Search results for: Discrete ill-posed problem

Authors: Ben Mohamed Ahemed Mohamed, Yassine Adnan

Abstract:

The problem of bin-packing in two dimensions (2BP) consists in placing a given set of rectangular items in a minimum number of rectangular and identical containers, called bins. This article treats the case of objects with a free orientation of 90Ôùª. We propose an approach of resolution combining optimization by colony of ants (ACO) and the heuristic method IMA to resolve this NP-Hard problem.

Keywords: Ant colony algorithm, bin-packing problem, heuristics methods.

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Authors: Shih-Ching Lo, Yu-Ping Liao

Abstract:

Social-economic variables influence transportation demand largely. Analyses of discrete choice model consider social-economic variables to study traveler-s mode choice and demand. However, to calibrate the discrete choice model needs to have plenty of questionnaire survey. Also, an aggregative model is proposed. The historical data of passenger volumes for high speed rail and domestic civil aviation are employed to calibrate and validate the model. In this study, models with different social-economic variables, which are oil price, GDP per capita, CPI and economic growth rate, are compared. From the results, the model with the oil price is better than models with the other social-economic variables.

Keywords: forecasting, passenger volume, dynamic competitive model, social-economic variables, oil price.

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Authors: Ali Akbar Attari, Ali Asghar Beheshti Shirazi

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In this paper, we propose a blind and robust audio watermarking scheme based on spread spectrum in Discrete Wavelet Transform (DWT) domain. Watermarks are embedded in the low-frequency coefficients, which is less audible. The key idea is dividing the audio signal into small frames, and magnitude of the 6^th level of DWT approximation coefficients is modifying based upon the Direct Sequence Spread Spectrum (DSSS) technique. Also, the psychoacoustic model for enhancing in imperceptibility, as well as Savitsky-Golay filter for increasing accuracy in extraction, is used. The experimental results illustrate high robustness against most common attacks, i.e. Gaussian noise addition, Low pass filter, Resampling, Requantizing, MP3 compression, without significant perceptual distortion (ODG is higher than -1). The proposed scheme has about 83 bps data payload.

Keywords: Audio watermarking, spread spectrum, discrete wavelet transform, psychoacoustic, Savitsky-Golay filter.

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Authors: Ibrahim A. El rube, Mohamad Abou El Nasr , Mostafa M. Naim, Mahmoud Farouk

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In this paper, a watermarking algorithm that uses the wavelet transform with Multiple Description Coding (MDC) and Quantization Index Modulation (QIM) concepts is introduced. Also, the paper investigates the role of Contourlet Transform (CT) versus Wavelet Transform (WT) in providing robust image watermarking. Two measures are utilized in the comparison between the waveletbased and the contourlet-based methods; Peak Signal to Noise Ratio (PSNR) and Normalized Cross-Correlation (NCC). Experimental results reveal that the introduced algorithm is robust against different attacks and has good results compared to the contourlet-based algorithm.

Keywords: image watermarking; discrete wavelet transform, discrete contourlet transform, multiple description coding, quantization index modulation

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Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai

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Elliptic curve discrete logarithm problem(ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard’s rho method to evaluate the security of ECDLP on Barreto-Naehrig(BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.

Keywords: Pollard’s rho method, BN curve, Montgomery multiplication.

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Authors: M. Hassan, I. Osman, M. Yahia

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This Paper proposes a new facial feature extraction approach, Wash-Hadamard Transform (WHT). This approach is based on correlation between local pixels of the face image. Its primary advantage is the simplicity of its computation. The paper compares the proposed approach, WHT, which was traditionally used in data compression with two other known approaches: the Principal Component Analysis (PCA) and the Discrete Cosine Transform (DCT) using the face database of Olivetti Research Laboratory (ORL). In spite of its simple computation, the proposed algorithm (WHT) gave very close results to those obtained by the PCA and DCT. This paper initiates the research into WHT and the family of frequency transforms and examines their suitability for feature extraction in face recognition applications.

