Search results for: Naturally-inspired algorithms and particle swarm optimization.

Authors: Mohamed Abdelwahed

Abstract:

The aeration process via injectors is used to combat the lack of oxygen in lakes due to eutrophication. A 3D numerical simulation of the resulting flow using a simplified model is presented. In order to generate the best dynamic in the fluid with respect to the aeration purpose, the optimization of the injectors location is considered. We propose to adapt to this problem the topological sensitivity analysis method which gives the variation of a criterion with respect to the creation of a small hole in the domain. The main idea is to derive the topological sensitivity analysis of the physical model with respect to the insertion of an injector in the fluid flow domain. We propose in this work a topological optimization algorithm based on the studied asymptotic expansion. Finally we present some numerical results, showing the efficiency of our approach

Keywords: Quasi Stokes equations, Numerical simulation, topological optimization, sensitivity analysis.

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Authors: Mahmoud M. Mhashi

Abstract:

A new algorithm called Character-Comparison to Character-Access (CCCA) is developed to test the effect of both: 1) converting character-comparison and number-comparison into character-access and 2) the starting point of checking on the performance of the checking operation in string searching. An experiment is performed; the results are compared with five algorithms, namely, Naive, BM, Inf_Suf_Pref, Raita, and Circle. With the CCCA algorithm, the results suggest that the evaluation criteria of the average number of comparisons are improved up to 74.0%. Furthermore, the results suggest that the clock time required by the other algorithms is improved in range from 28% to 68% by the new CCCA algorithm

Keywords: Pattern matching, string searching, charactercomparison, character-access, and checking.

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Authors: A. K. Al-Othman

Abstract:

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

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

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Authors: Turgay Temel, John Hallam

Abstract:

A recent neurospiking coding scheme for feature extraction from biosonar echoes of various plants is examined with avariety of stochastic classifiers. Feature vectors derived are employedin well-known stochastic classifiers, including nearest-neighborhood,single Gaussian and a Gaussian mixture with EM optimization.Classifiers' performances are evaluated by using cross-validation and bootstrapping techniques. It is shown that the various classifers perform equivalently and that the modified preprocessing configuration yields considerably improved results.

Keywords: Classification, neuro-spike coding, non-parametricmodel, parametric model, Gaussian mixture, EM algorithm.

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Authors: Nkechi Neboh, Josiah Adeyemo, Abimbola Enitan, Oludayo Olugbara

Abstract:

Evolutionary Algorithms (EAs) have been used widely through evolution theory to discover acceptable solutions that corresponds to challenges such as natural resources management. EAs are also used to solve varied problems in the real world. EAs have been rapidly identified for its ease in handling multiple objective problems. Reservoir operations is a vital and researchable area which has been studied in the last few decades due to the limited nature of water resources that is found mostly in the semi-arid regions of the world. The state of some developing economy that depends on electricity for overall development through hydropower production, a renewable form of energy, is appalling due to water scarcity. This paper presents a review of the applications of evolutionary algorithms to reservoir operation for hydropower production. This review includes the discussion on areas such as genetic algorithm, differential evolution, and reservoir operation. It also identified the research gaps discovered in these areas. The results of this study will be an eye opener for researchers and decision makers to think deeply of the adverse effect of water scarcity and drought towards economic development of a nation. Hence, it becomes imperative to identify evolutionary algorithms that can address this issue which can hamper effective hydropower generation.

Keywords: Evolutionary algorithms, genetic algorithm, hydropower, multi-objective, reservoir operations.

