Search results for: metaheuristic optimization

Authors: I Made Gatot Karohika, Shigeyuki Haruyama, Ken Kaminishi

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In this study, we proposed a three-layer metal gasket with Al, Cu, and SUS304 as the material, respectively. A finite element method was employed to develop simulation solution and design of experiment (DOE). Taguchi method was used to analysis the effect of each parameter design and predicts optimal design of new 25A-size three layer corrugated metal gasket. The L18 orthogonal array of Taguchi method was applied to design experiment matrix for eight factors with three levels. Based on elastic mode and plastic mode, optimum design gasket is gasket with core metal SUS304, surface layer aluminum, p1 = 4.5 mm, p2 = 4.5 mm, p3 = 4 mm, Tg = 1.2 mm, R = 3.5 mm, h = 0.4 mm and Ts = 0.3 mm.

Keywords: contact width, contact stress, layer, metal gasket, corrugated, simulation

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Authors: Ritsuko Kawasaki, Takeshi Hiromatsu

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Management is required to understand all information security risks within an organization, and to make decisions on which information security risks should be treated in what level by allocating how much amount of cost. However, such decision-making is not usually easy, because various measures for risk treatment must be selected with the suitable application levels. In addition, some measures may have objectives conflicting with each other. It also makes the selection difficult. Therefore, this paper provides a model which supports the selection of measures by applying multi-objective analysis to find an optimal solution. Additionally, a list of measures is also provided to make the selection easier and more effective without any leakage of measures.

Keywords: information security risk treatment, selection of risk measures, risk acceptance, multi-objective optimization

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Authors: Tadele Tesfaw, Ajit Pal Singh, Abebaw Mekonnen Gezahegn

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Welding is a basic manufacturing process for making components or assemblies. Recent welding economics research has focused on developing the reliable machinery database to ensure optimum production. Research on welding of materials like steel is still critical and ongoing. Welding input parameters play a very significant role in determining the quality of a weld joint. The metal active gas (MAG) welding parameters are the most important factors affecting the quality, productivity and cost of welding in many industrial operations. The aim of this study is to investigate the optimization process parameters for metal active gas welding for 60x60x5mm dead mild steel plate work-piece using Taguchi method to formulate the statistical experimental design using semi-automatic welding machine. An experimental study was conducted at Bishoftu Automotive Industry, Bishoftu, Ethiopia. This study presents the influence of four welding parameters (control factors) like welding voltage (volt), welding current (ampere), wire speed (m/min.), and gas (CO2) flow rate (lit./min.) with three different levels for variability in the welding hardness. The objective functions have been chosen in relation to parameters of MAG welding i.e., welding hardness in final products. Nine experimental runs based on an L9 orthogonal array Taguchi method were performed. An orthogonal array, signal-to-noise (S/N) ratio and analysis of variance (ANOVA) are employed to investigate the welding characteristics of dead mild steel plate and used in order to obtain optimum levels for every input parameter at 95% confidence level. The optimal parameters setting was found is welding voltage at 22 volts, welding current at 125 ampere, wire speed at 2.15 m/min and gas flow rate at 19 l/min by using the Taguchi experimental design method within the constraints of the production process. Finally, six conformations welding have been carried out to compare the existing values; the predicated values with the experimental values confirm its effectiveness in the analysis of welding hardness (quality) in final products. It is found that welding current has a major influence on the quality of welded joints. Experimental result for optimum setting gave a better hardness of welding condition than initial setting. This study is valuable for different material and thickness variation of welding plate for Ethiopian industries.

Keywords: Weld quality, metal active gas welding, dead mild steel plate, orthogonal array, analysis of variance, Taguchi method

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Authors: H. Abderrezek, M. N. Harmas

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DC-DC converters are widely used as reliable power source for many industrial and military applications, computers and electronic devices. Several control methods were developed for DC-DC converters control mostly with asymptotic convergence. Synergetic control (SC) is a proven robust control approach and will be used here in a so-called terminal scheme to achieve finite time convergence. Lyapunov synthesis is adopted to assure controlled system stability. Furthermore particle swarm optimization (PSO) algorithm, based on an integral time absolute of error (ITAE) criterion will be used to optimize controller parameters. Simulation of terminal synergetic control of a DC-DC converter is carried out for different operating conditions and results are compared to classic synergetic control performance, that which demonstrate the effectiveness and feasibility of the proposed control method.

