Search results for: Integer%20Wavelet%20Tranform.

Authors: Ahmet Tekcan, Betül Gezer, Osman Bizim

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Let k ≥ 1 and t ≥ 0 be two integers and let d = k2 + k be a positive non-square integer. In this paper, we consider the integer solutions of Pell equation x2 - dy2 = 2t. Further we derive a recurrence relation on the solutions of this equation.

Keywords: Pell equation, Diophantine equation.

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Authors: Ahmet Tekcan, Arzu Özkoç, Canan Kocapınar, Hatice Alkan

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Let p be a prime number such that p ≡ 1(mod 4), say p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2. In this paper, we consider the integer solutions of the Pell equation x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce some relations on the integer solutions (xn, yn) of it.

Keywords: Pell equation, solutions of Pell equation.

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Authors: Thomas Behan, Zaiyi Liao, Lian Zhao, Chunting Yang

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In this paper, low end Digital Signal Processors (DSPs) are applied to accelerate integer neural networks. The use of DSPs to accelerate neural networks has been a topic of study for some time, and has demonstrated significant performance improvements. Recently, work has been done on integer only neural networks, which greatly reduces hardware requirements, and thus allows for cheaper hardware implementation. DSPs with Arithmetic Logic Units (ALUs) that support floating or fixed point arithmetic are generally more expensive than their integer only counterparts due to increased circuit complexity. However if the need for floating or fixed point math operation can be removed, then simpler, lower cost DSPs can be used. To achieve this, an integer only neural network is created in this paper, which is then accelerated by using DSP instructions to improve performance.

Keywords: Digital Signal Processor (DSP), Integer Neural Network(INN), Low Cost Neural Network, Integer Neural Network DSPImplementation.

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Authors: G. Shojatalab

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In this paper, all variables are supposed to be integer and positive. In this modern method, objective function is assumed to be maximized or minimized but constraints are always explained like less or equal to. In this method, choosing a dual combination of ideal nonequivalent and omitting one of variables. With continuing this act, finally, having one nonequivalent with (n-m+1) unknown quantities in which final nonequivalent, m is counter for constraints, n is counter for variables of decision.

Keywords: Integer, Programming, Operation Research, Variables of decision.

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Authors: Sakol Udomsiri, Masahiro Iwahashi

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This paper presents comparative study on recent integer DCTs and a new method to construct a low sensitive structure of integer DCT for colored input signals. The method refers to sensitivity of multiplier coefficients to finite word length as an indicator of how word length truncation effects on quality of output signal. The sensitivity is also theoretically evaluated as a function of auto-correlation and covariance matrix of input signal. The structure of integer DCT algorithm is optimized by combination of lower sensitive lifting structure types of IRT. It is evaluated by the sensitivity of multiplier coefficients to finite word length expression in a function of covariance matrix of input signal. Effectiveness of the optimum combination of IRT in integer DCT algorithm is confirmed by quality improvement comparing with existing case. As a result, the optimum combination of IRT in each integer DCT algorithm evidently improves output signal quality and it is still compatible with the existing one.

Keywords: DCT, sensitivity, lossless, wordlength.

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Authors: Hsian Ming Goo

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The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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Authors: Yuan-Kang Shih, Shu-Li Chang, Shin-Shin Kao

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Qk n has been shown as an alternative to the hypercube family. For any even integer k ≥ 4 and any integer n ≥ 2, Qk n is a bipartite graph. In this paper, we will prove that given any pair of vertices, w and b, from different partite sets of Qk n, there exist 2n internally disjoint paths between w and b, denoted by {Pi | 0 ≤ i ≤ 2n-1}, such that 2n-1 i=0 Pi covers all vertices of Qk n. The result is optimal since each vertex of Qk n has exactly 2n neighbors.

Keywords: container, Hamiltonian, k-ary n-cube, m*-connected.

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Authors: Vijaya K. Srivastava, Davide Spinello

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This paper presents established 3ⁿ enumeration procedure for mixed integer optimization problems for solving multi-objective reliability and redundancy allocation problem subject to design constraints. The formulated problem is to find the optimum level of unit reliability and the number of units for each subsystem. A number of illustrative examples are provided and compared to indicate the application of the superiority of the proposed method.

Keywords: Integer programming, mixed integer programming, multi-objective optimization, reliability redundancy allocation.

