Search results for: Shortest Path Algorithm for Shopping.

Authors: Babak H. Tabrizi, Seyed Farid Ghaderi

Abstract:

Concurrent planning of the resource constraint project scheduling and material ordering problems have received significant attention within the last decades. Hence, the issue has been investigated here with the aim to minimize total project costs. Furthermore, the presented model considers different discount options in order to approach the real world conditions. The incorporated alternatives consist of all-unit and incremental discount strategies. On the other hand, a modified version of the genetic algorithm is applied in order to solve the model for larger sizes, in particular. Finally, the applicability and efficiency of the given model is tested by different numerical instances.

Keywords: Genetic algorithm, material ordering, project management, project scheduling.

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Authors: Sam S. Hashemi

Abstract:

The breakage of bonding between sand particles and their dislodgment from the borehole wall are among the main factors resulting in a borehole failure in poorly cemented granular formations. The grain debonding usually precedes the borehole failure and it can be considered as a sign that the onset of the borehole collapse is imminent. Detecting the bonding breakage point and introducing an appropriate failure criterion will play an important role in borehole stability analysis. To study the influence of different factors on the initiation of sand bonding breakage at the borehole wall, a series of laboratory tests was designed and conducted on poorly cemented sand samples. The total absorbed strain energy per volume of material up to the point of the observed particle debonding was computed. The results indicated that the particle bonding breakage point at the borehole wall was reached both before and after the peak strength of the thick-walled hollow cylinder specimens depending on the stress path and cement content. Three different cement contents and two borehole sizes were investigated to study the influence of the bonding strength and scale on the particle dislodgment. Test results showed that the stress path has a significant influence on the onset of the sand bonding breakage. It was shown that for various stress paths, there is a near linear relationship between the absorbed energy and the normal effective mean stress.

Keywords: Borehole stability, experimental studies, total strain energy, poorly cemented sands, particle bonding breakage.

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Authors: Benjamin Gorry, Zezhi Chen, Kevin Hammond, Andy Wallace, Greg Michaelson

Abstract:

This paper describes new computer vision algorithms that have been developed to track moving objects as part of a long-term study into the design of (semi-)autonomous vehicles. We present the results of a study to exploit variable kernels for tracking in video sequences. The basis of our work is the mean shift object-tracking algorithm; for a moving target, it is usual to define a rectangular target window in an initial frame, and then process the data within that window to separate the tracked object from the background by the mean shift segmentation algorithm. Rather than use the standard, Epanechnikov kernel, we have used a kernel weighted by the Chamfer distance transform to improve the accuracy of target representation and localization, minimising the distance between the two distributions in RGB color space using the Bhattacharyya coefficient. Experimental results show the improved tracking capability and versatility of the algorithm in comparison with results using the standard kernel. These algorithms are incorporated as part of a robot test-bed architecture which has been used to demonstrate their effectiveness.

Keywords: Hume, functional programming, autonomous vehicle, pioneer robot, vision.

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Authors: Susovan Chakrabortty, Madhumangal Pal, Prasun Kumar Nayak

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A manufacturing inventory model with shortages with carrying cost, shortage cost, setup cost and demand quantity as imprecise numbers, instead of real numbers, namely interval number is considered here. First, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented. A common algorithm for the optimum production quantity (Economic lot-size) per cycle of a single product (so as to minimize the total average cost) is developed which works well on interval number optimization under consideration. Finally, the designed algorithm is illustrated with numerical example.

Keywords: EOQ, Inventory, Interval Number, Demand, Production, Simulation

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Authors: Yao-Hong Tsai

Abstract:

Salient points are frequently used to represent local properties of the image in content-based image retrieval. In this paper, we present a reduction algorithm that extracts the local most salient points such that they not only give a satisfying representation of an image, but also make the image retrieval process efficiently. This algorithm recursively reduces the continuous point set by their corresponding saliency values under a top-down approach. The resulting salient points are evaluated with an image retrieval system using Hausdoff distance. In this experiment, it shows that our method is robust and the extracted salient points provide better retrieval performance comparing with other point detectors.

Keywords: Barnard detector, Content-based image retrieval, Points reduction, Salient point.

