Search results for: a method of problem solving.

Authors: Morteza Kazemi Torbaghan, Seyed Mehran Kazemi, Rahele Zhiani, Fakhriye Hamed

Abstract:

Truss optimization problem has been vastly studied during the past 30 years and many different methods have been proposed for this problem. Even though most of these methods assume that the design variables are continuously valued, in reality, the design variables of optimization problems such as cross-sectional areas are discretely valued. In this paper, an improved hill climbing and an improved simulated annealing algorithm have been proposed to solve the truss optimization problem with discrete values for crosssectional areas. Obtained results have been compared to other methods in the literature and the comparison represents that the proposed methods can be used more efficiently than other proposed methods

Keywords: Size Optimization of Trusses, Hill Climbing, Simulated Annealing.

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Authors: Sami Baraketi, Jean-Marie Garcia, Olivier Brun

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Wavelength Division Multiplexing (WDM) is the dominant transport technology used in numerous high capacity backbone networks, based on optical infrastructures. Given the importance of costs (CapEx and OpEx) associated to these networks, resource management is becoming increasingly important, especially how the optical circuits, called “lightpaths”, are routed throughout the network. This requires the use of efficient algorithms which provide routing strategies with the lowest cost. We focus on the lightpath routing and wavelength assignment problem, known as the RWA problem, while optimizing wavelength fragmentation over the network. Wavelength fragmentation poses a serious challenge for network operators since it leads to the misuse of the wavelength spectrum, and then to the refusal of new lightpath requests. In this paper, we first establish a new Integer Linear Program (ILP) for the problem based on a node-link formulation. This formulation is based on a multilayer approach where the original network is decomposed into several network layers, each corresponding to a wavelength. Furthermore, we propose an efficient heuristic for the problem based on a greedy algorithm followed by a post-treatment procedure. The obtained results show that the optimal solution is often reached. We also compare our results with those of other RWA heuristic methods

Keywords: WDM, lightpath, RWA, wavelength fragmentation, optimization, linear programming, heuristic

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Authors: Svitov David, Alyamkin Sergey

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The usage of convolutional neural networks (CNNs) in conjunction with the margin-based softmax approach demonstrates the state-of-the-art performance for the face recognition problem. Recently, lightweight neural network models trained with the margin-based softmax have been introduced for the face identification task for edge devices. In this paper, we propose a distillation method for lightweight neural network architectures that outperforms other known methods for the face recognition task on LFW, AgeDB-30 and Megaface datasets. The idea of the proposed method is to use class centers from the teacher network for the student network. Then the student network is trained to get the same angles between the class centers and face embeddings predicted by the teacher network.

Keywords: ArcFace, distillation, face recognition, margin-based softmax.

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Authors: A. K. Al-Othman

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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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Authors: Wahyudin P. Syam, Ibrahim M. Al-Harkan

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This study compares three meta heuristics to minimize makespan (Cmax) for Hybrid Flow Shop (HFS) Scheduling Problem with Parallel Machines. This problem is known to be NP-Hard. This study proposes three algorithms among improvement heuristic searches which are: Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS). SA and TS are known as deterministic improvement heuristic search. GA is known as stochastic improvement heuristic search. A comprehensive comparison from these three improvement heuristic searches is presented. The results for the experiments conducted show that TS is effective and efficient to solve HFS scheduling problems.

Keywords: Flow shop, genetic algorithm, simulated annealing, tabu search.

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Authors: Theologos Athanaselis, Stelios Bakamidis, Ioannis Dologlou

Abstract:

There are multiple reasons to expect that detecting the word order errors in a text will be a difficult problem, and detection rates reported in the literature are in fact low. Although grammatical rules constructed by computer linguists improve the performance of grammar checker in word order diagnosis, the repairing task is still very difficult. This paper presents an approach for repairing word order errors in English text by reordering words in a sentence and choosing the version that maximizes the number of trigram hits according to a language model. The novelty of this method concerns the use of an efficient confusion matrix technique for reordering the words. The comparative advantage of this method is that works with a large set of words, and avoids the laborious and costly process of collecting word order errors for creating error patterns.