Keywords: DC-DC converter, PSO, finite time, terminal, synergetic control

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Authors: T. Mushiri, K. Tengende, C. Mbohwa, T. Garikayi

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This paper introduces finite element analysis of Run off Mine (ROM) silo subjected to dynamic loading. The proposed procedure is based on the use of theoretical equations to come up with pressure and forces exerted by Platinum Group Metals (PGMs) ore to the silo wall. Finite Element Analysis of the silo involves the use of CAD software (AutoCAD) for3D creation and CAE software (T-FLEX) for the simulation work with an optimization routine to minimize the mass and also ensure structural stiffness and stability. In this research an efficient way to design and analysis of a silo in 3D T-FLEX (CAD) program was created the silo to stay within the constrains and so as to know the points of failure due dynamic loading.

Keywords: reinforced concrete silo, finite element analysis, T-FLEX software, AutoCAD

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Authors: S. Periyadharshini, K. Ramkumar, S. Jayalalitha, M. GuruPrasath, R. Manikandan

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This paper presents a formulation and solution for industrial load management and product grade problem. The formulation is created using linear programming technique thereby optimizing the electricity cost by scheduling the loads satisfying the process, storage, time zone and production constraints which will create an impact of reducing maximum demand and thereby reducing the electricity cost. Product grade problem is formulated using integer linear programming technique of optimization using lingo software and the results show that overall increase in profit margin. In this paper, time of use tariff is utilized and this technique will provide significant reductions in peak electricity consumption.

Keywords: cement industries, integer programming, optimal formulation, objective function, constraints

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Authors: Hyunwon Moon

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It is necessary to realize new biomedical wireless communication systems which send the signals collected from various bio sensors located at human body in order to monitor our health. Also, it should seamlessly connect to the existing wireless communication systems. A 5.8 GHz ISM band low power RF front-end receiver for a biomedical wireless communication system is implemented using a 0.5 µm SiGe BiCMOS process. To achieve low power RF front-end, the current optimization technique for selecting device size is utilized. The implemented low noise amplifier (LNA) shows a power gain of 9.8 dB, a noise figure (NF) of below 1.75 dB, and an IIP3 of higher than 7.5 dBm while current consumption is only 6 mA at supply voltage of 2.5 V. Also, the performance of a down-conversion mixer is measured as a conversion gain of 11 dB and SSB NF of 10 dB.

Keywords: biomedical, LNA, mixer, receiver, RF front-end, SiGe

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Authors: Mahmoud M. Othman, Y. G. Hegazy, A. Y. Abdelaziz

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This paper proposes a novel heuristic algorithm that aims to determine the best size and location of distributed generators in unbalanced distribution networks. The proposed heuristic algorithm can deal with the planning cases where power loss is to be optimized without violating the system practical constraints. The distributed generation units in the proposed algorithm is modeled as voltage controlled node with the flexibility to be converted to constant power factor node in case of reactive power limit violation. The proposed algorithm is implemented in MATLAB and tested on the IEEE 37 -node feeder. The results obtained show the effectiveness of the proposed algorithm.

Keywords: distributed generation, heuristic approach, optimization, planning

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Authors: Anastasiia Yu. Timofeeva

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Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: grade point average, orthogonal regression, penalized regression spline, locally weighted regression

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Authors: Man Guo, Wenyong Tan

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By combining spatial syntax with data obtained from field visits, this paper interprets the internal relationship between spatial morphology and spatial cognition in Lidukou Village. By comparing the obtained data, it is recognized that the spatial integration degree of Lidukou Village is positively correlated with the spatial cognitive intention of local villagers. The part with a higher spatial cognitive degree within the village is distributed along the axis mainly composed of Shuxiang Road. And the accessibility of historical relics is weak, and there is no systematic relationship between them. Aiming at the morphological problem of Lidukou Village, optimization strategies have been proposed from multiple perspectives, such as optimizing spatial mechanisms and shaping spatial nodes.

Keywords: traditional villages, spatial syntax, spatial integration degree, morphological problem

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Authors: A. Mansouri, F. Krim

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This paper presents two techniques for DC motor parameters identification. We propose a numerical method using the adaptive extensive recursive least squares (AERLS) algorithm for real time parameters estimation. This algorithm, based on minimization of quadratic criterion, is realized in simulation for parameters identification of DC motor autoregressive moving average with extra inputs (ARMAX). As advanced technique, we use genetic algorithms (GA) identification with biased estimation for high dynamic performance speed regulation. DC motors are extensively used in variable speed drives, for robot and solar panel trajectory control. GA effectiveness is derived through comparison of the two approaches.