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Authors: Zhan Haiyang, Zhang Lei, Ning Juan

Abstract:

This paper presents a configuration software solution in Linux, which is used for the control of space environment simulator. After introducing the structure and basic principle, it is said that the developing of QT software frame and the dynamic data exchanging between PLC and computer. The OPC driver in Linux is also developed. This driver realizes many-to-many communication between hardware devices and SCADA software. Moreover, an algorithm named “Scan PRI” is put forward. This algorithm is much more optimizable and efficient compared with "Scan in sequence" in Windows. This software has been used in practical project. It has a good control effect and can achieve the expected goal.

Keywords: Linux OS, configuration software, OPC server driver, MYSQL database.

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Authors: Dipankar Dhabak, Soumya Pandit

Abstract:

This paper presents an adaptive technique for generation of data required for construction of artificial neural network-based performance model of nano-scale CMOS inverter circuit. The training data are generated from the samples through SPICE simulation. The proposed algorithm has been compared to standard progressive sampling algorithms like arithmetic sampling and geometric sampling. The advantages of the present approach over the others have been demonstrated. The ANN predicted results have been compared with actual SPICE results. A very good accuracy has been obtained.

Keywords: CMOS Inverter, Nano-scale, Adaptive Sampling, ArtificialNeural Network

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Authors: Thomas Bryan, Veton Kepuska, Ivica Kostanic

Abstract:

A simple adaptive voice activity detector (VAD) is implemented using Gabor and gammatone atomic decomposition of speech for high Gaussian noise environments. Matching pursuit is used for atomic decomposition, and is shown to achieve optimal speech detection capability at high data compression rates for low signal to noise ratios. The most active dictionary elements found by matching pursuit are used for the signal reconstruction so that the algorithm adapts to the individual speakers dominant time-frequency characteristics. Speech has a high peak to average ratio enabling matching pursuit greedy heuristic of highest inner products to isolate high energy speech components in high noise environments. Gabor and gammatone atoms are both investigated with identical logarithmically spaced center frequencies, and similar bandwidths. The algorithm performs equally well for both Gabor and gammatone atoms with no significant statistical differences. The algorithm achieves 70% accuracy at a 0 dB SNR, 90% accuracy at a 5 dB SNR and 98% accuracy at a 20dB SNR using 30d B SNR as a reference for voice activity.

Keywords: Atomic Decomposition, Gabor, Gammatone, Matching Pursuit, Voice Activity Detection.

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Authors: Kanate Pantusavase, Jaramporn Hassamontr

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This research aims to develop an algorithm to generate a schedule of multiple cranes that will maximize load throughputs in anodizing operation. The algorithm proposed utilizes an enumerative strategy to search for constant time between successive loads and crane covering range over baths. The computer program developed is able to generate a near-optimal crane schedule within reasonable times, i.e. within 10 minutes. Its results are compared with existing solutions from an aluminum extrusion industry. The program can be used to generate crane schedules for mixed products, thus allowing mixed-model line balancing to improve overall cycle times.

Keywords: Crane scheduling, anodizing operations, cycle time minimization.

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Authors: Yang Weiping, Zhang Zhilong, Li Jicheng, Chen Zengping, He Jun

Abstract:

The background estimation approach using a small window median filter is presented on the bases of analyzing IR point target, noise and clutter model. After simplifying the two-dimensional filter, a simple method of adopting one-dimensional median filter is illustrated to make estimations of background according to the characteristics of IR scanning system. The adaptive threshold is used to segment canceled image in the background. Experimental results show that the algorithm achieved good performance and satisfy the requirement of big size image-s real-time processing.

Keywords: Point target, background estimation, median filter, adaptive threshold, target detection.

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Authors: Theerawat Songyot, Tham Manjing, Bunyarit Uyyanonvara, Chanjira Sinthanayothin

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Corner detection and optical flow are common techniques for feature-based video stabilization. However, these algorithms are computationally expensive and should be performed at a reasonable rate. This paper presents an algorithm for discarding irrelevant feature points and maintaining them for future use so as to improve the computational cost. The algorithm starts by initializing a maintained set. The feature points in the maintained set are examined against its accuracy for modeling. Corner detection is required only when the feature points are insufficiently accurate for future modeling. Then, optical flows are computed from the maintained feature points toward the consecutive frame. After that, a motion model is estimated based on the simplified affine motion model and least square method, with outliers belonging to moving objects presented. Studentized residuals are used to eliminate such outliers. The model estimation and elimination processes repeat until no more outliers are identified. Finally, the entire algorithm repeats along the video sequence with the points remaining from the previous iteration used as the maintained set. As a practical application, an efficient video stabilization can be achieved by exploiting the computed motion models. Our study shows that the number of times corner detection needs to perform is greatly reduced, thus significantly improving the computational cost. Moreover, optical flow vectors are computed for only the maintained feature points, not for outliers, thus also reducing the computational cost. In addition, the feature points after reduction can sufficiently be used for background objects tracking as demonstrated in the simple video stabilizer based on our proposed algorithm.