Keywords: Permutations filtering, Statistical languagemodel N-grams, Word order errors

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Authors: Sajjad Farashi

Abstract:

Neurons in the nervous system communicate with each other by producing electrical signals called spikes. To investigate the physiological function of nervous system it is essential to study the activity of neurons by detecting and sorting spikes in the recorded signal. In this paper a method is proposed for considering the spike sorting problem which is based on the nonlinear modeling of spikes using exponential autoregressive model. The genetic algorithm is utilized for model parameter estimation. In this regard some selected model coefficients are used as features for sorting purposes. For optimal selection of model coefficients, self-organizing feature map is used. The results show that modeling of spikes with nonlinear autoregressive model outperforms its linear counterpart. Also the extracted features based on the coefficients of exponential autoregressive model are better than wavelet based extracted features and get more compact and well-separated clusters. In the case of spikes different in small-scale structures where principal component analysis fails to get separated clouds in the feature space, the proposed method can obtain well-separated cluster which removes the necessity of applying complex classifiers.

Keywords: Exponential autoregressive model, Neural data, spike sorting, time series modeling.

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Authors: Guyue Zhu, Liangping Hong

Abstract:

Chinese overall urban design faces a large number of problems such as the neglect of urban characteristics, generalization of content, and difficulty in implementation. Focusing on these issues, this paper proposes the main points of shaping urban characteristics in overall urban design: focuses on core problems in city function and scale, landscape pattern, historical culture, social resources and modern city style and digs the urban characteristic genes. Then, we put forward “core problem location and characteristic gene enhancement” as a kind of overall urban design technical method. Firstly, based on the main problems in urban space as a whole, for the operability goal, the method extracts the key genes and integrates into the multi-dimension system in a targeted manner. Secondly, hierarchical management and guidance system is established which may be in line with administrative management. Finally, by converting the results, action plan is drawn up that can be dynamically implemented. Based on the above idea and method, a practical exploration has been performed in the case of Xiangyang central city.

Keywords: City characteristics, overall urban design, planning implementation, Xiangyang central city.

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Authors: A. M. El-Zonkoly

Abstract:

In this paper, based on steady-state models of Flexible AC Transmission System (FACTS) devices, the sizing of static synchronous series compensator (SSSC) controllers in transmission network is formed as an optimization problem. The objective of this problem is to reduce the transmission losses in the network. The optimization problem is solved using particle swarm optimization (PSO) technique. The Newton-Raphson load flow algorithm is modified to consider the insertion of the SSSC devices in the network. A numerical example, illustrating the effectiveness of the proposed algorithm, is introduced. In addition, a novel model of a 3- phase voltage source converter (VSC) that is suitable for series connected FACTS a controller is introduced. The model is verified by simulation using Power System Blockset (PSB) and Simulink software.

Keywords: FACTS, Modeling, PSO, SSSC, Transmission lossreduction.

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Authors: Wenyu Song, Bingxi Li, Zhongbin Fu, Bo Zhang

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Although water only takes a little percentage in the total mass of soil, it indeed plays an important role to the strength of structure. Moisture transfer can be carried out by many different mechanisms which may involve heat and mass transfer, thermodynamic phase change, and the interplay of various forces such as viscous, buoyancy, and capillary forces. The continuum models are not well suited for describing those phenomena in which the connectivity of the pore space or the fracture network, or that of a fluid phase, plays a major role. However, Lattice Boltzmann methods (LBMs) are especially well suited to simulate flows around complex geometries. Lattice Boltzmann methods were initially invented for solving fluid flows. Recently, fluid with multicomponent and phase change is also included in the equations. By comparing the numerical result with experimental result, the Lattice Boltzmann methods with phase change will be optimized.

Keywords: Frozen soil, Lattice Boltzmann method, Phase change, Test rig.