Keywords: Face Recognition, Facial Feature Extraction, Principal Component Analysis, and Discrete Cosine Transform, Wash-Hadamard Transform.

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Authors: Jaroslav Masek, Juraj Camaj, Eva Nedeliakova

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The paper is focused on the operational model for transport the single wagon consignments on railway network by using two different models of train formation. The paper gives an overview of possibilities of improving the quality of transport services. Paper deals with two models used in problematic of train formatting - time continuously and time discrete. By applying these models in practice, the transport company can guarantee a higher quality of service and expect increasing of transport performance. The models are also applicable into others transport networks. The models supplement a theoretical problem of train formation by new ways of looking to affecting the organization of wagon flows.

Keywords: Train formation, wagon flows, marshalling yard, railway technology.

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Authors: Maricar G. Misola, Bryan B. Navarro

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Facility Layout Problem (FLP) is one of the essential problems of several types of manufacturing and service sector. It is an optimization problem on which the main objective is to obtain the efficient locations, arrangement and order of the facilities. In the literature, there are numerous facility layout problem research presented and have used meta-heuristic approaches to achieve optimal facility layout design. This paper presented genetic algorithm to solve facility layout problem; to minimize total cost function. The performance of the proposed approach was verified and compared using problems in the literature.

Keywords: Facility Layout Problem, Genetic Algorithm, Material Handling Cost, Meta-heuristic Approach.

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Authors: R. K. Chaurasiya, N. D. Londhe, S. Ghosh

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The study of the electrical signals produced by neural activities of human brain is called Electroencephalography. In this paper, we propose an automatic and efficient EEG signal classification approach. The proposed approach is used to classify the EEG signal into two classes: epileptic seizure or not. In the proposed approach, we start with extracting the features by applying Discrete Wavelet Transform (DWT) in order to decompose the EEG signals into sub-bands. These features, extracted from details and approximation coefficients of DWT sub-bands, are used as input to Principal Component Analysis (PCA). The classification is based on reducing the feature dimension using PCA and deriving the supportvectors using Support Vector Machine (SVM). The experimental are performed on real and standard dataset. A very high level of classification accuracy is obtained in the result of classification.

Keywords: Discrete Wavelet Transform, Electroencephalogram, Pattern Recognition, Principal Component Analysis, Support Vector Machine.

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Authors: Aldy Gunawan, Kien Ming Ng, Kim Leng Poh

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This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.

Keywords: Timetabling problem, mathematical programming model, hybrid algorithm, simulated annealing.

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Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

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Authors: Biao Qin, Jin Huang, Jiaojiao Ren, Wei Kang

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This paper deals with the problem of passivity analysis for stochastic neural networks with leakage, discrete and distributed delays. By using delay partitioning technique, free weighting matrix method and stochastic analysis technique, several sufficient conditions for the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), in which both the time-delay and its time derivative can be fully considered. A numerical example is given to show the usefulness and effectiveness of the obtained results.

Keywords: Passivity, Stochastic neural networks, Multiple time delays, Linear matrix inequalities (LMIs).

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Authors: M. G. M. Khan, V. D. Prasad, D. K. Rao

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In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.

Keywords: Auxiliary variable, Dynamic programming technique, Nonlinear programming problem, Optimum stratification, Uniform distribution.

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Authors: Yiqin Lin, Liang Bao

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This paper is devoted to the numerical solution of large-scale linear ill-posed systems. A multilevel regularization method is proposed. This method is based on a synthesis of the Arnoldi-Tikhonov regularization technique and the multilevel technique. We show that if the Arnoldi-Tikhonov method is a regularization method, then the multilevel method is also a regularization one. Numerical experiments presented in this paper illustrate the effectiveness of the proposed method.

Keywords: Discrete ill-posed problem, Tikhonov regularization, discrepancy principle, Arnoldi process, multilevel method.