Keywords: ARMAX model, DC motor, AERLS, GA, optimization, parameter identification, PID speed regulation

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Authors: Kittipong Tripetch

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This paper proposes for the first time symbolic formula of the power spectrum of cross couple oscillator and its modified circuit. Many principle existed to derived power spectrum in microwave textbook such as impedance, admittance parameters, ABCD, H parameters, etc. It can be compared by graph of power spectrum which methodology is the best from the point of view of practical measurement setup such as condition of impedance parameter which used superposition of current to derived (its current injection of the other port of the circuit is zero, which is impossible in reality). Four Graphs of impedance parameters of cross couple oscillator is proposed. After that four graphs of Scattering parameters of cross couple oscillator will be shown.

Keywords: optimization, power spectrum, impedance parameters, scattering parameter

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Authors: N. Hachemi, A. Nouani, A. Benchabane

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The influence of cultivation factors such as content of ammonium sulfate, glucose and water in the culture medium and particle size of dry orange waste, on their bioconversion for pectinase production was studied using complete factorial design. a polygalacturonase (PG) was isolated using ion exchange chromatography under gradient elution 0-0,5 m/l NaCl (column equilibrate with acetate buffer pH 4,5), subsequently by sephadex G75 column chromatography was applied and the molecular weight was obtained about 51,28 KDa . Purified PG enzyme exhibits a pH and temperature optima of activity at 5 and 35°C respectively. Treatment of apple juice by purified enzyme extract yielded a clear juice, which was competitive with juice yielded by pure Sigma Aldrich Aspergillus niger enzyme.

Keywords: bioconversion, orange wastes, optimization, pectinase

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Authors: Ocotlán Díaz-Parra, Jorge A. Ruiz-Vanoye, Alejandro Fuentes-Penna, Beatriz Bernabe-Loranca, Patricia Ambrocio-Cruz, José J. Hernández-Flores

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The Maritime Platform Transport Problem of Solid, Special and Dangerous Waste consist of to minimize the monetary value of carry different types of waste from one location to another location using ships. We offer a novel mathematical, the characterization of the problem and the use CPLEX to find the optimal values to solve the Solid, Special and Hazardous Waste Transportation Problem of offshore platforms instances of Mexican state-owned petroleum company (PEMEX). The set of instances used are WTPLib real instances and the tool CPLEX solver to solve the MPTPSSDW problem.

Keywords: oil platform, transport problem, waste, solid waste

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Authors: Hamed Bazrafshan, Saeideh Dabirnia, Zahra Alipour Tesieh, Samaneh Alavi, Bahram Dabir

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In this study, the removal of pollutants of a real produced water sample from an oil reservoir (a light oil reservoir), using a photocatalytic degradation process in a cylindrical glass reactor, was investigated. Using TiO₂ and Ag-TiO₂ in slurry form, the photocatalytic degradation was studied by measuring the COD parameter, qualitative analysis, and GC-MS. At first, optimization of the parameters on photocatalytic degradation of hydrocarbon pollutants in real produced water, using TiO₂ nanoparticles as photocatalysts under UV light, was carried out applying response surface methodology. The results of the design of the experiment showed that the optimum conditions were at a catalyst concentration of 1.14 g/lit and pH of 2.67, and the percentage of COD removal was 72.65%.

Keywords: photocatalyst, Ag-doped, TiO₂, produced water, nanoparticles

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Authors: M. H. Abedi, A. Jalilvand

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The economic development benefits of wind energy may be the most tangible basis for the local and state officials’ interests. In addition to the direct salaries associated with building and operating wind projects, the wind energy industry provides indirect jobs and benefits. The optimal planning of a wind farm is one most important topic in renewable energy technology. Many methods have been implemented to optimize the cost and output benefit of wind farms, but the contribution of this paper is mentioning different types of service providers and also time of installation of wind turbines during planning horizon years. Genetic algorithm (GA) is used to optimize the problem. It is observed that an appropriate layout of wind farm can cause to minimize the different types of cost.