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Authors: A. Shayeghi, H. Eimani Kalasar, H. Shayeghi

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This paper emphasizes on the application of genetic algorithm (GA) to optimize the parameters of the TMD for achieving the best results in the reduction of the building response under earthquake excitations. The Integral of the Time multiplied Absolute value of the Error (ITAE) based on relative displacement of all floors in the building is taken as a performance index of the optimization criterion. The problem of robustly TMD controller design is formatted as an optimization problem based on the ITAE performance index to be solved using GA that has a story ability to find the most optimistic results. An 11–story realistic building, located in the city of Rasht, Iran is considered as a test system to demonstrate effectiveness of the proposed GA based TMD (GATMD) controller without specifying which mode should be controlled. The results of the proposed GATMD controller are compared with the uncontrolled structure through timedomain simulation and some performance indices. The results analysis reveals that the designed GA based TMD controller has an excellent capability in reduction of the seismically excited example building and the ITAE performance, that is so for remains as unknown, can be introduced a new criteria - method for structural dynamic design.

Keywords: Tuned Mass Damper, Genetic Algorithm, TallBuildings, Structural Dynamics.

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Authors: María S. Avila-García, John N. Carter, Robert I. Damper

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An important problem in speech research is the automatic extraction of information about the shape and dimensions of the vocal tract during real-time speech production. We have previously developed Southampton dynamic magnetic resonance imaging (SDMRI) as an approach to the solution of this problem.However, the SDMRI images are very noisy so that shape extraction is a major challenge. In this paper, we address the problem of tongue shape extraction, which poses difficulties because this is a highly deforming non-parametric shape. We show that combining active shape models with the dynamic Hough transform allows the tongue shape to be reliably tracked in the image sequence.

Keywords: Vocal tract imaging, speech production, active shapemodels, dynamic Hough transform, object tracking.

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Authors: Nancy, Ling Sze Leung

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Hong Kong is one of the regions in the world where Total Fertility Rate (TFR) is very low. In 2001, the TFR dropped until 0.931, which means 1 woman even cannot give birth to one child on average. However, after the reformation of the 'Right of Abode of Hong Kong' in 2001 and the Chinese Central Government loosened the disembarkation procedure of mainland Chinese (mainlander) to enter Hong Kong in 2003; mainlander couples started to cross the border for giving births in Hong Kong. This action raises Hong Kong-s TFR quickly from 0.931 (2001) to 1.094 (2010). Usually, an increasing trend of TFR means a sign of rejuvenation in low-fertility, but in the case of Hong Kong, the increase of TFR does not, rather it generates other population problems. This paper is going to discuss do mainlanders- births help to solve the low-fertility problem in Hong Kong.

Keywords: Cross Border Birth, Low-fertility, Mainlander, Total Fertility Rate

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Authors: Arash Karimipour, A. Hossein Nezhad, E. Shirani, A. Safaei

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In this paper, Lattice Boltzmann Method (LBM) is used to study laminar flow with mixed convection heat transfer inside a two-dimensional inclined lid-driven rectangular cavity with aspect ratio AR = 3. Bottom wall of the cavity is maintained at lower temperature than the top lid, and its vertical walls are assumed insulated. Top lid motion results in fluid motion inside the cavity. Inclination of the cavity causes horizontal and vertical components of velocity to be affected by buoyancy force. To include this effect, calculation procedure of macroscopic properties by LBM is changed and collision term of Boltzmann equation is modified. A computer program is developed to simulate this problem using BGK model of lattice Boltzmann method. The effects of the variations of Richardson number and inclination angle on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles, stream function contours and isotherms. It is concluded that LBM has good potential to simulate mixed convection heat transfer problems.

Keywords: gravity, inclined lid driven cavity, lattice Boltzmannmethod, mixed convection.