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Authors: A. K. Bhandari, A. Kumar, P. K. Padhy

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In this paper, a novel contrast enhancement technique for contrast enhancement of a low-contrast satellite image has been proposed based on the singular value decomposition (SVD) and discrete cosine transform (DCT). The singular value matrix represents the intensity information of the given image and any change on the singular values change the intensity of the input image. The proposed technique converts the image into the SVD-DCT domain and after normalizing the singular value matrix; the enhanced image is reconstructed by using inverse DCT. The visual and quantitative results suggest that the proposed SVD-DCT method clearly shows the increased efficiency and flexibility of the proposed method over the exiting methods such as Linear Contrast Stretching technique, GHE technique, DWT-SVD technique, DWT technique, Decorrelation Stretching technique, Gamma Correction method based techniques.

Keywords: Singular Value Decomposition (SVD), discretecosine transforms (DCT), image equalization and satellite imagecontrast enhancement.

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

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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: Muhammed Ordu, Eren Demir, Chris Tofallis

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Over the past decade, the non-elective admissions in the UK have increased significantly. Taking into account limited resources (i.e. beds), the related service managers are obliged to manage their resources effectively due to the non-elective admissions which are mostly admitted to inpatient specialities via A&E departments. Geriatric medicine is one of specialities that have long length of stay for the non-elective admissions. This study aims to develop a discrete event simulation model to understand how possible increases on non-elective demand over the next 12 months affect the bed occupancy rate and to determine required number of beds in a geriatric medicine speciality in a UK hospital. In our validated simulation model, we take into account observed frequency distributions which are derived from a big data covering the period April, 2009 to January, 2013, for the non-elective admission and the length of stay. An experimental analysis, which consists of 16 experiments, is carried out to better understand possible effects of case studies and scenarios related to increase on demand and number of bed. As a result, the speciality does not achieve the target level in the base model although the bed occupancy rate decreases from 125.94% to 96.41% by increasing the number of beds by 30%. In addition, the number of required beds is more than the number of beds considered in the scenario analysis in order to meet the bed requirement. This paper sheds light on bed management for service managers in geriatric medicine specialities.

Keywords: Bed management, bed occupancy rate, discrete event simulation, geriatric medicine, non-elective admission.

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Authors: Prasanta Kundu, N.K. Kishore, A.K. Sinha

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Insulation used in transformer is mostly oil pressboard insulation. Insulation failure is one of the major causes of catastrophic failure of transformers. It is established that partial discharges (PD) cause insulation degradation and premature failure of insulation. Online monitoring of PDs can reduce the risk of catastrophic failure of transformers. There are different techniques of partial discharge measurement like, electrical, optical, acoustic, opto-acoustic and ultra high frequency (UHF). Being non invasive and non interference prone, acoustic emission technique is advantageous for online PD measurement. Acoustic detection of p.d. is based on the retrieval and analysis of mechanical or pressure signals produced by partial discharges. Partial discharges are classified according to the origin of discharges. Their effects on insulation deterioration are different for different types. This paper reports experimental results and analysis for classification of partial discharges using acoustic emission signal of laboratory simulated partial discharges in oil pressboard insulation system using three different electrode systems. Acoustic emission signal produced by PD are detected by sensors mounted on the experimental tank surface, stored on an oscilloscope and fed to computer for further analysis. The measured AE signals are analyzed using discrete wavelet transform analysis and wavelet packet analysis. Energy distribution in different frequency bands of discrete wavelet decomposed signal and wavelet packet decomposed signal is calculated. These analyses show a distinct feature useful for PD classification. Wavelet packet analysis can sort out any misclassification arising out of DWT in most cases.

Keywords: Acoustic emission, discrete wavelet transform, partial discharge, wavelet packet analysis.