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Authors: A. K. Al-Othman, Nabil A. Ahmed, A. M. Al-Kandari, H. K. Ebraheem

Abstract:

Selective harmonic elimination-pulse width modulation techniques offer a tight control of the harmonic spectrum of a given voltage waveform generated by a power electronic converter along with a low number of switching transitions. Traditional optimization methods suffer from various drawbacks, such as prolonged and tedious computational steps and convergence to local optima; thus, the more the number of harmonics to be eliminated, the larger the computational complexity and time. This paper presents a novel method for output voltage harmonic elimination and voltage control of PWM AC/AC voltage converters using the principle of hybrid Real-Coded Genetic Algorithm-Pattern Search (RGA-PS) method. RGA is the primary optimizer exploiting its global search capabilities, PS is then employed to fine tune the best solution provided by RGA in each evolution. The proposed method enables linear control of the fundamental component of the output voltage and complete elimination of its harmonic contents up to a specified order. Theoretical studies have been carried out to show the effectiveness and robustness of the proposed method of selective harmonic elimination. Theoretical results are validated through simulation studies using PSIM software package.

Keywords: PWM, AC/AC voltage converters, selectiveharmonic elimination, direct search method, pattern search method, Real-coded Genetic algorithms, evolutionary algorithms andoptimization.

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Authors: K. Navaz, Kannan Balasubramanian

Abstract:

Due to the increasing growth of internet users, the emerging applications of multicast are growing day by day and there is a requisite for the design of high-speed switches/routers. Huge amounts of effort have been done into the research area of multicast switch fabric design and algorithms. Different traffic scenarios are the influencing factor which affect the throughput and delay of the switch. The pointer based multicast scheduling algorithms are not performed well under non-uniform traffic conditions. In this work, performance of the switch has been analyzed by applying the advanced multicast scheduling algorithm OQSMS (Optimal Queue Selection Based Multicast Scheduling Algorithm), MDDR (Multicast Due Date Round-Robin Scheduling Algorithm) and MDRR (Multicast Dual Round-Robin Scheduling Algorithm). The results show that OQSMS achieves better switching performance than other algorithms under the uniform, non-uniform and bursty traffic conditions and it estimates optimal queue in each time slot so that it achieves maximum possible throughput.

Keywords: Multicast, Switch, Delay, Scheduling.

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Authors: Zeyu Zhang, Guisheng Yin, Ziying Zhang, Liguo Zhang

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This paper mainly studies the path planning method based on ant colony optimization (ACO), and proposes heuristic integration ant colony optimization (HIACO). This paper not only analyzes and optimizes the principle, but also simulates and analyzes the parameters related to the application of HIACO in path planning. Compared with the original algorithm, the improved algorithm optimizes probability formula, tabu table mechanism and updating mechanism, and introduces more reasonable heuristic factors. The optimized HIACO not only draws on the excellent ideas of the original algorithm, but also solves the problems of premature convergence, convergence to the sub optimal solution and improper exploration to some extent. HIACO can be used to achieve better simulation results and achieve the desired optimization. Combined with the probability formula and update formula, several parameters of HIACO are tested. This paper proves the principle of the HIACO and gives the best parameter range in the research of path planning.

Keywords: Ant colony optimization, heuristic integration, path planning

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

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

Keywords: Depth estimation, image filters, stereo match.

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Authors: W. M. Wan Muhamad, E. Sujatmika, M.R. Idris, S.A. Syed Ahmad

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A finite element analysis (FEA) computer software HyperWorks is utilized in re-designing an automotive component to reduce its mass. Reduction of components mass contributes towards environmental sustainability by saving world-s valuable metal resources and by reducing carbon emission through improved overall vehicle fuel efficiency. A shape optimization analysis was performed on a rear spindle component. Pre-processing and solving procedures were performed using HyperMesh and RADIOSS respectively. Shape variables were defined using HyperMorph. Then optimization solver OptiStruct was utilized with fatigue life set as a design constraint. Since Stress-Number of Cycle (S-N) theory deals with uni-axial stress, the Signed von Misses stress on the component was used for looking up damage on S-N curve, and Gerber criterion for mean stress corrections. The optimization analysis resulted in mass reduction of 24% of the original mass. The study proved that the adopted approach has high potential use for environmental sustainability.

Keywords: Environmental Sustainability, Shape Optimization, Fatigue, Rear Spindle.