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Authors: Alaa A. Osman, Amgad M. Bayoumy, Ismail El baialy, Osama E. Abdellatif, Essam E. Khallil

Abstract:

In this paper, a numerical simulation of a finned store separating from a wing-pylon configuration has been studied and validated. A dynamic unstructured tetrahedral mesh approach is accomplished by using three grid sizes to numerically solving the discretized three dimensional, inviscid and compressible Euler equations. The method used for computations of separation of an external store assuming quasi-steady flow condition. Computations of quasi-steady flow have been directly coupled to a six degree-offreedom (6DOF) rigid-body motion code to generate store trajectories. The pressure coefficients at four different angular cuts and time histories of various trajectory parameters and wing pressure distribution during the store separation are compared for every grid size with published experimental data.

Keywords: CFD Modelling, Quasi-steady Flow, Moving-body Trajectories, Transonic Store Separation, Moving-body Trajectories.

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Authors: Pulak Swain, A. K. Ojha

Abstract:

Portfolio optimization is based on dealing with the problems of efficient asset allocation. Risk and Expected return are two conflicting criteria in such problems, where the investor prefers the return to be high and the risk to be low. Using multi-objective approach we can solve those type of problems. However the information which we have for the input parameters are generally ambiguous and the input values can fluctuate around some nominal values. We can not ignore the uncertainty in input values, as they can affect the asset allocation drastically. So we use Robust Optimization approach to the problems where the input parameters comes under box uncertainty. In this paper, we solve the multi criteria robust problem with the help of  E- constraint method.

Keywords: Portfolio optimization, multi-objective optimization, E-constraint method, box uncertainty, robust optimization.

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Authors: W. D. Wan Rosli, Z. Zainuddin, R. Lanouette, S. Sathasivam

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This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, Modeling, Neural Networks, Preconditioned Conjugate Gradient.

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Authors: Kanso Hassan, Elhore Ali, Soule-dupuy Chantal, Tazi Said

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Information Retrieval has the objective of studying models and the realization of systems allowing a user to find the relevant documents adapted to his need of information. The information search is a problem which remains difficult because the difficulty in the representing and to treat the natural languages such as polysemia. Intentional Structures promise to be a new paradigm to extend the existing documents structures and to enhance the different phases of documents process such as creation, editing, search and retrieval. The intention recognition of the author-s of texts can reduce the largeness of this problem. In this article, we present intentions recognition system is based on a semi-automatic method of extraction the intentional information starting from a corpus of text. This system is also able to update the ontology of intentions for the enrichment of the knowledge base containing all possible intentions of a domain. This approach uses the construction of a semi-formal ontology which considered as the conceptualization of the intentional information contained in a text. An experiments on scientific publications in the field of computer science was considered to validate this approach.

Keywords: Information research, text analyzes, intentionalstructure, segmentation, ontology, natural language processing.

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Authors: Semeh Ben Salem, Sami Naouali, Moetez Sallami

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Clustering is a well known data mining technique used in pattern recognition and information retrieval. The initial dataset to be clustered can either contain categorical or numeric data. Each type of data has its own specific clustering algorithm. In this context, two algorithms are proposed: the k-means for clustering numeric datasets and the k-modes for categorical datasets. The main encountered problem in data mining applications is clustering categorical dataset so relevant in the datasets. One main issue to achieve the clustering process on categorical values is to transform the categorical attributes into numeric measures and directly apply the k-means algorithm instead the k-modes. In this paper, it is proposed to experiment an approach based on the previous issue by transforming the categorical values into numeric ones using the relative frequency of each modality in the attributes. The proposed approach is compared with a previously method based on transforming the categorical datasets into binary values. The scalability and accuracy of the two methods are experimented. The obtained results show that our proposed method outperforms the binary method in all cases.

Keywords: Clustering, k-means, categorical datasets, pattern recognition, unsupervised learning, knowledge discovery.

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Authors: M. Anidha, K. Premalatha

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Feature Selection is significant in order to perform constructive classification in the area of cancer diagnosis. However, a large number of features compared to the number of samples makes the task of classification computationally very hard and prone to errors in microarray gene expression datasets. In this paper, we present an innovative method for selecting highly informative gene subsets of gene expression data that effectively classifies the cancer data into tumorous and non-tumorous. The hybrid gene selection technique comprises of combined Mutual Information and Fisher score to select informative genes. The gene selection is validated by classification using Support Vector Machine (SVM) which is a supervised learning algorithm capable of solving complex classification problems. The results obtained from improved Mutual Information and F-Score with SVM as a classifier has produced efficient results.