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Authors: I. Mahdavi, A. Jazayeri, M. Jahromi, R. Jafari, H. Iranmanesh

Abstract:

One of the most important problems in production planning of flexible manufacturing system (FMS) is machine tool selection and operation allocation problem that directly influences the production costs and times .In this paper minimizing machining cost, set-up cost and material handling cost as a multi-objective problem in flexible manufacturing systems environment are considered. We present a 0-1 integer linear programming model for the multiobjective machine tool selection and operation allocation problem and due to the large scale nature of the problem, solving the problem to obtain optimal solution in a reasonable time is infeasible, Paretoant colony optimization (P-ACO) approach for solving the multiobjective problem in reasonable time is developed. Experimental results indicate effectiveness of the proposed algorithm for solving the problem.

Keywords: Flexible manufacturing system, Production planning, Machine tool selection, Operation allocation, Multiobjective optimization, Metaheuristic.

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Authors: Anuj Kumar Sharma, Amit Sharma, Kulbhushan Agnihotri

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In this paper, a delayed plankton-nutrient interaction model consisting of phytoplankton, zooplankton and dissolved nutrient is considered. It is assumed that some species of phytoplankton releases toxin (known as toxin producing phytoplankton (TPP)) which is harmful for zooplankton growth and this toxin releasing process follows a discrete time variation. Using delay as bifurcation parameter, the stability of interior equilibrium point is investigated and it is shown that time delay can destabilize the otherwise stable non-zero equilibrium state by inducing Hopf-bifurcation when it crosses a certain threshold value. Explicit results are derived for stability and direction of the bifurcating periodic solution by using normal form theory and center manifold arguments. Finally, outcomes of the system are validated through numerical simulations.

Keywords: Plankton, Time delay, Hopf-bifurcation, Normal form theory, Center manifold theorem.

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Authors: Liu Shu, Dong Shangjia

Abstract:

Our goal is to effectively increase the number of boats in the river during a six month period. The main factors of determining the number of boats are duration and “select the priority trip". In the microcosmic simulation model, the best result is 4 to 24 nights with DSCF, and the number of boats is 812 with an increasing ratio of 9.0% related to the second best result. However, the number of boats is related to 31.6% less than the best one in 6 to 18 nights with FCFS. In the discrete duration model, we get from 6 to 18 nights, the numbers of boats have increased to 848 with an increase ratio of 29.7% than the best result in model I for the same time range. Moreover, from 4 to 24 nights, the numbers of boats have increase to 1194 with an increase ratio of 47.0% than the best result in model I for the same time range.

Keywords: Discrete duration model, “select the priority trip”, microcosmic simulation model.

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Authors: Filippo Ranalli, Forest Flager, Martin Fischer

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This paper presents a ground structure method to optimize the topology and discrete member sizing of steel frame structures in order to minimize total installed cost, including material, fabrication and erection components. The proposed method improves upon existing cost-based ground structure methods by incorporating constructability considerations well as satisfying both strength and serviceability constraints. The architecture for the method is a bi-level Multidisciplinary Feasible (MDF) architecture in which the discrete member sizing optimization is nested within the topology optimization process. For each structural topology generated, the sizing optimization process seek to find a set of discrete member sizes that result in the lowest total installed cost while satisfying strength (member utilization) and serviceability (node deflection and story drift) criteria. To accurately assess cost, the connection details for the structure are generated automatically using accurate site-specific cost information obtained directly from fabricators and erectors. Member continuity rules are also applied to each node in the structure to improve constructability. The proposed optimization method is benchmarked against conventional weight-based ground structure optimization methods resulting in an average cost savings of up to 30% with comparable computational efficiency.

Keywords: Cost-based structural optimization, cost-based topology and sizing optimization, steel frame ground structure optimization, multidisciplinary optimization of steel structures.

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Authors: I. Khutsishvili, G. Sirbiladze, B. Ghvaberidze

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This work proposes a fuzzy methodology to support the investment decisions. While choosing among competitive investment projects, the methodology makes ranking of projects using the new aggregation OWA operator – AsPOWA, presented in the environment of possibility uncertainty. For numerical evaluation of the weighting vector associated with the AsPOWA operator the mathematical programming problem is constructed. On the basis of the AsPOWA operator the projects’ group ranking maximum criteria is constructed. The methodology also allows making the most profitable investments into several of the project using the method developed by the authors for discrete possibilistic bicriteria problems. The article provides an example of the investment decision-making that explains the work of the proposed methodology.

