Search results for: optimization problems in signal processing.

Authors: T. Niknam, M. Nayeripour, B.Bahmani Firouzi

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Clustering techniques have received attention in many areas including engineering, medicine, biology and data mining. The purpose of clustering is to group together data points, which are close to one another. The K-means algorithm is one of the most widely used techniques for clustering. However, K-means has two shortcomings: dependency on the initial state and convergence to local optima and global solutions of large problems cannot found with reasonable amount of computation effort. In order to overcome local optima problem lots of studies done in clustering. This paper is presented an efficient hybrid evolutionary optimization algorithm based on combining Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO), called PSO-ACO, for optimally clustering N object into K clusters. The new PSO-ACO algorithm is tested on several data sets, and its performance is compared with those of ACO, PSO and K-means clustering. The simulation results show that the proposed evolutionary optimization algorithm is robust and suitable for handing data clustering.

Keywords: Ant Colony Optimization (ACO), Data clustering, Hybrid evolutionary optimization algorithm, K-means clustering, Particle Swarm Optimization (PSO).

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Authors: Kamran Turkoglu, Ugur Ozdemir, Melike Nikbay, Elbrous M. Jafarov

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In this paper, an automatic control system design based on Integral Squared Error (ISE) parameter optimization technique has been implemented on longitudinal flight dynamics of an UAV. It has been aimed to minimize the error function between the reference signal and the output of the plant. In the following parts, objective function has been defined with respect to error dynamics. An unconstrained optimization problem has been solved analytically by using necessary and sufficient conditions of optimality, optimum PID parameters have been obtained and implemented in control system dynamics.

Keywords: Optimum Design, KKT Conditions, UAV, Longitudinal Flight Dynamics, ISE Parameter Optimization.

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Authors: Susanta Kumar Gachhayat, S. K. Dash

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Multi objective non-convex economic dispatch problems of a thermal power plant are of grave concern for deciding the cost of generation and reduction of emission level for diminishing the global warming level for improving green-house effect. This paper deals with ramp rate constraints for achieving better inequality constraints so as to incorporate valve point loading for cost of generation in thermal power plant through ramp rate biogeography based optimization involving mutation and migration. Through 50 out of 100 trials, the cost function and emission objective function were found to have outperformed other classical methods such as lambda iteration method, quadratic programming method and many heuristic methods like particle swarm optimization method, weight improved particle swarm optimization method, constriction factor based particle swarm optimization method, moderate random particle swarm optimization method etc. Ramp rate biogeography based optimization applications prove quite advantageous in solving non convex multi objective economic dispatch problems subjected to nonlinear loads that pollute the source giving rise to third harmonic distortions and other such disturbances.

Keywords: Economic load dispatch, Biogeography based optimization, Ramp rate biogeography based optimization, Valve Point loading, Moderate random particle swarm optimization method, Weight improved particle swarm optimization method

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Authors: S. Khosroabadi, M. R. Salehi

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In this paper, all-optical signal processors that perform both microwave mixing and bandpass filtering in a radio-over-fiber (RoF) link are presented. The key device is a Mach-Zehnder modulator (MZM) which performs all-optical microwave mixing. An up-converted microwave signal is obtained and other unwanted frequency components are suppressed at the end of the fiber span.

Keywords: Microwave mixing, bandpass filtering, all-optical, signal processing, MZM.

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Authors: Liming Zhang

Abstract:

There have been different approaches to compute the analytic instantaneous frequency with a variety of background reasoning and applicability in practice, as well as restrictions. This paper presents an adaptive Fourier decomposition and (α-counting) based instantaneous frequency computation approach. The adaptive Fourier decomposition is a recently proposed new signal decomposition approach. The instantaneous frequency can be computed through the so called mono-components decomposed by it. Due to the fast energy convergency, the highest frequency of the signal will be discarded by the adaptive Fourier decomposition, which represents the noise of the signal in most of the situation. A new instantaneous frequency definition for a large class of so-called simple waves is also proposed in this paper. Simple wave contains a wide range of signals for which the concept instantaneous frequency has a perfect physical sense. The α-counting instantaneous frequency can be used to compute the highest frequency for a signal. Combination of these two approaches one can obtain the IFs of the whole signal. An experiment is demonstrated the computation procedure with promising results.