Keywords: Gene selection, mutual information, Fisher score, classification, SVM.

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Authors: Kero T., Söderberg R., Andersson M., Lindkvist L.

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The introduction of mass-customization has enabled new ways to treat patients within medicine. However, the introduction of industrialized treatments has also meant new obstacles. The purpose of this study was to introduce and theoretically test a method for improving dental crown fit. The optimization method allocates support points in order to check the final variation for dental crowns. Three different types of geometries were tested and compared. The three geometries were also divided into three sub-geometries: Current method, Optimized method and Feasible method. The Optimized method, using the whole surface for support points, provided the best results. The results support the objective of the study. It also seems that the support optimization method can dramatically improve the robustness of dental crown treatments.

Keywords: Bio-medicine, Dentistry, Mass-customization, Optimization and Robust design.

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Authors: Saeideh Hesam, Alireza Nazemi, Ahmad Haghbin

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This paper presents the approximate analytical solution of a Zakharov-Kuznetsov ZK(m, n, k) equation with the help of the differential transform method (DTM). The DTM method is a powerful and efficient technique for finding solutions of nonlinear equations without the need of a linearization process. In this approach the solution is found in the form of a rapidly convergent series with easily computed components. The two special cases, ZK(2,2,2) and ZK(3,3,3), are chosen to illustrate the concrete scheme of the DTM method in ZK(m, n, k) equations. The results demonstrate reliability and efficiency of the proposed method.

Keywords: Zakharov-Kuznetsov equation, differential transform method, closed form solution.

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Authors: Hany Osman, M. F. Baki

Abstract:

We address the balancing problem of transfer lines in this paper to find the optimal line balancing that minimizes the nonproductive time. We focus on the tool change time and face orientation change time both of which influence the makespane. We consider machine capacity limitations and technological constraints associated with the manufacturing process of auto cylinder heads. The problem is represented by a mixed integer programming model that aims at distributing the design features to workstations and sequencing the machining processes at a minimum non-productive time. The proposed model is solved by an algorithm established using linearization schemes and Benders- decomposition approach. The experiments show the efficiency of the algorithm in reaching the exact solution of small and medium problem instances at reasonable time.

Keywords: Transfer line balancing, Benders' decomposition, Linearization.

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Authors: Alireza Dehghani Pilehvarani, Mojtaba Hakimzadeh, Mohammad Jafari Far, Reza Sedaghati

Abstract:

Distributed Generation (DG) can help in reducing the cost of electricity to the costumer, relieve network congestion and provide environmentally friendly energy close to load centers. Its capacity is also scalable and it provides voltage support at distribution level. Hence, DG placement and penetration level is an important problem for both the utility and DG owner. DG allocation and capacity determination is a nonlinear optimization problem. The objective function of this problem is the minimization of the total loss of the distribution system. Also high levels of penetration of DG are a new challenge for traditional electric power systems. This paper presents a new methodology for the optimal placement of DG and penetration level of DG in distribution system based on General Algebraic Modeling System (GAMS) and Genetic Algorithm (GA).

Keywords: Distributed Generation, Location, Loss Reduction, Distribution Network, GA, GAMS.

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Authors: Merkisz Jerzy, Lijewski Piotr, Fuć Paweł, Siedlecki Maciej, Ziółkowski Andrzej, Weymann Sylwester

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The paper discusses the problem of load transport using farm tractors and road tractor units. This type of carriage of goods is often done with farm vehicles. The tests were performed with the PEMS equipment (Portable Emission Measurement System) under actual traffic conditions. The vehicles carried a load of 20000 kg. This research method is one of the most desired because it provides reliable information on the actual vehicle emissions and fuel consumption (carbon balance method). For the tests, a route was selected that simulated a trip from a small town to a food-processing facility located in a city. The analysis of the obtained results gave a clear answer as to what vehicles need to be used for carriage of this type of cargo in terms of exhaust emissions and fuel consumption.