Keywords: Expert evaluations, investment decision making, OWA operator, possibility uncertainty.

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Authors: D. Tedesco, G. Feletti, P. Trucco

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The present study aims to develop a Decision Support System (DSS) to support operational decisions in Emergency Medical Service (EMS) systems regarding the assignment of medical emergency requests to Emergency Departments (ED). This problem is called “hospital selection” and concerns the definition of policies for the selection of the ED to which patients who require further treatment are transported by ambulance. The employed research methodology consists of a first phase of review of the technical-scientific literature concerning DSSs to support the EMS management and, in particular, the hospital selection decision. From the literature analysis, it emerged that current studies mainly focused on the EMS phases related to the ambulance service and consider a process that ends when the ambulance is available after completing a mission. Therefore, all the ED-related issues are excluded and considered as part of a separate process. Indeed, the most studied hospital selection policy turned out to be proximity, thus allowing to minimize the travelling time and to free-up the ambulance in the shortest possible time. The purpose of the present study consists in developing an optimization model for assigning medical emergency requests to the EDs also considering the expected time performance in the subsequent phases of the process, such as the case mix, the expected service throughput times, and the operational capacity of different EDs in hospitals. To this end, a Discrete Event Simulation (DES) model was created to compare different hospital selection policies. The model was implemented with the AnyLogic software and finally validated on a realistic case. The hospital selection policy that returned the best results was the minimization of the Time To Provider (TTP), considered as the time from the beginning of the ambulance journey to the ED at the beginning of the clinical evaluation by the doctor. Finally, two approaches were further compared: a static approach, based on a retrospective estimation of the TTP, and a dynamic approach, focused on a predictive estimation of the TTP which is determined with a constantly updated Winters forecasting model. Findings reveal that considering the minimization of TTP is the best hospital selection policy. It allows to significantly reducing service throughput times in the ED with a negligible increase in travel time. Furthermore, an immediate view of the saturation state of the ED is produced and the case mix present in the ED structures (i.e., the different triage codes) is considered, as different severity codes correspond to different service throughput times. Besides, the use of a predictive approach is certainly more reliable in terms on TTP estimation, than a retrospective approach. These considerations can support decision-makers in introducing different hospital selection policies to enhance EMSs performance.

Keywords: Emergency medical services, hospital selection, discrete event simulation, forecast model.

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Authors: Jindřiška Šedová, Miloš Šeda

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This paper summarizes and compares approaches to solving the knapsack problem and its known application in capital budgeting. The first approach uses deterministic methods and can be applied to small-size tasks with a single constraint. We can also apply commercial software systems such as the GAMS modelling system. However, because of NP-completeness of the problem, more complex problem instances must be solved by means of heuristic techniques to achieve an approximation of the exact solution in a reasonable amount of time. We show the problem representation and parameter settings for a genetic algorithm framework.

Keywords: Capital budgeting, knapsack problem, GAMS, heuristic method, genetic algorithm.

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Authors: Tami Alghamdi, Terence Soule

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To study how to transfer knowledge from multiple source problems to the target problem, we modeled the Transfer Learning (TL) process using Genetic Algorithms as the model solver. TL is the process that aims to transfer learned data from one problem to another problem. The TL process aims to help Machine Learning (ML) algorithms find a solution to the problems. The Genetic Algorithms (GA) give researchers access to information that we have about how the old problem is solved. In this paper, we have five different source problems, and we transfer the knowledge to the target problem. We studied different scenarios of the target problem. The results showed that combined knowledge from multiple source problems improves the GA performance. Also, the process of combining knowledge from several problems results in promoting diversity of the transferred population.