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Authors: Takayuki Shiina

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Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic programming is a commonly used method for optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. In this study, we consider a stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure for solving this problem is developed by using a property of the expected recourse function. Numerical experiments demonstrate that the proposed algorithm is quite efficient. The stochastic programming model defined in this paper is quite useful for a variety of design and operational problems.

Keywords: stochastic programming problem with recourse, simple integer recourse, dynamic slope scaling procedure

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Authors: Takayuki Shiina

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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: Jinghao Sun, Guozhen Tan, Guangjian Hou

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The Chinese Postman Problem (CPP) is one of the classical problems in graph theory and is applicable in a wide range of fields. With the rapid development of hybrid systems and model based testing, Chinese Postman Problem with Time Dependent Travel Times (CPPTDT) becomes more realistic than the classical problems. In the literature, we have proposed the first integer programming formulation for the CPPTDT problem, namely, circuit formulation, based on which some polyhedral results are investigated and a cutting plane algorithm is also designed. However, there exists a main drawback: the circuit formulation is only available for solving the special instances with all circuits passing through the origin. Therefore, this paper proposes a new integer programming formulation for solving all the general instances of CPPTDT. Moreover, the size of the circuit formulation is too large, which is reduced dramatically here. Thus, it is possible to design more efficient algorithm for solving the CPPTDT in the future research.

Keywords: Chinese Postman Problem, Time Dependent, Integer Programming, Upper Bound Analysis.

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Authors: Ellips Masehian, Golnaz Habibi

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This paper presents a novel algorithm for path planning of mobile robots in known 3D environments using Binary Integer Programming (BIP). In this approach the problem of path planning is formulated as a BIP with variables taken from 3D Delaunay Triangulation of the Free Configuration Space and solved to obtain an optimal channel made of connected tetrahedrons. The 3D channel is then partitioned into convex fragments which are used to build safe and short paths within from Start to Goal. The algorithm is simple, complete, does not suffer from local minima, and is applicable to different workspaces with convex and concave polyhedral obstacles. The noticeable feature of this algorithm is that it is simply extendable to n-D Configuration spaces.

Keywords: 3D C-space, Binary Integer Programming (BIP), Delaunay Tessellation, Robot Motion Planning.

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Authors: N. A. H. Aizam, V. Uvaraja

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The agenda of showing the scheduled time for performing certain tasks is known as timetabling. It is widely used in many departments such as transportation, education, and production. Some difficulties arise to ensure all tasks happen in the time and place allocated. Therefore, many researchers invented various programming models to solve the scheduling problems from several fields. However, the studies in developing the general integer programming model for many timetabling problems are still questionable. Meanwhile, this thesis describes about creating a general model which solves different types of timetabling problems by considering the basic constraints. Initially, the common basic constraints from five different fields are selected and analyzed. A general basic integer programming model was created and then verified by using the medium set of data obtained randomly which is much similar to realistic data. The mathematical software, AIMMS with CPLEX as a solver has been used to solve the model. The model obtained is significant in solving many timetabling problems easily since it is modifiable to all types of scheduling problems which have same basic constraints.

Keywords: AIMMS mathematical software, integer linear programming, scheduling problems, timetabling.

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Authors: Decha Samana, Vites Longani

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For positive integer s and t, the Ramsey number R(s, t) is the least positive integer n such that for every graph G of order n, either G contains Ks as a subgraph or G contains Kt as a subgraph. We construct the circulant graphs and use them to obtain lower bounds of some small Ramsey numbers.

Keywords: Lower bound, Ramsey numbers, Graphs, Distance line.

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Authors: S. Annadurai, P. Geetha

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Lossless compression schemes with secure transmission play a key role in telemedicine applications that helps in accurate diagnosis and research. Traditional cryptographic algorithms for data security are not fast enough to process vast amount of data. Hence a novel Secured lossless compression approach proposed in this paper is based on reversible integer wavelet transform, EZW algorithm, new modified runlength coding for character representation and selective bit scrambling. The use of the lifting scheme allows generating truly lossless integer-to-integer wavelet transforms. Images are compressed/decompressed by well-known EZW algorithm. The proposed modified runlength coding greatly improves the compression performance and also increases the security level. This work employs scrambling method which is fast, simple to implement and it provides security. Lossless compression ratios and distortion performance of this proposed method are found to be better than other lossless techniques.

Keywords: EZW algorithm, lifting scheme, losslesscompression, reversible integer wavelet transform, securetransmission, selective bit scrambling, modified runlength coding .