Keywords: background object tracking, feature point reduction, low cost tracking, video stabilization.

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Authors: Min Kyung An, Hyuk Cho

Abstract:

In this paper, we study the Minimum Latency Broadcast Scheduling (MLBS) problem in wireless sensor networks (WSNs). The main issue of the MLBS problem is to compute schedules with the minimum number of timeslots such that a base station can broadcast data to all other sensor nodes with no collisions. Unlike existing works that utilize the traditional omni-directional WSNs, we target the directional WSNs where nodes can collaboratively determine and orientate their antenna directions. We first develop a 7-approximation algorithm, adopting directional WSNs. Our ratio is currently the best, to the best of our knowledge. We then validate the performance of the proposed algorithm through simulation.

Keywords: Broadcast, collision-free, directional antenna, approximation, wireless sensor networks.

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Authors: Naoya Ozaki, Takuya Watanabe, Ryosuke Matsumoto, Noriko Fukasawa

Abstract:

In the metropolitan areas in Japan, in many stations, shopping areas are set up, and escalators and elevators are installed to make the stations be barrier-free. Further, many areas around the stations are being redeveloped. Railway business operators want to know how much effect these circumstances have on attractiveness of the station or number of passengers using the station. So, we performed a questionnaire survey of the station users in the metropolitan areas for finding factors to affect the attractiveness of stations. Then, based on the analysis of the survey, we developed a method to quantitatively evaluate attractiveness of the stations. We also developed an estimation method for number of passengers based on combination of attractiveness of the station quantitatively evaluated and the residential and labor population around the station. Then, we derived precise linear regression models estimating the attractiveness of the station and number of passengers of the station.

Keywords: Attractiveness of the station, estimation method, number of passengers of the station, redevelopment around the station, renovation of the station.

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Authors: Richard Molyneux, Christopher Parrott, Kirill Horoshenkov

Abstract:

This paper aims to demonstrate how various algorithms can be implemented within swarms of autonomous robots to provide continuous inspection within underground pipeline networks. Current methods of fault detection within pipes are costly, time consuming and inefficient. As such, solutions tend toward a more reactive approach, repairing faults, as opposed to proactively seeking leaks and blockages. The paper presents an efficient inspection method, showing that autonomous swarm robotics is a viable way of monitoring underground infrastructure. Tailored adaptations of various Vehicle Routing Problems (VRP) and path-planning algorithms provide a customised inspection procedure for complicated networks of underground pipes. The performance of multiple algorithms is compared to determine their effectiveness and feasibility. Notable inspirations come from ant colonies and stigmergy, graph theory, the k-Chinese Postman Problem ( -CPP) and traffic theory. Unlike most swarm behaviours which rely on fast communication between agents, underground pipe networks are a highly challenging communication environment with extremely limited communication ranges. This is due to the extreme variability in the pipe conditions and relatively high attenuation of acoustic and radio waves with which robots would usually communicate. This paper illustrates how to optimise the inspection process and how to increase the frequency with which the robots pass each other, without compromising the routes they are able to take to cover the whole network.

Keywords: Autonomous inspection, buried pipes, stigmergy, swarm intelligence, vehicle routing problem.

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Authors: Jonah Gamba

Abstract:

In this paper the problem of estimating the time delay between two spatially separated noisy sinusoidal signals by system identification modeling is addressed. The system is assumed to be perturbed by both input and output additive white Gaussian noise. The presence of input noise introduces bias in the time delay estimates. Normally the solution requires a priori knowledge of the input-output noise variance ratio. We utilize the cascade of a self-tuned filter with the time delay estimator, thus making the delay estimates robust to input noise. Simulation results are presented to confirm the superiority of the proposed approach at low input signal-to-noise ratios.