Keywords: Transfer Learning, Multiple Sources, Knowledge Transfer, Domain Adaptation, Source, Target.

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Authors: Paul O'Leary, Matthew Harker

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This paper presents unified theory for local (Savitzky- Golay) and global polynomial smoothing. The algebraic framework can represent any polynomial approximation and is seamless from low degree local, to high degree global approximations. The representation of the smoothing operator as a projection onto orthonormal basis functions enables the computation of: the covariance matrix for noise propagation through the filter; the noise gain and; the frequency response of the polynomial filters. A virtually perfect Gram polynomial basis is synthesized, whereby polynomials of degree d = 1000 can be synthesized without significant errors. The perfect basis ensures that the filters are strictly polynomial preserving. Given n points and a support length ls = 2m + 1 then the smoothing operator is strictly linear phase for the points xi, i = m+1. . . n-m. The method is demonstrated on geometric surfaces data lying on an invariant 2D lattice.

Keywords: Gram polynomials, Savitzky-Golay Smoothing, Discrete Polynomial Moments

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Authors: Xiu Liu, Shouming Zhong, Xiuyong Ding

Abstract:

This paper focuses on the problem of a common linear copositive Lyapunov function(CLCLF) existence for discrete-time switched positive linear systems(SPLSs) with bounded time-varying delays. In particular, applying system matrices, a special class of matrices are constructed in an appropriate manner. Our results reveal that the existence of a common copositive Lyapunov function can be related to the Schur stability of such matrices. A simple example is provided to illustrate the implication of our results.

Keywords: Common linear co-positive Lyapunov functions, positive systems, switched systems, delays.

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Authors: S. Nasri, H. Bouziri

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Disasters are quite experienced in our days. They are caused by floods, landslides, and building fires that is the main objective of this study. To cope with these unexpected events, precautions must be taken to protect human lives. The emphasis on disposal work focuses on the resolution of the evacuation problem in case of no-notice disaster. The problem of evacuation is listed as a dynamic network flow problem. Particularly, we model the evacuation problem as an earliest arrival flow problem with load dependent transit time. This problem is classified as NP-Hard. Our challenge here is to propose a metaheuristic solution for solving the evacuation problem. We define our objective as the maximization of evacuees during earliest periods of a time horizon T. The objective provides the evacuation of persons as soon as possible. We performed an experimental study on emergency evacuation from the tunisian children’s hospital. This work prompts us to look for evacuation plans corresponding to several situations where the network dynamically changes.

Keywords: Dynamic network flow, Load dependent transit time, Evacuation strategy, Earliest arrival flow problem.

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Authors: Omaima N. Ahmad AL-Allaf

Abstract:

Over communication networks, images can be easily copied and distributed in an illegal way. The copyright protection for authors and owners is necessary. Therefore, the digital watermarking techniques play an important role as a valid solution for authority problems. Digital image watermarking techniques are used to hide watermarks into images to achieve copyright protection and prevent its illegal copy. Watermarks need to be robust to attacks and maintain data quality. Therefore, we discussed in this paper two approaches for image watermarking, first is based on Particle Swarm Optimization (PSO) and the second approach is based on Genetic Algorithm (GA). Discrete wavelet transformation (DWT) is used with the two approaches separately for embedding process to cover image transformation. Each of PSO and GA is based on co-relation coefficient to detect the high energy coefficient watermark bit in the original image and then hide the watermark in original image. Many experiments were conducted for the two approaches with different values of PSO and GA parameters. From experiments, PSO approach got better results with PSNR equal 53, MSE equal 0.0039. Whereas GA approach got PSNR equal 50.5 and MSE equal 0.0048 when using population size equal to 100, number of iterations equal to 150 and 3×3 block. According to the results, we can note that small block size can affect the quality of image watermarking based PSO/GA because small block size can increase the search area of the watermarking image. Better PSO results were obtained when using swarm size equal to 100.

Keywords: Image watermarking, genetic algorithm, particle swarm optimization, discrete wavelet transform.

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