Search results for: Hungarian algorithm

Authors: Arslan Ellahi, Syed Amjad Hussain

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Software Testing is a vital process in software development life cycle. We can attain the quality of software after passing it through software testing phase. We have tried to find out automatic test data generation techniques that are a key research area of software testing to achieve test automation that can eventually decrease testing time. In this paper, we review some of the approaches presented in the literature which use evolutionary search based algorithms like Genetic Algorithm, Particle Swarm Optimization (PSO), etc. to validate the test data generation process. We also look into the quality of test data generation which increases or decreases the efficiency of testing. We have proposed test data generation techniques for model-based testing. We have worked on tuning and fitness function of PSO algorithm.

Keywords: search based, evolutionary algorithm, particle swarm optimization, genetic algorithm, test data generation

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Authors: P. K. Singhal, R. Naresh, V. Sharma

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This paper presents the three optimization models, namely New Binary Artificial Bee Colony (NBABC) algorithm, NBABC with Local Search (NBABC-LS), and NBABC with Genetic Crossover (NBABC-GC) for solving the Wind-Thermal Unit Commitment (WTUC) problem. The uncertain nature of the wind power is incorporated using the Weibull probability density function, which is used to calculate the overestimation and underestimation costs associated with the wind power fluctuation. The NBABC algorithm utilizes a mechanism based on the dissimilarity measure between binary strings for generating the binary solutions in WTUC problem. In NBABC algorithm, an intelligent scout bee phase is proposed that replaces the abandoned solution with the global best solution. The local search operator exploits the neighboring region of the current solutions, whereas the integration of genetic crossover with the NBABC algorithm increases the diversity in the search space and thus avoids the problem of local trappings encountered with the NBABC algorithm. These models are then used to decide the units on/off status, whereas the lambda iteration method is used to dispatch the hourly load demand among the committed units. The effectiveness of the proposed models is validated on an IEEE 10-unit thermal system combined with a wind farm over the planning period of 24 hours.

Keywords: artificial bee colony algorithm, economic dispatch, unit commitment, wind power

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Authors: Deepa Das, Susmita Das

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Cognitive Radio (CR) is an emerging technology to combat the spectrum scarcity issues. This is achieved by consistently sensing the spectrum, and detecting the under-utilized frequency bands without causing undue interference to the primary user (PU). In soft decision fusion (SDF) based cooperative spectrum sensing, various evolutionary algorithms have been discussed, which optimize the weight coefficient vector for maximizing the detection performance. In this paper, we propose the hybrid invasive weed optimization and particle swarm optimization (IWO/PSO) algorithm as a fast and global optimization method, which improves the detection probability with a lesser sensing time. Then, the efficiency of this algorithm is compared with the standard invasive weed optimization (IWO), particle swarm optimization (PSO), genetic algorithm (GA) and other conventional SDF based methods on the basis of convergence and detection probability.

Keywords: cognitive radio, spectrum sensing, soft decision fusion, GA, PSO, IWO, hybrid IWO/PSO

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Authors: Jiahe Liu, HongyangYu, Feng Qian, Miao Luo

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The aim of this study was to improve the effects of human body 3D reconstruction. The MvP algorithm was adopted to obtain key point information from multiple perspectives. This algorithm allowed the capture of human posture and joint positions from multiple angles, providing more comprehensive and accurate data. The study also incorporated the SMPL-X model, which has been widely used for human body modeling, to achieve more accurate 3D reconstruction results. The use of the MvP algorithm made it possible to observe the reconstructed object from multiple angles, thus reducing the problems of blind spots and missing information. This algorithm was able to effectively capture key point information, including the position and rotation angle of limbs, providing key data for subsequent 3D reconstruction. Compared with traditional single-view methods, the method of multi-view fusion significantly improved the accuracy and stability of reconstruction. By combining the MvP algorithm with the SMPL-X model, we successfully achieved better human body 3D reconstruction effects. The SMPL-X model is highly scalable and can generate highly realistic 3D human body models, thus providing more detail and shape information.