Keywords: LMS algorithm, Self-tuned filter, Systemidentification, Time delay estimation, .

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Authors: Darwin Gouwanda, S. G. Ponnambalam

Abstract:

Set covering problem is a classical problem in computer science and complexity theory. It has many applications, such as airline crew scheduling problem, facilities location problem, vehicle routing, assignment problem, etc. In this paper, three different techniques are applied to solve set covering problem. Firstly, a mathematical model of set covering problem is introduced and solved by using optimization solver, LINGO. Secondly, the Genetic Algorithm Toolbox available in MATLAB is used to solve set covering problem. And lastly, an ant colony optimization method is programmed in MATLAB programming language. Results obtained from these methods are presented in tables. In order to assess the performance of the techniques used in this project, the benchmark problems available in open literature are used.

Keywords: Set covering problem, genetic algorithm, ant colony optimization, LINGO.

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Authors: Hélder Spínola

Abstract:

Sustainable development is highly dependent on the implementation of environmental education programs, which has as its ultimate goal to produce environmentally literate citizens that undertake environmentally friendly actions. Efforts on environmental education along past years are now perceived on the increase of citizens awareness on European countries and, particularly, in Portugal. However, we still have a lack of information on the prevalence of specific behaviors that contributes to sustainability, influenced by a new attitude toward the environment. The determination of pro-environmental behaviors prevalence in higher education students is an important approach to understand to which extend the next leading generation is, in practice, committed with the goals of sustainable development. Therefore, present study evaluates the prevalence of a specific set of behaviors (water savings, energy savings, environmental criteria on shopping, and mobility) on the University of Madeira students and discusses their commitment with sustainable development.

Keywords: Pro-environmental behaviors, sustainable development, environmental education, higher education students

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Authors: Hassan Haleh, Zohreh Nasiri, Parisa Farahpour

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During recent years, the traditional learning approaches have undergone fundamental changes due to the emergence of new technologies such as multimedia, hypermedia and telecommunication. E-learning is a modern world phenomenon that has come into existence in the information age and in a knowledgebased society. E-learning has developed significantly within a short period of time. Thus it is of a great significant to secure information, allow a confident access and prevent unauthorized accesses. Making use of individuals- physiologic or behavioral (biometric) properties is a confident method to make the information secure. Among the biometrics, fingerprint is more acceptable and most countries use it as an efficient methods of identification. This article provides a new method to compare the fingerprint comparison by pattern recognition and image processing techniques. To verify fingerprint, the shortest distance method is used together with perceptronic multilayer neural network functioning based on minutiae. This method is highly accurate in the extraction of minutiae and it accelerates comparisons due to elimination of false minutiae and is more reliable compared with methods that merely use directional images.

Keywords: Fingerprint, minutiae, extraction of properties, multilayer neural network

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Authors: Tudor Petreuş, Andrei Neamţu, Cristina Dascălu, Paul Dan Sîrbu, Carmen E. Cotrutz

Abstract:

Matrix metalloproteinases (MMP) are a class of structural and functional related enzymes involved in altering the natural elements of the extracellular matrix. Most of the MMP structures are cristalographycally determined and published in WorldWide ProteinDataBank, isolated, in full structure or bound to natural or synthetic inhibitors. This study proposes an algorithm to replace missing crystallographic structures in PDB database. We have compared the results of a chosen docking algorithm with a known crystallographic structure in order to validate enzyme sites reconstruction there where crystallographic data are missing.

Keywords: matrix metalloproteinases, molecular docking, structure superposition, surface complementarity.

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Authors: Akhilesh G. Naik, Dipankar Pal

Abstract:

In today’s scenario, the complexity of digital signal processing (DSP) applications and various microcontroller architectures have been increasing to such an extent that the traditional approaches to multiplier design in most processors are becoming outdated for being comparatively slow. Modern processing applications require suitable pipelined approaches, and therefore, algorithms that are friendlier with pipelined architectures. Traditional algorithms like Wallace Tree, Radix-4 Booth, Radix-8 Booth, Dadda architectures have been proven to be comparatively slow for pipelined architectures. These architectures, therefore, need to be optimized or combined with other architectures amongst them to enhance its performances and to be made suitable for pipelined hardware/architectures. Recently, Vedic algorithm mathematically has proven to be efficient by appearing to be less complex and with fewer steps for its output establishment and have assumed renewed importance. This paper describes and shows how the Vedic algorithm can be better suited for pipelined architectures and also can be combined with traditional architectures and algorithms for enhancing its ability even further. In this paper, we also established that for complex applications on DSP and other microcontroller architectures, using Vedic approach for multiplication proves to be the best available and efficient option.