Keywords: Adaptive Fourier decomposition, Fourier series, signal processing, instantaneous frequency

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Authors: Eng. Alaa K. Satti Salih

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Revolutions Applications such as telecommunications, hands-free communications, recording, etc. which need at least one microphone, the signal is usually infected by noise and echo. The important application is the speech enhancement, which is done to remove suppressed noises and echoes taken by a microphone, beside preferred speech. Accordingly, the microphone signal has to be cleaned using digital signal processing DSP tools before it is played out, transmitted, or stored. Engineers have so far tried different approaches to improving the speech by get back the desired speech signal from the noisy observations. Especially Mobile communication, so in this paper will do reconstruction of the speech signal, observed in additive background noise, using the Kalman filter technique to estimate the parameters of the Autoregressive Process (AR) in the state space model and the output speech signal obtained by the MATLAB. The accurate estimation by Kalman filter on speech would enhance and reduce the noise then compare and discuss the results between actual values and estimated values which produce the reconstructed signals.

Keywords: Autoregressive Process, Kalman filter, Matlab and Noise speech.

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Authors: Sasadhar Bera, Indrajit Mukherjee

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Ant colony optimization (ACO) and its variants are applied extensively to resolve various continuous optimization problems. As per the various diversification and intensification schemes of ACO for continuous function optimization, researchers generally consider components of multidimensional state space to generate the new search point(s). However, diversifying to a new search space by updating only components of the multidimensional vector may not ensure that the new point is at a significant distance from the current solution. If a minimum distance is not ensured during diversification, then there is always a possibility that the search will end up with reaching only local optimum. Therefore, to overcome such situations, a Mahalanobis distance-based diversification with Nelder-Mead simplex-based search scheme for each ant is proposed for the ACO strategy. A comparative computational run results, based on nine nonlinear standard test problems, confirms that the performance of ACO is improved significantly with the integration of the proposed schemes in the ACO.

Keywords: Ant Colony Optimization, Diversification Scheme, Intensification, Mahalanobis Distance, Nelder-Mead Simplex.

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Authors: Mustafa Abdalla, Khaled A. Madi, Rajab Farhat

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An array antenna system with innovative signal processing can improve the resolution of a source direction of arrival (DoA) estimation. High resolution techniques take the advantage of array antenna structures to better process the incoming waves. They also have the capability to identify the direction of multiple targets. This paper investigates performance of the DOA estimation algorithm namely; Capon and MUSIC on the uniform linear array (ULA). The simulation results show that in Capon and MUSIC algorithm the resolution of the DOA techniques improves as number of snapshots, number of array elements, signal-to-noise ratio and separation angle between the two sources θ increases.

Keywords: Antenna array, Capon, MUSIC, Direction-of-arrival estimation, signal processing, uniform linear arrays.

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Authors: Cheng Seong Khor, Xiao Qi Yeoh

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This work concerns the topological optimization problem for determining the optimal petroleum refinery configuration. We are interested in further investigating and hopefully advancing the existing optimization approaches and strategies employing logic propositions to conceptual process synthesis problems. In particular, we seek to contribute to this increasingly exciting area of chemical process modeling by addressing the following potentially important issues: (a) how the formulation of design specifications in a mixed-logical-and-integer optimization model can be employed in a synthesis problem to enrich the problem representation by incorporating past design experience, engineering knowledge, and heuristics; and (b) how structural specifications on the interconnectivity relationships by space (states) and by function (tasks) in a superstructure should be properly formulated within a mixed-integer linear programming (MILP) model. The proposed modeling technique is illustrated on a case study involving the alternative processing routes of naphtha, in which significant improvement in the solution quality is obtained.

Keywords: Mixed-integer linear programming (MILP), petroleum refinery, process synthesis, superstructure.

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Authors: Hidehiko Okada

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The author proposes an extension of particle swarm optimization (PSO) for solving interval-valued optimization problems and applies the extended PSO to evolutionary training of neural networks (NNs) with interval weights. In the proposed PSO, values in the genotypes are not real numbers but intervals. Experimental results show that interval-valued NNs trained by the proposed method could well approximate hidden target functions despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithms, swarm intelligence, particle swarm optimization, neural network, interval arithmetic.