Keywords: 3D human reconstruction, multi-view, joint point, SMPL-X

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Authors: Mafarja Majdi, Salwani Abdullah, Najmeh S. Jaddi

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One of the global combinatorial optimization problems in machine learning is feature selection. It concerned with removing the irrelevant, noisy, and redundant data, along with keeping the original meaning of the original data. Attribute reduction in rough set theory is an important feature selection method. Since attribute reduction is an NP-hard problem, it is necessary to investigate fast and effective approximate algorithms. In this paper, we proposed two feature selection mechanisms based on memetic algorithms (MAs) which combine the genetic algorithm with a fuzzy record to record travel algorithm and a fuzzy controlled great deluge algorithm to identify a good balance between local search and genetic search. In order to verify the proposed approaches, numerical experiments are carried out on thirteen datasets. The results show that the MAs approaches are efficient in solving attribute reduction problems when compared with other meta-heuristic approaches.

Keywords: rough set theory, attribute reduction, fuzzy logic, memetic algorithms, record to record algorithm, great deluge algorithm

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Authors: Qazi Salman Khalid, Muhammad Khalid, Shahid Maqsood

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This paper presents a solution for optimizing the cycle time in an assembly line with human-robot collaboration and diverse operators. A genetic algorithm with tailored parameters is used to address the assembly line balancing problem in the automobile sector. A mathematical model is developed, depicting the problem. Currently, the firm runs on the largest candidate rule; however, it causes a lag in orders, which ultimately gets penalized. The results of the study show that the proposed GA is effective in providing efficient solutions and that the cycle time has significantly impacted productivity.

Keywords: line balancing, cycle time, genetic algorithm, productivity

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Authors: Zhang Xiaodong, Tang Zixin, Liu Xin

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In order to avoid self-collision of space manipulators during operation process, a real-time detection method is proposed in this paper. The manipulator is fitted into a cylinder enveloping surface, and then the detection algorithm of collision between cylinders is analyzed. The collision model of space manipulator self-links can be detected by using this algorithm in real-time detection during the operation process. To ensure security of the operation, a safety threshold is designed. The simulation and experiment results verify the effectiveness of the proposed algorithm for a 7-DOF space manipulator.

Keywords: space manipulator, collision detection, self-collision, the real-time collision detection

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Authors: Konstantinos Metaxiotis, Konstantinos Liagkouras

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The objective of this study is to examine the performance of three well-known multiobjective evolutionary algorithms for solving optimization problems. The first algorithm is the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), the second one is the Strength Pareto Evolutionary Algorithm 2 (SPEA-2), and the third one is the Multiobjective Evolutionary Algorithms based on decomposition (MOEA/D). The examined multiobjective algorithms are analyzed and tested on the ZDT set of test functions by three performance metrics. The results indicate that the NSGA-II performs better than the other two algorithms based on three performance metrics.

Keywords: MOEAs, multiobjective optimization, ZDT test functions, evolutionary algorithms

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Authors: Rosa L. Figueroa, Christopher A. Flores, Qing Zeng-Treitler

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A regular expression consists of sequence characters which allow describing a text path. Usually, in clinical research, regular expressions are manually created by programmers together with domain experts. Lately, there have been several efforts to investigate how to generate them automatically. This article presents a text classification algorithm based on regexes. The algorithm named REX was designed, and then, implemented as a simplified method to create regexes to classify Spanish text automatically. In order to classify ambiguous cases, such as, when multiple labels are assigned to a testing example, REX includes an information gain method Two sets of data were used to evaluate the algorithm’s effectiveness in clinical text classification tasks. The results indicate that the regular expression based classifier proposed in this work performs statically better regarding accuracy and F-measure than Support Vector Machine and Naïve Bayes for both datasets.

Keywords: information gain, regular expressions, smith-waterman algorithm, text classification

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Authors: Ernesto Linan, Linda Cruz, Lucero Becerra

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In this paper, a new hybridized algorithm based on Chemical Reaction Optimization and Simulated Annealing is proposed to solve the alignment sequence Problem. The Chemical Reaction Optimization is a population-based meta-heuristic algorithm based on the principles of a chemical reaction. Simulated Annealing is applied to solve a large number of combinatorial optimization problems of general-purpose. In this paper, we propose hybridization between Chemical Reaction Optimization algorithm and Simulated Annealing in order to solve the Sequence Alignment Problem. An initial population of molecules is defined at beginning of the proposed algorithm, where each molecule represents a sequence alignment problem. In order to simulate inter-molecule collisions, the process of Chemical Reaction is placed inside the Metropolis Cycle at certain values of temperature. Inside this cycle, change of molecules is done due to collisions; some molecules are accepted by applying Boltzmann probability. The results with the hybrid scheme are better than the results obtained separately.