Keywords: renewable energy, wind farm, optimization, planning

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Authors: Mohammad Ali Aazami Mavaloo, Mohammad Bagher Hassanpouraghdam

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Intact leaves, leaf segments and petiole sections derived from nodal explants in vitro were employed for the optimization of Pelargonium odoratissimum micropropagation. MS and ½ MS media enriched with BAP (1, 1.5, 2 and 4.5 mg/l) and NAA (0.1, 1 and 1.5 mg/l) were the treatment combinations used for. With leaf segments, the lowest browning incidence, the greatest callogenesis and the highest number of shoots were obtained with the media containing 1.5 mg/L BAP and 1 mg/L NAA. Two mg/L BAP + 0.1 mg/L NAA hold the same results for petiole explants. Intact leaves showed the best results for the three before-mentioned traits with 1 mg/L BAP + 1 mg/L NAA. 0.2 mg/L NAA caused the highest rooting percentage and the greatest mean data for the number and length of the roots. Rooted plantlets were transferred to the pots containing 1:1 peat-moss and perlite. Acclimatization of the plantlets was followed by 90 percent of survival rate in the greenhouse.

Keywords: Pelargonium odoratissimum, micropropagation, BAP, NAA

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Authors: D. Remache, M. Semaan, C. Baron, M. Pithioux, P. Chabrand, J. M. Rossi, J. L. Milan

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A good understanding of the mechanical properties of the bone implies a better understanding of its various diseases, such as osteoporosis. Berkovich nanoindentation tests were performed on the human cortical bone to extract its orthotropic parameters. The nanoindentation experiments were then simulated by the finite element method. Different configurations of interactions between the tip indenter and the bone were simulated. The orthotropic parameters of the material were identified by the inverse method for each configuration. The friction effect on the bone mechanical properties was then discussed. It was found that the inverse method using the finite element method is a very efficient method to predict the mechanical behavior of the bone.

Keywords: mechanical behavior of bone, nanoindentation, finite element analysis, inverse optimization approaches

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Authors: Z. Ulukan, E. Demircioğlu,

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Facility location is a complex real-world problem which needs a strategic management decision. This paper provides a general review on studies, efforts and developments in Facility Location Problems which are classical optimization problems having a wide-spread applications in various areas such as transportation, distribution, production, supply chain decisions and telecommunication. Our goal is not to review all variants of different studies in FLPs or to describe very detailed computational techniques and solution approaches, but rather to provide a broad overview of major location problems that have been studied, indicating how they are formulated and what are proposed by researchers to tackle the problem. A brief, elucidative table based on a grouping according to “General Problem Type” and “Methods Proposed” used in the studies is also presented at the end of the work.

Keywords: discrete location problems, exact methods, heuristic algorithms, single source capacitated facility location problems

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Authors: Linda D. F. Bambara, Marie Sawadogo

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Jatropha curcas (jatropha) is the plant that has been the most studied for biofuel production in West Africa. There exist however other plants such as Balanites aegyptiaca (balanites) that have been targeted as a potential feedstock for biofuel production. This biomass could be an alternative feedstock for the production of straight vegetable oil (SVO) at costs lower than jatropha-based SVO production costs. This study aims firstly to determine, through an MILP model, the optimal organization that minimizes the costs of the oilseeds supply of two biomass conversion units (BCU) exploiting respectively jatropha seeds and the balanitès seeds. Secondly, the study aims to carry out a comparative study of these costs obtained for each BCU. The model was then implemented on two theoretical cases studies built on the basis of the common practices in Burkina Faso and two scenarios were carried out for each case study. In Scenario 1, 3 pre-processing locations ("at the harvesting area", "at the gathering points", "at the BCU") are possible. In scenario 2, only one location ("at the BCU") is possible. For each biomass, the system studied is the upstream supply chain (harvesting, transport and pre-processing (drying, dehulling, depulping)), including cultivation (for jatropha). The model optimizes the area of land to be exploited based on the productivity of the studied plants and material losses that may occur during the harvesting and the supply of the BCU. It then defines the configuration of the logistics network allowing an optimal supply of the BCU taking into account the most common means of transport in West African rural areas. For the two scenarios, the results of the implementation showed that the total area exploited for balanites (1807 ha) is 4.7 times greater than the total area exploited for Jatropha (381 ha). In both case studies, the location of pre-processing “at the harvesting area” was always chosen for scenario1. As the balanites trees were not planted and because the first harvest of the jatropha seeds took place 4 years after planting, the cost price of the seeds at the BCU without the pre-processing costs was about 430 XOF/kg. This cost is 3 times higher than the balanites's one, which is 140 XOF/kg. After the first year of harvest, i.e. 5 years after planting, and assuming that the yield remains constant, the same cost price is about 200 XOF/kg for Jatropha. This cost is still 1.4 times greater than the balanites's one. The transport cost of the balanites seeds is about 120 XOF/kg. This cost is similar for the jatropha seeds. However, when the pre-processing is located at the BCU, i.e. for scenario2, the transport costs of the balanites seeds is 1200 XOF/kg. These costs are 6 times greater than the transport costs of jatropha which is 200 XOF/kg. These results show that the cost price of the balanites seeds at the BCU can be competitive compared to the jatropha's one if the pre-processing is located at the harvesting area.