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Authors: J. P. Dubois, O. M. Abdul-Latif

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Support Vector Machine (SVM) is a recent class of statistical classification and regression techniques playing an increasing role in applications to detection problems in various engineering problems, notably in statistical signal processing, pattern recognition, image analysis, and communication systems. In this paper, SVM is applied to an infrared (IR) binary communication system with different types of channel models including Ricean multipath fading and partially developed scattering channel with additive white Gaussian noise (AWGN) at the receiver. The structure and performance of SVM in terms of the bit error rate (BER) metric is derived and simulated for these channel stochastic models and the computational complexity of the implementation, in terms of average computational time per bit, is also presented. The performance of SVM is then compared to classical binary signal maximum likelihood detection using a matched filter driven by On-Off keying (OOK) modulation. We found that the performance of SVM is superior to that of the traditional optimal detection schemes used in statistical communication, especially for very low signal-to-noise ratio (SNR) ranges. For large SNR, the performance of the SVM is similar to that of the classical detectors. The implication of these results is that SVM can prove very beneficial to IR communication systems that notoriously suffer from low SNR at the cost of increased computational complexity.

Keywords: Least square-support vector machine, on-off keying, matched filter, maximum likelihood detector, wireless infrared communication.

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Authors: Somkiat Lerkvaranyu, Yoshikazu Miyanaga

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In this paper, a new technique of signal detection has been proposed for detecting the orthogonal frequency-division multiplexing (OFDM) signal in the presence of nonlinear distortion.There are several advantages of OFDM communications system.However, one of the existing problems is remain considered as the nonlinear distortion generated by high-power-amplifier at the transmitter end due to the large dynamic range of an OFDM signal. The proposed method is the maximum likelihood detection with the symbol estimation. When the training data are available, the neural network has been used to learn the characteristic of received signal and to estimate the new positions of the transmitted symbol which are provided to the maximum likelihood detector. Resulting in the system performance, the nonlinear distortions of a traveling wave tube amplifier with OFDM signal are considered in this paper.Simulation results of the bit-error-rate performance are obtained with 16-QAM OFDM systems.

Keywords: OFDM, TWTA, nonlinear distortion, detection.

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Authors: Samee Ullah Khan, C.Ardil

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With data centers, end-users can realize the pervasiveness of services that will be one day the cornerstone of our lives. However, data centers are often classified as computing systems that consume the most amounts of power. To circumvent such a problem, we propose a self-adaptive weighted sum methodology that jointly optimizes the performance and power consumption of any given data center. Compared to traditional methodologies for multi-objective optimization problems, the proposed self-adaptive weighted sum technique does not rely on a systematical change of weights during the optimization procedure. The proposed technique is compared with the greedy and LR heuristics for large-scale problems, and the optimal solution for small-scale problems implemented in LINDO. the experimental results revealed that the proposed selfadaptive weighted sum technique outperforms both of the heuristics and projects a competitive performance compared to the optimal solution.

Keywords: Meta-heuristics, distributed systems, adaptive methods, resource allocation.

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Authors: D. Mondal, A. Chakrabarti, A. Sengupta

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This paper aims to select the optimal location and setting parameters of TCSC (Thyristor Controlled Series Compensator) controller using Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) to mitigate small signal oscillations in a multimachine power system. Though Power System Stabilizers (PSSs) are prime choice in this issue, installation of FACTS device has been suggested here in order to achieve appreciable damping of system oscillations. However, performance of any FACTS devices highly depends upon its parameters and suitable location in the power network. In this paper PSO as well as GA based techniques are used separately and compared their performances to investigate this problem. The results of small signal stability analysis have been represented employing eigenvalue as well as time domain response in face of two common power system disturbances e.g., varying load and transmission line outage. It has been revealed that the PSO based TCSC controller is more effective than GA based controller even during critical loading condition.

Keywords: Genetic Algorithm, Particle Swarm Optimization, Small Signal Stability, Thyristor Controlled Series Compensator.