Keywords: chemical reaction optimization, sequence alignment problem, simulated annealing algorithm, metaheuristics

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Authors: Ousmane Youme, Jean Marie Dembele, Eugene Ezin, Christophe Cambier

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In recent years, the convolutional neural networks (CNN) architectures designed by evolution algorithms have proven to be competitive with handcrafted architectures designed by experts. However, these algorithms need a lot of computational power, which is beyond the capabilities of most researchers and engineers. To overcome this problem, we propose an evolution architecture under length constraints. It consists of two algorithms: a search length strategy to find an optimal space and a search architecture strategy based on a genetic algorithm to find the best individual in the optimal space. Our algorithms drastically reduce resource costs and also keep good performance. On the Cifar-10 dataset, our framework presents outstanding performance with an error rate of 5.12% and only 4.6 GPU a day to converge to the optimal individual -22 GPU a day less than the lowest cost automatic evolutionary algorithm in the peer competition.

Keywords: CNN architecture, genetic algorithm, evolution algorithm, length constraints

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Authors: Mohammed Salem Alzahrani

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In this paper, student admission process is studied to optimize the assignment of vacant seats with three main objectives. Utilizing all vacant seats, satisfying all program of study admission requirements and maintaining fairness among all candidates are the three main objectives of the optimization model. Seat Assignment Method (SAM) is used to build the model and solve the optimization problem with help of Northwest Coroner Method and Least Cost Method. A closed formula is derived for applying the priority of assigning seat to candidate based on SAM.

Keywords: admission process model, assignment problem, Hungarian Method, Least Cost Method, Northwest Corner Method, SAM

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Authors: Yan-Ren Chen, Jenn-Kaie Lain

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This paper proposes a novel indoor positioning algorithm based on visible light communications, implemented by light-emitting diode fixtures. In the proposed positioning algorithm, distances between light-emitting diode fixtures and mobile terminal are derived from the assumption of ideal Lambertian optic radiation model, and Trilateration positioning method is proceeded immediately to get the coordinates of mobile terminal. The proposed positioning algorithm directly obtains distance information from the optical signal modeling, and therefore, statistical distribution of received signal strength at different positions in interior space has no need to be pre-established. Numerically, simulation results have shown that the proposed indoor positioning algorithm can provide accurate location coordinates estimation.

Keywords: indoor positioning, received signal strength, trilateration, visible light communications

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: Seyyedeh Faezeh Hassani Ziabari, Sadegh Eskandari, Maziar Salahi

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Infinite Feature Selection (IFS) algorithm is an efficient feature selection algorithm that selects a subset of features of all sizes (including infinity). In this paper, we present an improved version of it, called clustering IFS (CIFS), by clustering the dataset in advance. To do so, first, we apply the K-means algorithm to cluster the dataset, then we apply IFS. In the CIFS method, the spatial and temporal complexities are reduced compared to the IFS method. Experimental results on 6 datasets show the superiority of CIFS compared to IFS in terms of accuracy, running time, and memory consumption.

Keywords: feature selection, infinite feature selection, clustering, graph

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Authors: Alireza Gholami, Amir H. D. Markazi

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In this paper, an observer-based direct adaptive fuzzy sliding mode (OAFSM) algorithm is proposed. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. The input connection matrix is used to combine the sliding surfaces of individual subsystems, and an adaptive fuzzy algorithm is used to estimate an equivalent sliding mode control input directly. The fuzzy membership functions, which were determined by time consuming try and error processes in previous works, are adjusted by adaptive algorithms. The other advantage of the proposed controller is that the input gain matrix is not limited to be diagonal, i.e. the plant could be over/under actuated provided that controllability and observability are preserved. An observer is constructed to directly estimate the state tracking error, and the nonlinear part of the observer is constructed by an adaptive fuzzy algorithm. The main advantage of the proposed observer is that, the measured outputs is not limited to the first entry of a canonical-form state vector. The closed-loop stability of the proposed method is proved using a Lyapunov-based approach. The proposed method is applied numerically on a multi-link robot manipulator, which verifies the performance of the closed-loop control. Moreover, the performance of the proposed algorithm is compared with some conventional control algorithms.