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Authors: Amirhossein Chambari, Seyed Habib Rahmaty, Vahid Hajipour, Aida Karimi

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This paper proposes a bi-objective model for the facility location problem under a congestion system. The idea of the model is motivated by applications of locating servers in bank automated teller machines (ATMS), communication networks, and so on. This model can be specifically considered for situations in which fixed service facilities are congested by stochastic demand within queueing framework. We formulate this model with two perspectives simultaneously: (i) customers and (ii) service provider. The objectives of the model are to minimize (i) the total expected travelling and waiting time and (ii) the average facility idle-time. This model represents a mixed-integer nonlinear programming problem which belongs to the class of NP-hard problems. In addition, to solve the model, two metaheuristic algorithms including nondominated sorting genetic algorithms (NSGA-II) and non-dominated ranking genetic algorithms (NRGA) are proposed. Besides, to evaluate the performance of the two algorithms some numerical examples are produced and analyzed with some metrics to determine which algorithm works better.

Keywords: Queuing, Location, Bi-objective, NSGA-II, NRGA

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Authors: N. H. Harun, A. S. Abdul Nasir, M. Y. Mashor, R. Hassan

Abstract:

Leukaemia is a blood cancer disease that contributes to the increment of mortality rate in Malaysia each year. There are two main categories for leukaemia, which are acute and chronic leukaemia. The production and development of acute leukaemia cells occurs rapidly and uncontrollable. Therefore, if the identification of acute leukaemia cells could be done fast and effectively, proper treatment and medicine could be delivered. Due to the requirement of prompt and accurate diagnosis of leukaemia, the current study has proposed unsupervised pixel segmentation based on clustering algorithm in order to obtain a fully segmented abnormal white blood cell (blast) in acute leukaemia image. In order to obtain the segmented blast, the current study proposed three clustering algorithms which are k-means, fuzzy c-means and moving k-means algorithms have been applied on the saturation component image. Then, median filter and seeded region growing area extraction algorithms have been applied, to smooth the region of segmented blast and to remove the large unwanted regions from the image, respectively. Comparisons among the three clustering algorithms are made in order to measure the performance of each clustering algorithm on segmenting the blast area. Based on the good sensitivity value that has been obtained, the results indicate that moving kmeans clustering algorithm has successfully produced the fully segmented blast region in acute leukaemia image. Hence, indicating that the resultant images could be helpful to haematologists for further analysis of acute leukaemia.

Keywords: Acute Leukaemia Images, Clustering Algorithms, Image Segmentation, Moving k-Means.

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Authors: Clark Van Dam, Gagan Mirchandani

Abstract:

The Continuously Adaptive Mean-Shift (CamShift) algorithm, incorporating scene depth information is combined with the l1-minimization sparse representation based method to form a hybrid kernel and state space-based tracking algorithm. We take advantage of the increased efficiency of the former with the robustness to occlusion property of the latter. A simple interchange scheme transfers control between algorithms based upon drift and occlusion likelihood. It is quantified by the projection of target candidates onto a depth map of the 2D scene obtained with a low cost stereo vision webcam. Results are improved tracking in terms of drift over each algorithm individually, in a challenging practical outdoor multiple occlusion test case.

Keywords: CamShift, l1-minimization, particle filter, stereo vision, video tracking.

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Authors: R. Chithra, B. Kalavathi, J. Christy Lavanya

Abstract:

WiMAX is a telecommunications technology and it is specified by the Institute of Electrical and Electronics Engineers Inc., as the IEEE 802.16 standard. The goal of this technology is to provide a wireless data over long distances in a variety of ways. IEEE 802.16 is a recent standard for mobile communication. In this paper, we provide an overview of various key management algorithms to provide security for WiMAX.

Keywords: Broadcast, Rekeying, Scalability, Secrecy, Unicast, WiMAX.

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Authors: Xinyue Zhao, Yutaka Satoh, Hidenori Takauji, Shun'ichi Kaneko

Abstract:

A hybrid feature based adaptive particle filter algorithm is presented for object tracking in real scenarios with static camera. The hybrid feature is combined by two effective features: the Grayscale Arranging Pairs (GAP) feature and the color histogram feature. The GAP feature has high discriminative ability even under conditions of severe illumination variation and dynamic background elements, while the color histogram feature has high reliability to identify the detected objects. The combination of two features covers the shortage of single feature. Furthermore, we adopt an updating target model so that some external problems such as visual angles can be overcame well. An automatic initialization algorithm is introduced which provides precise initial positions of objects. The experimental results show the good performance of the proposed method.