Keywords: Emission, transport, fuel consumption, PEMS.

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Authors: Hanieh Tarbiat Khosrowshahi, Mojtaba Shakeri

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Wireless Sensor Networks (WSNs) consist of a set of sensor nodes with limited capability. WSNs may suffer from multiple node failures when they are exposed to harsh environments such as military zones or disaster locations and lose connectivity by getting partitioned into disjoint segments. Relay nodes (RNs) are alternatively introduced to restore connectivity. They cost more than sensors as they benefit from mobility, more power and more transmission range, enforcing a minimum number of them to be used. This paper addresses the problem of RN placement in a multiple disjoint network by developing a genetic algorithm (GA). The problem is reintroduced as the Steiner tree problem (which is known to be an NP-hard problem) by the aim of finding the minimum number of Steiner points where RNs are to be placed for restoring connectivity. An upper bound to the number of RNs is first computed to set up the length of initial chromosomes. The GA algorithm then iteratively reduces the number of RNs and determines their location at the same time. Experimental results indicate that the proposed GA is capable of establishing network connectivity using a reasonable number of RNs compared to the best existing work.

Keywords: Connectivity restoration, genetic algorithms, multiple-node failure, relay nodes, wireless sensor networks.

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Authors: Wen-Lung Huang, Shih-Pin Chen

Abstract:

This paper investigates the optimization problem of multi-product aggregate production planning (APP) with fuzzy data. From a comprehensive viewpoint of conserving the fuzziness of input information, this paper proposes a method that can completely describe the membership function of the performance measure. The idea is based on the well-known Zadeh-s extension principle which plays an important role in fuzzy theory. In the proposed solution procedure, a pair of mathematical programs parameterized by possibility level a is formulated to calculate the bounds of the optimal performance measure at a . Then the membership function of the optimal performance measure is constructed by enumerating different values of a . Solutions obtained from the proposed method contain more information, and can offer more chance to achieve the feasible disaggregate plan. This is helpful to the decision-maker in practical applications.

Keywords: fuzzy data, aggregate production planning, membership function, parametric programming

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Authors: Fl. Loury, P. Sablonière

Abstract:

In this paper a stochastic scenario-based model predictive control applied to molten salt storage systems in concentrated solar tower power plant is presented. The main goal of this study is to build up a tool to analyze current and expected future resources for evaluating the weekly power to be advertised on electricity secondary market. This tool will allow plant operator to maximize profits while hedging the impact on the system of stochastic variables such as resources or sunlight shortage.

Solving the problem first requires a mixed logic dynamic modeling of the plant. The two stochastic variables, respectively the sunlight incoming energy and electricity demands from secondary market, are modeled by least square regression. Robustness is achieved by drawing a certain number of random variables realizations and applying the most restrictive one to the system. This scenario approach control technique provides the plant operator a confidence interval containing a given percentage of possible stochastic variable realizations in such a way that robust control is always achieved within its bounds. The results obtained from many trajectory simulations show the existence of a ‘’reliable’’ interval, which experimentally confirms the algorithm robustness.

Keywords: Molten Salt Storage System, Concentrated Solar Tower Power Plant, Robust Stochastic Model Predictive Control.

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Authors: Anatoli Torokhti, Stan Miklavcic

Abstract:

We study a new technique for optimal data compression subject to conditions of causality and different types of memory. The technique is based on the assumption that some information about compressed data can be obtained from a solution of the associated problem without constraints of causality and memory. This allows us to consider two separate problem related to compression and decompression subject to those constraints. Their solutions are given and the analysis of the associated errors is provided.

Keywords: stochastic signals, optimization problems in signal processing.

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Authors: Sarun Phibanchon

Abstract:

The solitary wave solution of the quadratic nonlinear Schrdinger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution.

Keywords: soliton, iterative method, spectral method, plasma

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