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Authors: Jörg Lassig, Stefanie Thiem

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The objective of this paper is the introduction to a unified optimization framework for research and education. The OPTILIB framework implements different general purpose algorithms for combinatorial optimization and minimum search on standard continuous test functions. The preferences of this library are the straightforward integration of new optimization algorithms and problems as well as the visualization of the optimization process of different methods exploring the search space exclusively or for the real time visualization of different methods in parallel. Further the usage of several implemented methods is presented on the basis of two use cases, where the focus is especially on the algorithm visualization. First it is demonstrated how different methods can be compared conveniently using OPTILIB on the example of different iterative improvement schemes for the TRAVELING SALESMAN PROBLEM. A second study emphasizes how the framework can be used to find global minima in the continuous domain.

Keywords: Global Optimization Heuristics, Particle Swarm Optimization, Ensemble Based Threshold Accepting, Ruin and Recreate

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Authors: Tushnik Sarkar, Mofazzal H. Khondekar, Subrata Banerjee

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This paper investigates the nature of the fluctuation of the daily average Solar wind speed time series collected over a period of 2492 days, from 1^st January, 1997 to 28^th October, 2003. The degree of self-similarity and scalability of the Solar Wind Speed signal has been explored to characterise the signal fluctuation. Multi-fractal Detrended Fluctuation Analysis (MFDFA) method has been implemented on the signal which is under investigation to perform this task. Furthermore, the singularity spectra of the signals have been also obtained to gauge the extent of the multifractality of the time series signal.

Keywords: Detrended fluctuation analysis, generalized Hurst exponent, holder exponents, multifractal exponent, multifractal spectrum, singularity spectrum, time series analysis.

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Authors: Jiratta Phuboon-ob, Raweewan Auepanwiriyakul

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A data warehouse (DW) is a system which has value and role for decision-making by querying. Queries to DW are critical regarding to their complexity and length. They often access millions of tuples, and involve joins between relations and aggregations. Materialized views are able to provide the better performance for DW queries. However, these views have maintenance cost, so materialization of all views is not possible. An important challenge of DW environment is materialized view selection because we have to realize the trade-off between performance and view maintenance. Therefore, in this paper, we introduce a new approach aimed to solve this challenge based on Two-Phase Optimization (2PO), which is a combination of Simulated Annealing (SA) and Iterative Improvement (II), with the use of Multiple View Processing Plan (MVPP). Our experiments show that 2PO outperform the original algorithms in terms of query processing cost and view maintenance cost.

Keywords: Data warehouse, materialized views, view selectionproblem, two-phase optimization.

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Authors: Y. Abdelrazig

Abstract:

Evolutionary optimization methods such as genetic algorithms have been used extensively for the construction site layout problem. More recently, ant colony optimization algorithms, which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to benchmark combinatorial optimization problems. This paper proposes a formulation of the site layout problem in terms of a sequencing problem that is suitable for solution using an ant colony optimization algorithm. In the construction industry, site layout is a very important planning problem. The objective of site layout is to position temporary facilities both geographically and at the correct time such that the construction work can be performed satisfactorily with minimal costs and improved safety and working environment. During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the construction site layout problem. This paper proposes an ant colony optimization model for construction site layout. A simple case study for a highway project is utilized to illustrate the application of the model.

Keywords: Construction site layout, optimization, ant colony.

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Authors: Mohamed A. G. H. Abdalsadig, Amir Nourian, G. G. Nasr, Meisam Babaie

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Gas lift optimization is becoming more important now a day in petroleum industry. A proper lift optimization can reduce the operating cost, increase the net present value (NPV) and maximize the recovery from the asset. A widely accepted definition of gas lift optimization is to obtain the maximum output under specified operating conditions. In addition, gas lift, a costly and indispensable means to recover oil from high depth reservoir entails solving the gas lift optimization problems. Gas lift optimization is a continuous process; there are two levels of production optimization. The total field optimization involves optimizing the surface facilities and the injection rate that can be achieved by standard tools softwares. Well level optimization can be achieved by optimizing the well parameters such as point of injection, injection rate, and injection pressure. All these aspects have been investigated and presented in this study by using experimental data and PROSPER simulation program. The results show that the well head pressure has a large influence on the gas lift performance and also proved that smart gas lift valve can be used to improve gas lift performance by controlling gas injection from down hole. Obtaining the optimum gas injection rate is important because excessive gas injection reduces production rate and consequently increases the operation cost.

Keywords: Optimization, production rate, reservoir pressure effect, gas injection rate effect, gas injection pressure.