Keywords: adaptive algorithm, fuzzy systems, membership functions, observer

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Authors: Ehsan Yadegari

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While there are several metaheuristics and exact approaches to solving the Supply Chain Network Design (SCND) problem, there still remains an unfilled gap in using the Teaching-Learning-Based Optimization (TLBO) algorithm. The algorithm has demonstrated desirable results with problems with complicated combinational optimization. The present study introduces a Discrete Self-Study TLBO (DSS-TLBO) with priority-based solution representation that can solve a supply chain network configuration model to lower the total expenses of establishing facilities and the flow of materials. The network features four layers, namely suppliers, plants, distribution centers (DCs), and customer zones. It is designed to meet the customer’s demand through transporting the material between layers of network and providing facilities in the best economic Potential locations. To have a higher quality of the solution and increase the speed of TLBO, a distinct operator was introduced that ensures self-adaptation (self-study) in the algorithm based on the four types of local search. In addition, while TLBO is used in continuous solution representation and priority-based solution representation is discrete, a few modifications were added to the algorithm to remove the solutions that are infeasible. As shown by the results of experiments, the superiority of DSS-TLBO compared to pure TLBO, genetic algorithm (GA) and firefly Algorithm (FA) was established.

Keywords: supply chain network design, teaching–learning-based optimization, improved metaheuristics, discrete solution representation

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Authors: Md Habibul Ansary, Chandan Garai, Ranjan Dasgupta

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Utilization of resources is always a great challenge for any allocation problem, particularly when resource availability is dynamic in nature. In this work VM allocation mechanism has been augmented by providing resources in a combined manner. This approach has some inherent advantages in terms of reduction of wait state for the pending jobs of some users and better utilization of unused resources from the service providers’ point of view. Moreover the algorithm takes care of released resources from the finished jobs as soon as those become available. The proposed algorithm has been explained by suitable example to make the work complete.

Keywords: Bid ratio, cloud service, virtualization, VM allocation problem

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Authors: Mona Heydari, Ehsan Motamedian, Seyed Abbas Shojaosadati

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Prediction of perturbations after genetic manipulation (especially gene knockout) is one of the important challenges in systems biology. In this paper, a new algorithm is introduced that integrates microarray data into the metabolic model. The algorithm was used to study the change in the cell phenotype after knockout of Gss gene in Escherichia coli BW25113. Algorithm implementation indicated that gene deletion resulted in more activation of the metabolic network. Growth yield was more and less regulating gene were identified for mutant in comparison with the wild-type strain.

Keywords: metabolic network, gene knockout, flux balance analysis, microarray data, integration

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Authors: Majid Pourahmadi

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The performance of time-reversal MUSIC algorithm will be dramatically degrades in presence of strong noise and multiple scattering (i.e. when scatterers are close to each other). This is due to error in determining the number of scatterers. The present paper provides a new approach to alleviate such a problem using an information theoretic criterion referred as minimum description length (MDL). The merits of the novel approach are confirmed by the numerical examples. The results indicate the time-reversal MUSIC yields accurate estimate of the target locations with considerable noise and multiple scattering in the received signals.

Keywords: microwave imaging, time reversal, MUSIC algorithm, minimum description length (MDL)

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Authors: Gennady P. Ginkul, Sergey Yu. Soloviov

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The article proposes to use so-called "quotation-based algorithm" for simulation of decision making process in distributed expert systems and multi-agent systems. The idea was adopted from the techniques for group decision-making. It is based on the assumption that one expert system to perform its logical inference may use rules from another expert system. The application of the algorithm was demonstrated on the example in which the consolidated decision is the decision that requires minimal quotation.