Keywords: Hybrid feature, adaptive Particle Filter, robust Object Tracking, Grayscale Arranging Pairs (GAP) feature.

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Authors: M. K. Jindal, G. S. Lehal, R. K. Sharma

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Character segmentation is an important preprocessing step for text recognition. In degraded documents, existence of touching characters decreases recognition rate drastically, for any optical character recognition (OCR) system. In this paper a study of touching Gurmukhi characters is carried out and these characters have been divided into various categories after a careful analysis.Structural properties of the Gurmukhi characters are used for defining the categories. New algorithms have been proposed to segment the touching characters in middle zone. These algorithms have shown a reasonable improvement in segmenting the touching characters in degraded Gurmukhi script. The algorithms proposed in this paper are applicable only to machine printed text.

Keywords: Character Segmentation, Middle Zone, Touching Characters.

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Authors: Ivan C. Mustakerov, Daniela I. Borissova

Abstract:

The paper proposes an approach for design of modular systems based on original technique for modeling and formulation of combinatorial optimization problems. The proposed approach is described on the example of personal computer configuration design. It takes into account the existing compatibility restrictions between the modules and can be extended and modified to reflect different functional and users- requirements. The developed design modeling technique is used to formulate single objective nonlinear mixedinteger optimization tasks. The practical applicability of the developed approach is numerically tested on the basis of real modules data. Solutions of the formulated optimization tasks define the optimal configuration of the system that satisfies all compatibility restrictions and user requirements.

Keywords: Constrained discrete combinatorial choice, modular systems design, optimization problem, PC configuration.

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Authors: Amir Hajian, Sepehr Damavandinejadmonfared

Abstract:

In this paper the issue of dimensionality reduction is investigated in finger vein recognition systems using kernel Principal Component Analysis (KPCA). One aspect of KPCA is to find the most appropriate kernel function on finger vein recognition as there are several kernel functions which can be used within PCA-based algorithms. In this paper, however, another side of PCA-based algorithms -particularly KPCA- is investigated. The aspect of dimension of feature vector in PCA-based algorithms is of importance especially when it comes to the real-world applications and usage of such algorithms. It means that a fixed dimension of feature vector has to be set to reduce the dimension of the input and output data and extract the features from them. Then a classifier is performed to classify the data and make the final decision. We analyze KPCA (Polynomial, Gaussian, and Laplacian) in details in this paper and investigate the optimal feature extraction dimension in finger vein recognition using KPCA.

Keywords: Biometrics, finger vein recognition, Principal Component Analysis (PCA), Kernel Principal Component Analysis (KPCA).

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Authors: H. Lang, M. Bader, A. Buchroithner

Abstract:

Holistic methods covering the development process as a whole – e.g. systems engineering – have established themselves in product design. However, technical product optimization, representing improvements in efficiency and/or minimization of loss, usually applies to single components of a system. A holistic approach is being defined based on a hierarchical point of view of systems engineering. This is subsequently presented using the example of an electromechanical flywheel energy storage system for automotive applications.

Keywords: Design, product development, product optimization, systems engineering, flywheel energy storage.

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Authors: Panpan Xu, Shulin Sui

Abstract:

The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

Keywords: Genetic algorithm, Adaptive genetic algorithm, Function optimization.

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Authors: José Maria A. Pangilinan, Gerrit K. Janssens

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This paper presents an overview of the multiobjective shortest path problem (MSPP) and a review of essential and recent issues regarding the methods to its solution. The paper further explores a multiobjective evolutionary algorithm as applied to the MSPP and describes its behavior in terms of diversity of solutions, computational complexity, and optimality of solutions. Results show that the evolutionary algorithm can find diverse solutions to the MSPP in polynomial time (based on several network instances) and can be an alternative when other methods are trapped by the tractability problem.