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Authors: Rand Alfaris, Mohamed Rushdan MD Said, Mohamed Othman, Fudziah Ismail

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This paper is introduced a modification to Diffie- Hellman protocol to be applicable on the decimal numbers, which they are the numbers between zero and one. For this purpose we extend the theory of the congruence. The new congruence is over the set of the real numbers and it is called the “real congruence" or the “real modulus". We will refer to the existing congruence by the “integer congruence" or the “integer modulus". This extension will define new terms and redefine the existing terms. As the properties and the theorems of the integer modulus are extended as well. Modified Diffie-Hellman key exchange protocol is produced a sharing, secure and decimal secret key for the the cryptosystems that depend on decimal numbers.

Keywords: Extended theory of the congruence, modified Diffie- Hellman protocol.

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Authors: Ahmad Thanyan Al-Sultan

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The check-in area of airport terminal is one of the busiest sections at airports at certain periods. The passengers are subjected to queues and delays during the check-in process. These delays and queues are due to constraints in the capacity of service facilities. In this project, the airport terminal is decomposed into several check-in areas. The airport check-in scheduling problem requires both a deterministic (integer programming) and stochastic (simulation) approach. Integer programming formulations are provided to minimize the total number of counters in each check-in area under the realistic constraint that counters for one and the same flight should be adjacent and the desired number of counters remaining in each area should be fixed during check-in operations. By using simulation, the airport system can be modeled to study the effects of various parameters such as number of passengers on a flight and check-in counter opening and closing time.

Keywords: Airport terminal, Integer programming, Scheduling, Simulation.

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Authors: Ahmet Tekcan

Abstract:

Let k, t, d be arbitrary integers with k ≥ 2, t ≥ 0 and d = k2 - k. In the first section we give some preliminaries from Pell equations x2 - dy2 = 1 and x2 - dy2 = N, where N be any fixed positive integer. In the second section, we consider the integer solutions of Pell equations x2 - dy2 = 1 and x2 - dy2 = 2t. We give a method for the solutions of these equations. Further we derive recurrence relations on the solutions of these equations

Keywords: Pell equation, solutions of Pell equation.

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Authors: H. Mahboubi, B. Moshiri, A. Khaki Seddigh

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Recently, a great amount of interest has been shown in the field of modeling and controlling hybrid systems. One of the efficient and common methods in this area utilizes the mixed logicaldynamical (MLD) systems in the modeling. In this method, the system constraints are transformed into mixed-integer inequalities by defining some logic statements. In this paper, a system containing three tanks is modeled as a nonlinear switched system by using the MLD framework. Comparing the model size of the three-tank system with that of a two-tank system, it is deduced that the number of binary variables, the size of the system and its complexity tremendously increases with the number of tanks, which makes the control of the system more difficult. Therefore, methods should be found which result in fewer mixed-integer inequalities.

Keywords: Hybrid systems, mixed-integer inequalities, mixed logical dynamical systems, multi-tank system.

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Authors: Taeung Yoon, Youngpo Lee, Chonghan Song, Na Young Ha, Seokho Yoon

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Ren et al. presented an efficient carrier frequency offset (CFO) estimation method for orthogonal frequency division multiplexing (OFDM), which has an estimation range as large as the bandwidth of the OFDM signal and achieves high accuracy without any constraint on the structure of the training sequence. However, its detection probability of the integer frequency offset (IFO) rapidly varies according to the fractional frequency offset (FFO) change. In this paper, we first analyze the Ren-s method and define two criteria suitable for detection of IFO. Then, we propose a novel method for the IFO estimation based on the maximum-likelihood (ML) principle and the detection criteria defined in this paper. The simulation results demonstrate that the proposed method outperforms the Ren-s method in terms of the IFO detection probability irrespective of a value of the FFO.

Keywords: Orthogonal frequency division multiplexing, integer frequency offset, estimation, training symbol

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Authors: Taehan Lee

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We consider a network design problem which has shortest routing restriction based on the values determined by the installed facilities on each arc. In conventional multicommodity network design problem, a commodity can be routed through any possible path when the capacity is available. But, we consider a problem in which the commodity between two nodes must be routed on a path which has shortest metric value and the link metric value is determined by the installed facilities on the link. By this routing restriction, the problem has a distinct characteristic. We present an integer programming formulation containing the primal-dual optimality conditions to the shortest path routing. We give some computational results for the model.

Keywords: Integer programming, multicommodity network design, routing, shortest path.