Keywords: Balanites aegyptiaca, biomass conversion, Jatropha curcas, optimization, post-harvest operations

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Authors: Hamed Zolfaghari, Mojtaba Kord

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After feasibility study the design phase is started and the rest of other phases are highly dependent on this phase. forecasting the duration of design phase could do a miracle and would save a lot of time. This study provides a fast and accurate Machine learning (ML) and optimization framework, which allows a quick duration estimation of project design phase, hence improving operational efficiency and competitiveness of a design construction company. 3 data sets of three years composed of daily time spent for different design projects are used to train and validate the ML models to perform multiple projects. Our study concluded that Artificial Neural Network (ANN) performed an accuracy of 0.94.

Keywords: time estimation, machine learning, Artificial neural network, project design phase

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Authors: Kriuk Boris, Kriuk Fedor

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This paper presents a comparative study of fundamental similarity functions for Siamese networks in semantic textual similarity (STS) tasks. We evaluate various similarity functions using the STS Benchmark dataset, analyzing their performance and stability. Additionally, we introduce a multi-objective approach for optimal threshold selection. Our findings provide insights into the effectiveness of different similarity functions and offer a straightforward method for threshold selection optimization, contributing to the advancement of Siamese network architectures in STS applications.

Keywords: siamese networks, semantic textual similarity, similarity functions, STS benchmark dataset, threshold selection

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Authors: Hussam Elias, Ninovic Perez, Holger Hirsch

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The completion of the EMC regulations worldwide is growing steadily as the usage of electronics in our daily lives is increasing more than ever. In this paper, we introduce a novel method to perform the final phase of Electromagnetic compatibility (EMC) measurement and to reduce the required test time according to the norm EN 55032 by using a developed tool and the conventional neural network(CNN). The neural network was trained using real EMC measurements, which were performed in the Semi Anechoic Chamber (SAC) by CETECOM GmbH in Essen, Germany. To implement our proposed method, we wrote software to perform the radiated electromagnetic interference (EMI) measurements and use the CNN to predict and determine the position of the turntable that meets the maximum radiation value.

Keywords: conventional neural network, electromagnetic compatibility measurement, mean absolute error, position error

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Authors: Abbas Mirakhorli

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A hub covering problem is a type of hub location problem that tries to maximize the coverage area with the least amount of installed hubs. There have not been many studies in the literature about multi-objective hubs covering location problems. Thus, in this paper, a bi-objective model for the hub covering problem is presented. The two objectives that are considered in this paper are the minimization of total transportation costs and the maximization of coverage of origin-destination nodes. A genetic algorithm is presented to solve the model when the number of nodes is increased. The genetic algorithm is capable of solving the model when the number of nodes increases by more than 20. Moreover, the genetic algorithm solves the model in less amount of time.

Keywords: facility location, hub covering, multi-objective optimization, genetic algorithm

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Authors: Toshinori Nawata

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In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designing the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics

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Authors: Dana Alghool, Tarek ElMekkawy, Mohamed Haouari, Adel Elomari

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District cooling systems have captured the attentions of many researchers recently due to the enormous benefits offered by such system in comparison with traditional cooling technologies. It is considered a major component of urban cities due to the significant reduction of energy consumption. This paper aims to find the optimal design and operation of district cooling systems by developing a mixed integer linear programming model to minimize the annual total system cost and satisfy the end-user cooling demand. The proposed model is experimented with different cooling demand scenarios. The results of the very high cooling demand scenario are only presented in this paper. A sensitivity analysis on different parameters of the model was performed.

Keywords: Annual Cooling Demand, Compression Chiller, Mathematical Modeling, District Cooling Systems, Optimization

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Authors: Jose D. Herrera, Mario A. Rios

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This paper deals with the coordinated tuning of the Power System Stabilizer (PSS) controller and Power Oscillation Damping (POD) Controller of Flexible AC Transmission System (FACTS) in a multi-machine power systems. The coordinated tuning is based on the critical eigenvalues of the power system and a model reduction technique where the Hankel Singular Value method is applied. Through the linearized system model and the parameter-constrained nonlinear optimization algorithm, it can compute the parameters of both controllers. Moreover, the parameters are optimized simultaneously obtaining the gains of both controllers. Then, the nonlinear simulation to observe the time response of the controller is performed.