Keywords: Multiobjective evolutionary optimization, geneticalgorithms, shortest paths.

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Authors: Buthainah Fahran Al-Dulaimi, Hamza A. Ali

Abstract:

The well known NP-complete problem of the Traveling Salesman Problem (TSP) is coded in genetic form. A software system is proposed to determine the optimum route for a Traveling Salesman Problem using Genetic Algorithm technique. The system starts from a matrix of the calculated Euclidean distances between the cities to be visited by the traveling salesman and a randomly chosen city order as the initial population. Then new generations are then created repeatedly until the proper path is reached upon reaching a stopping criterion. This search is guided by a solution evaluation function.

Keywords: Genetic algorithms, traveling salesman problem solving, optimization.

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Authors: D. Toghraie, A. R. Azimian

Abstract:

In this paper, the Lennard -Jones potential is applied to molecules of liquid argon as well as its vapor and platinum as solid surface in order to perform a non-equilibrium molecular dynamics simulation to study the microscopic aspects of liquid-vapor-solid interactions. The channel is periodic in x and y directions and along z direction it is bounded by atomic walls. It was found that density of the liquids near the solid walls fluctuated greatly and that the structure was more like a solid than a liquid. This indicates that the interactions of solid and liquid molecules are very strong. The resultant surface tension, liquid density and vapor density are found to be well predicted when compared with the experimental data for argon. Liquid and vapor densities were found to depend on the cutoff radius which induces the use of P3M (particle-particle particle-mesh) method which was implemented for evaluation of force and surface tension.

Keywords: Lennard-Jones Potential, Molecular DynamicsSimulation, Periodic Boundary Conditions (PBC), Non-EquilibriumMolecular Dynamics (NEMD).

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Authors: Apirak Sombat, Teerapol Saleewong, Poom Kumam, Parin Chaipunya, Wiyada Kumam, Anantachai Padcharoen, Yeol Je Cho, Thana Sutthibutpong

Abstract:

This research is aimed to study a two-step iteration process defined over a finite family of σ-asymptotically quasi-nonexpansive nonself-mappings. The strong convergence is guaranteed under the framework of Banach spaces with some additional structural properties including strict and uniform convexity, reflexivity, and smoothness assumptions. With similar projection technique for nonself-mapping in Hilbert spaces, we hereby use the generalized projection to construct a point within the corresponding domain. Moreover, we have to introduce the use of duality mapping and its inverse to overcome the unavailability of duality representation that is exploit by Hilbert space theorists. We then apply our results for σ-asymptotically quasi-nonexpansive nonself-mappings to solve for ideal efficiency of vector optimization problems composed of finitely many objective functions. We also showed that the obtained solution from our process is the closest to the origin. Moreover, we also give an illustrative numerical example to support our results.

Keywords: σ-asymptotically quasi-nonexpansive nonselfmapping, strong convergence, fixed point, uniformly convex and uniformly smooth Banach space.

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Authors: Soham De, Nupur Biswas, Abhijit Sanyal, Pulak Ray, Alokmay Datta

Abstract:

Particle detection in very noisy and low contrast images is an active field of research in image processing. In this article, a method is proposed for the efficient detection and sizing of subsurface spherical particles, which is used for the processing of softly fused Au nanoparticles. Transmission Electron Microscopy is used for imaging the nanoparticles, and the proposed algorithm has been tested with the two-dimensional projected TEM images obtained. Results are compared with the data obtained by transmission optical spectroscopy, as well as with conventional circular object detection algorithms.

Keywords: Transmission Electron Microscopy, Circular Hough Transform, Au Nanoparticles, Median Filter, Laplacian Sharpening Filter, Canny Edge Detection

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Authors: J. D. Mallapur, Supriya H., Santosh B. K., Tej H.