Keywords: Wallace tree, Radix-4 Booth, Radix-8 Booth, Dadda, Vedic, Single-Stage Karatsuba, Looped Karatsuba.

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Authors: Kunyanuth Kularbphettong, Kunnika Tenprakhon, Pattarapan Roonrakwit

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In this paper, we present a recommendation library application on Android system. The objective of this system is to support and advice user to use library resources based on mobile application. We describe the design approaches and functional components of this system. The system was developed based on under association rules, Apriori algorithm. In this project, it was divided the result by the research purposes into 2 parts: developing the Mobile application for online library service and testing and evaluating the system. Questionnaires were used to measure user satisfaction with system usability by specialists and users. The results were satisfactory both specialists and users.

Keywords: Online library, Apriori algorithm, android application, black box.

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Authors: Maxat Bokambayev, Bella Tussupova, Aisha Mamyrova, Erlan Izbasarov

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Optimization of business processes in trading companies is reviewed in the report. There is the presentation of the “Wholesale Customer Order Handling Process” business process model applicable for small and medium businesses. It is proposed to apply the algorithm for automation of the customer order processing which will significantly reduce labor costs and time expenditures and increase the profitability of companies. An optimized business process is an element of the information system of accounting of spare parts trading network activity. The considered algorithm may find application in the trading industry as well.

Keywords: Business processes, discrete-event simulation.

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Authors: Sauravjyoti Sarmah, Rosy Das, Dhruba Kr. Bhattacharyya

Abstract:

Clustering algorithms help to understand the hidden information present in datasets. A dataset may contain intrinsic and nested clusters, the detection of which is of utmost importance. This paper presents a Distributed Grid-based Density Clustering algorithm capable of identifying arbitrary shaped embedded clusters as well as multi-density clusters over large spatial datasets. For handling massive datasets, we implemented our method using a 'sharednothing' architecture where multiple computers are interconnected over a network. Experimental results are reported to establish the superiority of the technique in terms of scale-up, speedup as well as cluster quality.

Keywords: Clustering, Density-based, Grid-based, Adaptive Grid.

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Authors: El-Said Badr, Mahmoud Moussa, Konstantinos Paparrizos, Nikolaos Samaras, Angelo Sifaleras

Abstract:

There are two major variants of the Simplex Algorithm: the revised method and the standard, or tableau method. Today, all serious implementations are based on the revised method because it is more efficient for sparse linear programming problems. Moreover, there are a number of applications that lead to dense linear problems so our aim in this paper is to present some computational results on parallel implementation of dense Simplex Method. Our implementation is implemented on a SMP cluster using C programming language and the Message Passing Interface MPI. Preliminary computational results on randomly generated dense linear programs support our results.

Keywords: Linear Programming, MPI, Parallel Implementation, Simplex Algorithm.

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Authors: Ali Vaseghi Ardekani, Hamid Reza Forutan, Amir Habibi, Ali Reza Rajabi, Hasan Adloo

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Distributed generation units (DGs) are grid-connected or stand-alone electric generation units located within the electric distribution system at or near the end user. It is generally accepted that centralized electric power plants will remain the major source of the electric power supply for the near future. DGs, however, can complement central power by providing incremental capacity to the utility grid or to an end user. This paper presents an efficient power dispatching model for hybrid wind-Solar power generation system, to satisfy some essential requirements, such as dispersed electric power demand, electric power quality and reducing generation cost and so on. In this paper, presented some elements of the main parts in the hybrid system; and then made fundamental dispatching strategies according to different situations; then pointed out four improving measures to improve genetic algorithm, such as: modify the producing way of selection probability, improve the way of crossover, protect excellent chromosomes, and change mutation range and so on. Finally, propose a technique for solving the unit's commitment for dispatching problem based on an improved genetic algorithm.