Keywords: backward chaining inference, distributed expert systems, group decision making, multi-agent systems

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Authors: Ganesh Nandakumaran, Mehmet Karaata

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A wave is a distributed execution, often made up of a broadcast phase followed by a feedback phase, requiring the participation of all the system processes before a particular event called decision is taken. Wave algorithms with one initiator such as the 1-wave algorithm have been shown to be very efficient for broadcasting messages in tree networks. Extensions of this algorithm broadcasting a sequence of waves using a single initiator have been implemented in algorithms such as the m-wave algorithm. However as the network size increases, having a single initiator adversely affects the message delivery times to nodes further away from the initiator. As a remedy, broadcast waves can be allowed to be initiated by multiple initiator nodes distributed across the network to reduce the completion time of broadcasts. These waves initiated by one or more initiator processes form a collection of waves covering the entire network. Solutions to global-snapshots, distributed broadcast and various synchronization problems can be solved efficiently using waves with multiple concurrent initiators. In this paper, we propose the first stabilizing multi-wave sequence algorithm implementing waves started by multiple initiator processes such that every process in the network receives at least one sequence of broadcasts. Due to being stabilizing, the proposed algorithm can withstand transient faults and do not require initialization. We view a fault as a transient fault if it perturbs the configuration of the system but not its program.

Keywords: distributed computing, multi-node broadcast, propagation of information with feedback and cleaning (PFC), stabilization, wave algorithms

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Authors: Irum Matloob, Shoab Ahmad Khan, Fahim Arif

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As Indo-pak has been the victim of heart diseases since many decades. Many surveys showed that percentage of cardiac patients is increasing in Pakistan day by day, and special attention is needed to pay on this issue. The framework is proposed for performing detailed analysis of ECG survey data which is conducted for measuring the prevalence of heart diseases statistics in Pakistan. The ECG survey data is evaluated or filtered by using automated Minnesota codes and only those ECGs are used for further analysis which is fulfilling the standardized conditions mentioned in the Minnesota codes. Then feature selection is performed by applying proposed algorithm based on discernibility matrix, for selecting relevant features from the database. Clustering is performed for exposing natural clusters from the ECG survey data by applying spectral clustering algorithm using fuzzy c means algorithm. The hidden patterns and interesting relationships which have been exposed after this analysis are useful for further detailed analysis and for many other multiple purposes.

Keywords: arrhythmias, centroids, ECG, clustering, discernibility matrix

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Authors: P. S. Jagadeesh Kumar, Mingmin Pan, Yang Yung, Tracy Lin Huan

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Glaucoma is a group of visual maladies represented by the scheduled optic nerve neuropathy; means to the increasing dwindling in vision ground, resulting in loss of sight. In this paper, a novel support vector machine based retinal therapeutic for glaucoma using machine learning algorithm is conservative. The algorithm has fitting pragmatism; subsequently sustained on correlation clustering mode, it visualizes perfect computations in the multi-dimensional space. Support vector clustering turns out to be comparable to the scale-space advance that investigates the cluster organization by means of a kernel density estimation of the likelihood distribution, where cluster midpoints are idiosyncratic by the neighborhood maxima of the concreteness. The predicted planning has 91% attainment rate on data set deterrent on a consolidation of 500 realistic images of resolute and glaucoma retina; therefore, the computational benefit of depending on the cluster overlapping system pedestal on machine learning algorithm has complete performance in glaucoma therapeutic.

Keywords: machine learning algorithm, correlation clustering mode, cluster overlapping system, glaucoma, kernel density estimation, retinal therapeutic

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Authors: Ali Allahverdi

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The m-machine no-wait flowshop scheduling problem is addressed in this paper. The objective is to minimize total completion time subject to the constraint that the makespan value is not greater than a certain value. Setup times are treated as separate from processing times. Several recent algorithms are adapted and proposed for the problem. An extensive computational analysis has been conducted for the evaluation of the proposed algorithms. The computational analysis indicates that the best proposed algorithm performs significantly better than the earlier existing best algorithm.

Keywords: scheduling, no-wait flowshop, algorithm, setup times, total completion time, makespan

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Authors: Bhrugesh Radadiya, Jaydeep Shah

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In Indian foundry industry, there is a need of defect free casting with minimum production cost in short lead time. Casting defect is a very large issue in foundry shop which increases the rejection rate of casting and wastage of materials. The various parameters influences on casting process such as mold machine related parameters, green sand related parameters, cast metal related parameters, mold related parameters and shake out related parameters. The mold related parameters are most influences on casting defects in sand casting process. This paper review the casting produced by foundry with shrinkage and blow holes as a major defects was analyzed and identified that mold related parameters such as mold temperature, pouring temperature and runner size were not properly set in sand casting process. These parameters were optimized using different optimization techniques such as Taguchi method, Response surface methodology, Genetic algorithm and Teaching-learning based optimization algorithm. Finally, concluded that a Teaching-learning based optimization algorithm give better result than other optimization techniques.