Abstract:

The cellular network is one of the emerging areas of communication, in which the mobile nodes act as member for one base station. The cluster based communication is now an emerging area of wireless cellular multimedia networks. The cluster renders fast communication and also a convenient way to work with connectivity. In our scheme we have proposed an optimization technique for the fuzzy cluster nodes, by categorizing the group members into three categories like long refreshable member, medium refreshable member and short refreshable member. By considering long refreshable nodes as static nodes, we compute the new membership values for the other nodes in the cluster. We compare their previous and present membership value with the threshold value to categorize them into three different members. By which, we optimize the nodes in the fuzzy clusters. The simulation results show that there is reduction in the cluster computational time and iterational time after optimization.

Keywords: Clusters, fuzzy and optimization.

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Authors: A. Udomsakdigool, S. Bangsaranthip

Abstract:

This paper presents an algorithm which combining ant colony optimization in the dynamic programming for solving a dynamic facility layout problem. The problem is separated into 2 phases, static and dynamic phase. In static phase, ant colony optimization is used to find the best ranked of layouts for each period. Then the dynamic programming (DP) procedure is performed in the dynamic phase to evaluate the layout set during multi-period planning horizon. The proposed algorithm is tested over many problems with size ranging from 9 to 49 departments, 2 and 4 periods. The experimental results show that the proposed method is an alternative way for the plant layout designer to determine the layouts during multi-period planning horizon.

Keywords: Ant colony optimization, Dynamicprogramming, Dynamic facility layout planning, Metaheuristic

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Authors: Jiho Park, Yong-Gyu Lee, Gilwon Yoon

Abstract:

Data security in u-Health system can be an important issue because wireless network is vulnerable to hacking. However, it is not easy to implement a proper security algorithm in an embedded u-health monitoring because of hardware constraints such as low performance, power consumption and limited memory size and etc. To secure data that contain personal and biosignal information, we implemented several security algorithms such as Blowfish, data encryption standard (DES), advanced encryption standard (AES) and Rivest Cipher 4 (RC4) for our u-Health monitoring system and the results were successful. Under the same experimental conditions, we compared these algorithms. RC4 had the fastest execution time. Memory usage was the most efficient for DES. However, considering performance and safety capability, however, we concluded that AES was the most appropriate algorithm for a personal u-Health monitoring system.

Keywords: biosignal, data encryption, security measures, u-health

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Authors: C. Ardil

Abstract:

A multiple-criteria decision support system is proposed for the best aircraft selection decision. Various strategic, economic, environmental, and risk-related factors can directly or indirectly influence this choice, and they should be taken into account in the decision-making process. The paper suggests a multiple-criteria analysis to aid in the airline management's decision-making process when choosing an appropriate aircraft. In terms of the suggested approach, an integrated entropic preference optimization programming (POP) for fleet modeling risk analysis is applied. The findings of the study of multiple criteria analysis indicate that the A321(neo) aircraft type is the best alternative in this particular optimization instance. The proposed methodology can be applied to other complex engineering problems involving multiple criteria analysis.

Keywords: Aircraft selection, decision making, multiple criteria decision making, preference optimization programming, POP, entropic weight method, TOPSIS, WSM, WPM

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Authors: R. Srinivasa Rao, S.V.L. Narasimham, M. Ramalingaraju

Abstract:

Network reconfiguration in distribution system is realized by changing the status of sectionalizing switches to reduce the power loss in the system. This paper presents a new method which applies an artificial bee colony algorithm (ABC) for determining the sectionalizing switch to be operated in order to solve the distribution system loss minimization problem. The ABC algorithm is a new population based metaheuristic approach inspired by intelligent foraging behavior of honeybee swarm. The advantage of ABC algorithm is that it does not require external parameters such as cross over rate and mutation rate as in case of genetic algorithm and differential evolution and it is hard to determine these parameters in prior. The other advantage is that the global search ability in the algorithm is implemented by introducing neighborhood source production mechanism which is a similar to mutation process. To demonstrate the validity of the proposed algorithm, computer simulations are carried out on 14, 33, and 119-bus systems and compared with different approaches available in the literature. The proposed method has outperformed the other methods in terms of the quality of solution and computational efficiency.

Keywords: Distribution system, Network reconfiguration, Loss reduction, Artificial Bee Colony Algorithm.

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