutrino mass matrix as either charged lepton or up-quark mass matrix, the heavy right-handed mass matrices are constructed from the light neutrino mass matrix. Only the normal hierarchical model leads to the best predictions of baryon asymmetry of the universe, consistent with observations in non-thermal leptogenesis scenario.

Keywords: Thermal leptogenesis, Non-thermal leptogenesis.

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740 An Analytical Framework for Multi-Site Supply Chain Planning Problems

Authors: Yin-Yann Chen

Abstract:

As the gradual increase of the enterprise scale, the firms may possess many manufacturing plants located in different places geographically. This change will result in the multi-site production planning problems under the environment of multiple plants or production resources. Our research proposes the structural framework to analyze the multi-site planning problems. The analytical framework is composed of six elements: multi-site conceptual model, product structure (bill of manufacturing), production strategy, manufacturing capability and characteristics, production planning constraints, and key performance indicators. As well as the discussion of these six ingredients, we also review related literatures in this paper to match our analytical framework. Finally we take a real-world practical example of a TFT-LCD manufacturer in Taiwan to explain our proposed analytical framework for the multi-site production planning problems.

Keywords: Multi-Site, Production Planning, Supply Chain, TFT-LCD.

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739 Impact of MAC Layer on the Performance of Routing Protocols in Mobile Ad hoc Networks

Authors: T.G. Basavaraju, Subir Kumar Sarkar, C Puttamadappa

Abstract:

Mobile Ad hoc Networks is an autonomous system of mobile nodes connected by multi-hop wireless links without centralized infrastructure support. As mobile communication gains popularity, the need for suitable ad hoc routing protocols will continue to grow. Efficient dynamic routing is an important research challenge in such a network. Bandwidth constrained mobile devices use on-demand approach in their routing protocols because of its effectiveness and efficiency. Many researchers have conducted numerous simulations for comparing the performance of these protocols under varying conditions and constraints. Most of them are not aware of MAC Protocols, which will impact the relative performance of routing protocols considered in different network scenarios. In this paper we investigate the choice of MAC protocols affects the relative performance of ad hoc routing protocols under different scenarios. We have evaluated the performance of these protocols using NS2 simulations. Our results show that the performance of routing protocols of ad hoc networks will suffer when run over different MAC Layer protocols.

Keywords: AODV, DSR, DSDV, MAC, MANETs, relativeperformance

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738 An Innovative Approach to the Formulation of Connection Admission Control Problem

Authors: Carlo Bruni, Francesco Delli Priscoli, Giorgio Koch, Ilaria Marchetti

Abstract:

This paper proposes an innovative approach for the Connection Admission Control (CAC) problem. Starting from an abstract network modelling, the CAC problem is formulated in a technology independent fashion allowing the proposed concepts to be applied to any wireless and wired domain. The proposed CAC is decoupled from the other Resource Management procedures, but cooperates with them in order to guarantee the desired QoS requirements. Moreover, it is based on suitable performance measurements which, by using proper predictors, allow to forecast the domain dynamics in the next future. Finally, the proposed CAC control scheme is based on a feedback loop aiming at maximizing a suitable performance index accounting for the domain throughput, whilst respecting a set of constraints accounting for the QoS requirements.

Keywords: Network Management, Quality of Service (QoS) requirements, Optimal Control.

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737 Airport Check-In Optimization by IP and Simulation in Combination

Authors: Ahmad Thanyan Al-Sultan

Abstract:

The check-in area of airport terminal is one of the busiest sections at airports at certain periods. The passengers are subjected to queues and delays during the check-in process. These delays and queues are due to constraints in the capacity of service facilities. In this project, the airport terminal is decomposed into several check-in areas. The airport check-in scheduling problem requires both a deterministic (integer programming) and stochastic (simulation) approach. Integer programming formulations are provided to minimize the total number of counters in each check-in area under the realistic constraint that counters for one and the same flight should be adjacent and the desired number of counters remaining in each area should be fixed during check-in operations. By using simulation, the airport system can be modeled to study the effects of various parameters such as number of passengers on a flight and check-in counter opening and closing time.

Keywords: Airport terminal, Integer programming, Scheduling, Simulation.

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736 A Preliminary Study for Design of Automatic Block Reallocation Algorithm with Genetic Algorithm Method in the Land Consolidation Projects

Authors: Tayfun Çay, Yaşar İnceyol, Abdurrahman Özbeyaz

Abstract:

Land reallocation is one of the most important steps in land consolidation projects. Many different models were proposed for land reallocation in the literature such as Fuzzy Logic, block priority based land reallocation and Spatial Decision Support Systems. A model including four parts is considered for automatic block reallocation with genetic algorithm method in land consolidation projects. These stages are preparing data tables for a project land, determining conditions and constraints of land reallocation, designing command steps and logical flow chart of reallocation algorithm and finally writing program codes of Genetic Algorithm respectively. In this study, we designed the first three steps of the considered model comprising four steps.