Keywords: Power Quality, Wind-Solar System, Genetic Algorithm, Hybrid System.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

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The Maximum Weighted Independent Set (MWIS) problem is a classic graph optimization NP-hard problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the MWIS problem is to find a vertex set S V whose total weight is maximum subject to no two vertices in S are adjacent. This paper presents a novel approach to approximate the MWIS of a graph using minimum weighted vertex cover of the graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the proposed algorithm can yield better solutions than other existing algorithms found in the literature for solving the MWIS.

Keywords: weighted independent set, vertex cover, vertex support, heuristic, NP - hard problem.

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Authors: Rongli Gai, Zhiyuan Chang, Xiaohong Wang, Jingyu Liu

Abstract:

In view of various situations in the interpolation process, most researchers use self-adaptation to adjust the interpolation process, which is also one of the current and future research hotspots in the field of CNC (Computerized Numerical Control) machining. In the interpolation process, according to the overview of the spline curve interpolation algorithm, the adaptive analysis is carried out from the factors affecting the interpolation process. The adaptive operation is reflected in various aspects, such as speed, parameters, errors, nodes, feed rates, random period, sensitive point, step size, curvature, adaptive segmentation, adaptive optimization, etc. This paper will analyze and summarize the research of adaptive imputation in the direction of the above factors affecting imputation.

Keywords: Adaptive algorithm, CNC machining, interpolation constraints, spline curve interpolation.

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Authors: Sidhartha Panda, Narayana Prasad Padhy

Abstract:

This paper presents a systematic procedure for modelling and simulation of a power system installed with a power system stabilizer (PSS) and a flexible ac transmission system (FACTS)-based controller. For the design purpose, the model of example power system which is a single-machine infinite-bus power system installed with the proposed controllers is developed in MATLAB/SIMULINK. In the developed model synchronous generator is represented by model 1.1. which includes both the generator main field winding and the damper winding in q-axis so as to evaluate the impact of PSS and FACTS-based controller on power system stability. The model can be can be used for teaching the power system stability phenomena, and also for research works especially to develop generator controllers using advanced technologies. Further, to avoid adverse interactions, PSS and FACTS-based controller are simultaneously designed employing genetic algorithm (GA). The non-linear simulation results are presented for the example power system under various disturbance conditions to validate the effectiveness of the proposed modelling and simultaneous design approach.

Keywords: Genetic algorithm, modelling and simulation, MATLAB/SIMULINK, power system stabilizer, thyristor controlledseries compensator, simultaneous design, power system stability.

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Authors: Niousha Bagheri Khulenjani, Mohammad Saniee Abadeh

Abstract:

Learning from very big datasets is a significant problem for most present data mining and machine learning algorithms. MicroRNA (miRNA) is one of the important big genomic and non-coding datasets presenting the genome sequences. In this paper, a hybrid method for the classification of the miRNA data is proposed. Due to the variety of cancers and high number of genes, analyzing the miRNA dataset has been a challenging problem for researchers. The number of features corresponding to the number of samples is high and the data suffer from being imbalanced. The feature selection method has been used to select features having more ability to distinguish classes and eliminating obscures features. Afterward, a Convolutional Neural Network (CNN) classifier for classification of cancer types is utilized, which employs a Genetic Algorithm to highlight optimized hyper-parameters of CNN. In order to make the process of classification by CNN faster, Graphics Processing Unit (GPU) is recommended for calculating the mathematic equation in a parallel way. The proposed method is tested on a real-world dataset with 8,129 patients, 29 different types of tumors, and 1,046 miRNA biomarkers, taken from The Cancer Genome Atlas (TCGA) database.

Keywords: Cancer classification, feature selection, deep learning, genetic algorithm.

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Authors: Yu-Jen Chang, Shih-Chieh Chen, Yu-Wei Kuo

Abstract:

In this study, we are interested in the economic lot scheduling problem (ELSP) that considers manufacturing of the serviceable products and remanufacturing of the reworked products. In this paper, we formulate a mathematical model for the ELSP with reworks using the basic period approach. In order to solve this problem, we propose a search algorithm to find the cyclic multiplier ki of each product that can be cyclically produced for every ki basic periods. This research also uses two heuristics to search for the optimal production sequence of all lots and the optimal time length of the basic period so as to minimize the average total cost. This research uses a numerical example to show the effectiveness of our approach.

Keywords: Economic lot, reworks, inventory, basic period.

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