Keywords: casting defects, genetic algorithm, parametric optimization, Taguchi method, TLBO algorithm

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Authors: Xingxing Peng

Abstract:

With the development of society, there are more and more online communication scenarios such as teleconference and online education. In the process of conference communication, the quality of voice communication is a very important part, and noise may cause the communication effect of participants to be greatly reduced. Therefore, voice noise reduction has an important impact on scenarios such as voice calls. This research focuses on the key technologies of the sound transmission process. The purpose is to maintain the audio quality to the maximum so that the listener can hear clearer and smoother sound. Firstly, to solve the problem that the traditional speech enhancement algorithm is not ideal when dealing with non-stationary noise, an adaptive speech noise reduction algorithm is studied in this paper. Traditional noise estimation methods are mainly used to deal with stationary noise. In this chapter, we study the spectral characteristics of different noise types, especially the characteristics of non-stationary Burst noise, and design a noise estimator module to deal with non-stationary noise. Noise features are extracted from non-speech segments, and the noise estimation module is adjusted in real time according to different noise characteristics. This adaptive algorithm can enhance speech according to different noise characteristics, improve the performance of traditional algorithms to deal with non-stationary noise, so as to achieve better enhancement effect. The experimental results show that the algorithm proposed in this chapter is effective and can better adapt to different types of noise, so as to obtain better speech enhancement effect.

Keywords: speech noise reduction, speech enhancement, self-adaptation, Wiener filter algorithm

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Authors: Luong A. Nguyen, Elihu Deneke, Thomas L. Harman

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This paper describes a multibody dynamics algorithm formulated for parallel implementation on multiprocessor computing platforms using the divide-and-conquer approach. The system of interest is a general topology of rigid and elastic articulated bodies with or without loops. The algorithm is an extension of Featherstone’s divide and conquer approach to include the flexible-body dynamics formulation. The equations of motion, configured for the International Space Station (ISS) with its robotic manipulator arm as a system of articulated flexible bodies, are implemented in separate computer processors. The performance of this divide-and-conquer algorithm implementation in multiple processors is compared with an existing method implemented on a single processor.

Keywords: multibody dynamics, multiple processors, multithreading, divide-and-conquer algorithm, computational efficiency, flexible body dynamics

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Authors: R. Rama Kishore, Sunesh

Abstract:

Recent development in the usage of internet for different purposes creates a great threat for the copyright protection of the digital images. Digital watermarking can be used to address the problem. This paper presents detailed review of the different watermarking techniques, latest trends in the field of secured, robust and imperceptible watermarking. It also discusses the different optimization techniques used in the field of watermarking in order to improve the robustness and imperceptibility of the method. Different measures are discussed to evaluate the performance of the watermarking algorithm. At the end, this paper proposes a watermarking algorithm using (2, 2) share visual cryptography and Bezier curve based algorithm to improve the security of the watermark. The proposed method uses fractional transformation to improve the robustness of the copyright protection of the method. The algorithm is optimized using fuzzy entropy for better results.

Keywords: digital watermarking, fractional transform, visual cryptography, Bezier curve, fuzzy entropy

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Authors: Sourabh Joshi, Geetinder Kaur, Sarabjit Kaur, Gulwatanpreet Singh, Geetika Mannan

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In this paper, we have use an algorithm that able to obtain an optimal solution to travelling salesman problem from a huge search space, quickly. This algorithm is based upon the ant colony optimization technique and employees roulette wheel selection mechanism. To illustrate it more clearly, a program has been implemented which is based upon this algorithm, that presents the changing process of route iteration in a more intuitive way. In the event, we had find the optimal path between hundred cities and also calculate the distance between two cities.

Keywords: ant colony, optimization, travelling salesman problem, roulette wheel selection

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