Keywords: Genetic algorithm, land consolidation, landholding, land reallocation.

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735 Economic Dispatch Fuzzy Linear Regression and Optimization

Authors: A. K. Al-Othman

Abstract:

This study presents a new approach based on Tanaka's fuzzy linear regression (FLP) algorithm to solve well-known power system economic load dispatch problem (ELD). Tanaka's fuzzy linear regression (FLP) formulation will be employed to compute the optimal solution of optimization problem after linearization. The unknowns are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the unknowns. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the unknowns, subject to double inequality constraints. Linear programming technique is employed to obtain the middle and the symmetric spread for every unknown (power generation level). Simulation results of the proposed approach will be compared with those reported in literature.

Keywords: Economic Dispatch, Fuzzy Linear Regression (FLP)and Optimization.

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734 Low Cost Chip Set Selection Algorithm for Multi-way Partitioning of Digital System

Authors: Jae Young Park, Soongyu Kwon, Kyu Han Kim, Hyeong Geon Lee, Jong Tae Kim

Abstract:

This paper considers the problem of finding low cost chip set for a minimum cost partitioning of a large logic circuits. Chip sets are selected from a given library. Each chip in the library has a different price, area, and I/O pin. We propose a low cost chip set selection algorithm. Inputs to the algorithm are a netlist and a chip information in the library. Output is a list of chip sets satisfied with area and maximum partitioning number and it is sorted by cost. The algorithm finds the sorted list of chip sets from minimum cost to maximum cost. We used MCNC benchmark circuits for experiments. The experimental results show that all of chip sets found satisfy the multiple partitioning constraints.

Keywords: lowest cost chip set, MCNC benchmark, multi-way partitioning.

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733 Liquid-Liquid Equilibrium Data for Butan-2-ol - Ethanol - Water, Pentan-1-ol - Ethanol - Water and Toluene - Acetone - Water Systems

Authors: Tinuade Jolaade Afolabi, Theresa Ibibia Edewor

Abstract:

Experimental liquid-liquid equilibra of butan-2-ol - ethanol -water; pentan-1-ol - ethanol - water and toluene - acetone - water ternary systems were investigated at (25oC). The reliability of the experimental tie-line data was ascertained by using Othmer-Tobias and Hand plots. The distribution coefficients (D) and separation factors (S) of the immiscibility region were evaluated for the three systems.

Keywords: Distribution coefficient, Liquid-liquid equilibrium, separation factors, thermodynamic models

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732 A Fuzzy Mathematical Model for Order Acceptance and Scheduling Problem

Authors: E. Koyuncu

Abstract:

The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: Fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling.

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731 Hybrid Hierarchical Routing Protocol for WSN Lifetime Maximization

Authors: H. Aoudia, Y. Touati, E. H. Teguig, A. Ali Cherif

Abstract:

Conceiving and developing routing protocols for wireless sensor networks requires considerations on constraints such as network lifetime and energy consumption. In this paper, we propose a hybrid hierarchical routing protocol named HHRP combining both clustering mechanism and multipath optimization taking into account residual energy and RSSI measures. HHRP consists of classifying dynamically nodes into clusters where coordinators nodes with extra privileges are able to manipulate messages, aggregate data and ensure transmission between nodes according to TDMA and CDMA schedules. The reconfiguration of the network is carried out dynamically based on a threshold value which is associated with the number of nodes belonging to the smallest cluster. To show the effectiveness of the proposed approach HHRP, a comparative study with LEACH protocol is illustrated in simulations.

Keywords: Routing protocols, energy optimization, clustering.

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730 Modeling Hybrid Systems with MLD Approach and Analysis of the Model Size and Complexity

Authors: H. Mahboubi, B. Moshiri, A. Khaki Seddigh

Abstract:

Recently, a great amount of interest has been shown in the field of modeling and controlling hybrid systems. One of the efficient and common methods in this area utilizes the mixed logicaldynamical (MLD) systems in the modeling. In this method, the system constraints are transformed into mixed-integer inequalities by defining some logic statements. In this paper, a system containing three tanks is modeled as a nonlinear switched system by using the MLD framework. Comparing the model size of the three-tank system with that of a two-tank system, it is deduced that the number of binary variables, the size of the system and its complexity tremendously increases with the number of tanks, which makes the control of the system more difficult. Therefore, methods should be found which result in fewer mixed-integer inequalities.

Keywords: Hybrid systems, mixed-integer inequalities, mixed logical dynamical systems, multi-tank system.

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