Keywords: electromechanical oscillations, power system stabilizers, power oscillation damping, hankel singular values

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Authors: Roli Saini, Pradeep Kumar

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A coagulation/flocculation process was adopted for the reduction of carbamate insecticide (carbofuran) from aqueous solution. Ferric chloride (FeCl₃) was used as a coagulant to treat the carbofuran. To exploit the reduction efficiency of pesticide concentration and COD, the jar-test experiments were carried out and process was optimized through response surface methodology (RSM). The effects of two independent factors; i.e., FeCl₃ dosage and pH on the reduction efficiency were estimated by using central composite design (CCD). The initial COD of the 30 mg/L concentrated solution was found to be 510 mg/L. Results exposed that the maximum reduction occurred at an optimal condition of FeCl₃ = 80 mg/L, and pH = 5.0, from which the reduction of concentration and COD 75.13% and 65.34%, respectively. The present study also predicted that the obtained regression equations could be helpful as the theoretical basis for the coagulation process of pesticide wastewater.

Keywords: carbofuran, coagulation, optimization, response surface methodology

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Authors: K. Djellabi, M. E. H. Latreche

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Induction heating computer simulation is a powerful tool for process design and optimization, induction coil design, equipment selection, as well as education and business presentations. The authors share their vast experience in the practical use of computer simulation for different induction heating and heat treating processes. In this paper deals with mathematical modeling and numerical simulation of induction heating furnaces with axisymmetric geometries. For the numerical solution, we propose finite element methods combined with boundary (FEM) for the electromagnetic model using COMSOL® Multiphysics Software. Some numerical results for an industrial furnace are shown with high frequency.

Keywords: numerical methods, induction furnaces, induction heating, finite element method, Comsol multiphysics software

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Authors: Wenjun Hou, Marek Perkowski

Abstract:

The Traveling Salesman problem is famous in computing and graph theory. In short, it asks for the Hamiltonian cycle of the least total weight in a given graph with N nodes. All variations on this problem, such as those with K-bounded-degree nodes, are classified as NP-complete in classical computing. Although several papers propose theoretical high-level designs of quantum algorithms for the Traveling Salesman Problem, no quantum circuit implementation of these algorithms has been created up to our best knowledge. In contrast to previous papers, the goal of this paper is not to optimize some abstract complexity measures based on the number of oracle iterations, but to be able to evaluate the real circuit and time costs of the quantum computer. Using the emerging quantum programming language Q# developed by Microsoft, which runs quantum circuits in a quantum computer simulation, an implementation of the bounded-degree problem and its respective quantum circuit were created. To apply Grover’s algorithm to this problem, a quantum oracle was designed, evaluating the cost of a particular set of edges in the graph as well as its validity as a Hamiltonian cycle. Repeating the Grover algorithm with an oracle that finds successively lower cost each time allows to transform the decision problem to an optimization problem, finding the minimum cost of Hamiltonian cycles. N log₂ K qubits are put into an equiprobablistic superposition by applying the Hadamard gate on each qubit. Within these N log₂ K qubits, the method uses an encoding in which every node is mapped to a set of its encoded edges. The oracle consists of several blocks of circuits: a custom-written edge weight adder, node index calculator, uniqueness checker, and comparator, which were all created using only quantum Toffoli gates, including its special forms, which are Feynman and Pauli X. The oracle begins by using the edge encodings specified by the qubits to calculate each node that this path visits and adding up the edge weights along the way. Next, the oracle uses the calculated nodes from the previous step and check that all the nodes are unique. Finally, the oracle checks that the calculated cost is less than the previously-calculated cost. By performing the oracle an optimal number of times, a correct answer can be generated with very high probability. The oracle of the Grover Algorithm is modified using the recalculated minimum cost value, and this procedure is repeated until the cost cannot be further reduced. This algorithm and circuit design have been verified, using several datasets, to generate correct outputs.

Keywords: quantum computing, quantum circuit optimization, quantum algorithms, hybrid quantum algorithms, quantum programming, Grover’s algorithm, traveling salesman problem, bounded-degree TSP, minimal cost, Q# language

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