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Authors: Sun K. Yoo, Hee Cheol Kang

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Analysis of amplitude and phase characteristics for delta, theta, and alpha bands at localized time instant from EEG signals is important for the characterizing information processing in the brain. In this paper, complex demodulation method was used to analyze EEG (Electroencephalographic) signal, particularly for auditory evoked potential response signal, with sufficient time resolution and designated frequency bandwidth resolution required. The complex demodulation decomposes raw EEG signal into 3 designated delta, theta, and alpha bands with complex EEG signal representation at sampled time instant, which can enable the extraction of amplitude envelope and phase information. Throughout simulated test data, and real EEG signal acquired during auditory attention task, it can extract the phase offset, phase and frequency changing instant and decomposed amplitude envelope for delta, theta, and alpha bands. The complex demodulation technique can be efficiently used in brain signal analysis in case of phase, and amplitude information required.

Keywords: EEG, Complex Demodulation, Amplitude, Phase.

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Authors: C. Bunsanit

Abstract:

This paper presents the refinement method for two beams formation of wideband smart antenna. The refinement method for weighting coefficients is based on Fully Spatial Signal Processing by taking Inverse Discrete Fourier Transform (IDFT), and its simulation results are presented using MATLAB. The radiation pattern is created by multiplying the incoming signal with real weights and then summing them together. These real weighting coefficients are computed by IDFT method; however, the range of weight values is relatively wide. Therefore, for reducing this range, the refinement method is used. The radiation pattern concerns with five input parameters to control. These parameters are maximum weighting coefficient, wideband signal, direction of mainbeam, beamwidth, and maximum of minor lobe level. Comparison of the obtained simulation results between using refinement method and taking only IDFT shows that the refinement method works well for wideband two beams formation.

Keywords: Fully spatial signal processing, beam forming, refinement method, smart antenna, weighting coefficient, wideband.

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Authors: Wen-Bao Qiao, Jean-Charles Créput

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To accelerate the solution for large scale traveling salesman problems (TSP), a parallel 2-opt local search algorithm with simple implementation based on Graphics Processing Unit (GPU) is presented and tested in this paper. The parallel scheme is based on technique of data decomposition by dynamically assigning multiple K processors on the integral tour to treat K edges’ 2-opt local optimization simultaneously on independent sub-tours, where K can be user-defined or have a function relationship with input size N. We implement this algorithm with doubly linked list on GPU. The implementation only requires O(N) memory. We compare this parallel 2-opt local optimization against sequential exhaustive 2-opt search along integral tour on TSP instances from TSPLIB with more than 10000 cities.

Keywords: Doubly linked list, parallel 2-opt, tour division, GPU.

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Authors: O. Hasançebi, S. Kazemzadeh Azad

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In the present study the efficiency of Big Bang-Big Crunch (BB-BC) algorithm is investigated in discrete structural design optimization. It is shown that a standard version of the BB-BC algorithm is sometimes unable to produce reasonable solutions to problems from discrete structural design optimization. Two reformulations of the algorithm, which are referred to as modified BB-BC (MBB-BC) and exponential BB-BC (EBB-BC), are introduced to enhance the capability of the standard algorithm in locating good solutions for steel truss and frame type structures, respectively. The performances of the proposed algorithms are experimented and compared to its standard version as well as some other algorithms over several practical design examples. In these examples, steel structures are sized for minimum weight subject to stress, stability and displacement limitations according to the provisions of AISC-ASD.

Keywords: Structural optimization, discrete optimization, metaheuristics, big bang-big crunch (BB-BC) algorithm, design optimization of steel trusses and frames.

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Authors: Antonio Mauricio F. L. Miranda de Sá

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Partial coherence between two signals removing the contribution of a periodic, deterministic signal is proposed for evaluating the interrelationship in multivariate systems. The estimator expression was derived and shown to be independent of such periodic signal. Simulations were used for obtaining its critical value, which were found to be the same as those for Gaussian signals, as well as for evaluating the technique. An Illustration with eletroencephalografic (EEG) signals during photic stimulation is also provided. The application of the proposed technique in both simulation and real EEG data indicate that it seems to be very specific in removing the contribution of periodic sources. The estimate independence of the periodic signal may widen partial coherence application to signal analysis, since it could be used together with simple coherence to test for contamination in signals by a common, periodic noise source.

Keywords: Partial coherence, periodic input, spectral analysis, statistical signal processing.

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Authors: Phakhapong Thanitakul, Worawat Sa-ngiamvibool, Apinan Aurasopon, Saravuth Pothiya

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This paper presents an improved ant colony optimization (IACO) for solving the reliability redundancy allocation problem (RAP) in order to maximize system reliability. To improve the performance of ACO algorithm, two additional techniques, i.e. neighborhood search, and re-initialization process are presented. To show its efficiency and effectiveness, the proposed IACO is applied to solve three RAPs. Additionally, the results of the proposed IACO are compared with those of the conventional heuristic approaches i.e. genetic algorithm (GA), particle swarm optimization (PSO) and ant colony optimization (ACO). The experimental results show that the proposed IACO approach is comparatively capable of obtaining higher quality solution and faster computational time.

Keywords: Ant colony optimization, Heuristic algorithm, Mixed-integer nonlinear programming, Redundancy allocation problem, Reliability optimization.

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Authors: Tao Zhao, Xin Wang

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With the increasing complexity of engineering problems, the traditional, single-objective and deterministic optimization method can not meet people-s requirements. A multi-objective fuzzy optimization model of resource input is built for M chlor-alkali chemical eco-industrial park in this paper. First, the model is changed into the form that can be solved by genetic algorithm using fuzzy theory. And then, a fitness function is constructed for genetic algorithm. Finally, a numerical example is presented to show that the method compared with traditional single-objective optimization method is more practical and efficient.

Keywords: Fitness function, genetic algorithm, multi-objectivefuzzy optimization, satisfaction degree membership function.

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Authors: Kumaresh Sarmah, Kandarpa Kumar Sarma

Abstract:

Artificial Neural Network (ANN)s are best suited for prediction and optimization problems. Trained ANNs have found wide spread acceptance in several antenna design systems. Four parameters namely antenna radiation resistance, loss resistance, efficiency, and inductance can be used to design an antenna layout though there are several other parameters available. An ANN can be trained to provide the best and worst case precisions of an antenna design problem defined by these four parameters. This work describes the use of an ANN to generate the four mentioned parameters for a loop antenna for the specified frequency range. It also provides insights to the prediction of best and worst-case design problems observed in applications and thereby formulate a model for physical layout design of a loop antenna.

Keywords: MLP, ANN, parameter, prediction, optimization.

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Authors: Ramin Javadzadeh, Emad Javadzadeh

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Locating the critical slip surface with the minimum factor of safety for a rock slope is a difficult problem. In recent years, some modern global optimization methods have been developed with success in treating various types of problems, but very few of such methods have been applied to rock mechanical problems. In this paper, use of hybrid model based on artificial immune system and cellular learning automata is proposed. The results show that the algorithm is an effective and efficient optimization method with a high level of confidence rate.

Keywords: CLA-AIS, failure surface, optimization methods, rock slope.

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Authors: C. Deepika, J. Nithya

Abstract:

Segmentation is one of the essential tasks in image processing. Thresholding is one of the simplest techniques for performing image segmentation. Multilevel thresholding is a simple and effective technique. The primary objective of bi-level or multilevel thresholding for image segmentation is to determine a best thresholding value. To achieve multilevel thresholding various techniques has been proposed. A study of some nature inspired metaheuristic algorithms for multilevel thresholding for image segmentation is conducted. Here, we study about Particle swarm optimization (PSO) algorithm, artificial bee colony optimization (ABC), Ant colony optimization (ACO) algorithm and Cuckoo search (CS) algorithm.

Keywords: Ant colony optimization, Artificial bee colony optimization, Cuckoo search algorithm, Image segmentation, Multilevel thresholding, Particle swarm optimization.

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Authors: Gamal Abd El-Nasser A. Said, El-Sayed M. El-Horbaty

Abstract:

Container handling problems at container terminals are NP-hard problems. This paper presents an approach using discrete-event simulation modeling to optimize solution for storage space allocation problem, taking into account all various interrelated container terminal handling activities. The proposed approach is applied on a real case study data of container terminal at Alexandria port. The computational results show the effectiveness of the proposed model for optimization of storage space allocation in container terminal where 54% reduction in containers handling time in port is achieved.

Keywords: Container terminal, discrete-event simulation, optimization, storage space allocation.

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