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Authors: Daniela I. Borissova, Ivan C. Mustakerov

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The paper describes an approach for defining of k-best night vision devices based on multi-criteria mixed-integer optimization modeling. The parameters of night vision devices are considered as criteria that have to be optimized. Using different user preferences for the relative importance between parameters different choice of k-best devices can be defined. An ideal device with all of its parameters at their optimum is used to determine how far the particular device from the ideal one is. A procedure for evaluation of deviation between ideal solution and k-best solutions is presented. The applicability of the proposed approach is numerically illustrated using real night vision devices data. The proposed approach contributes to quality of decisions about choice of night vision devices by making the decision making process more certain, rational and efficient. 

Keywords: K-best devices, mixed-integer model, multi-criteria problem, night vision devices.

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Authors: Mohsen Ziaee

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In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

Keywords: Scheduling, flexible job shop, makespan, mixed integer linear programming.

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Authors: N. F. Jamaluddin, N. A. H. Aizam

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This paper explains the educational timetabling problem, a type of scheduling problem that is considered as one of the most challenging problem in optimization and operational research. The university examination timetabling problem (UETP), which involves assigning a set number of exams into a set number of timeslots whilst fulfilling all required conditions, has been widely investigated. The limitation of available timeslots and resources with the increasing number of examinations are the main reasons in the difficulty of solving this problem. Dynamical change in the examination scheduling system adds up the complication particularly in coping up with the demand and new requirements by the communities. Our objective is to investigate these demands and requirements with subjects taken from Universiti Malaysia Terengganu (UMT), through questionnaires. Integer linear programming model which reflects the preferences obtained to produce an effective examination timetabling was formed.

Keywords: Demands, educational timetabling, integer linear programming, scheduling, university examination timetabling problem.

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Authors: Chompunut Jantarasorn, Chutima Prommak

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The important issue considered in the widespread deployment of Wireless Sensor Networks (WSNs) is an efficiency of the energy consumption. In this paper, we present a study of the optimal relay station planning problems using Binary Integer Linear Programming (BILP) model to minimize the energy consumption in WSNs. Our key contribution is that the proposed model not only ensures the required network lifetime but also guarantees the radio connectivity at high level of communication quality. Specially, we take into account effects of noise, signal quality limitation and bit error rate characteristics. Numerical experiments were conducted in various network scenarios. We analyzed the effects of different sensor node densities and distribution on the energy consumption.

Keywords: Binary Integer Linear Programming, BILP, Energy consumption, Optimal node placement and Wireless sensor networks.

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Authors: Erik Delarue, David Bekaert, Ronnie Belmans, William D'haeseleer

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This paper presents the development of an electricity simulation model taking into account electrical network constraints, applied on the Belgian power system. The base of the model is optimizing an extensive Unit Commitment (UC) problem through the use of Mixed Integer Linear Programming (MILP). Electrical constraints are incorporated through the implementation of a DC load flow. The model encloses the Belgian power system in a 220 – 380 kV high voltage network (i.e., 93 power plants and 106 nodes). The model features the use of pumping storage facilities as well as the inclusion of spinning reserves in a single optimization process. Solution times of the model stay below reasonable values.

Keywords: Electricity generation modeling, Unit Commitment(UC), Mixed Integer Linear Programming (MILP), DC load flow.

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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3ⁿ enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3ⁿ integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

Keywords: Constrained integer problems, enumerative search algorithm, Heuristic algorithm, tunneling algorithm.

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Authors: Chaimongkol Limpianchob

Abstract:

This work addresses the problem of production planning that arises in the production of aromatic coconuts from Samudsakhorn province in Thailand. The planning involves the forwarding of aromatic coconuts from the harvest areas to the factory, which is classified into two groups; self-owned areas and contracted areas, the decisions of aromatic coconuts flow in the plant, and addressing a question of which warehouse will be in use. The problem is formulated as a mixed-integer linear programming model within supply chain management framework. The objective function seeks to minimize the total cost including the harvesting, labor and inventory costs. Constraints on the system include the production activities in the company and demand requirements. Numerical results are presented to demonstrate the feasibility of coconuts supply chain model compared with base case.

Keywords: Aromatic coconut, supply chain management, production planning, mixed-integer linear programming.

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Authors: Nisar Ahmed Memon

Abstract:

Embedding and extraction of a secret information as well as the restoration of the original un-watermarked image is highly desirable in sensitive applications like military, medical, and law enforcement imaging. This paper presents a novel reversible data-hiding method for digital images using integer to integer wavelet transform and companding technique which can embed and recover the secret information as well as can restore the image to its pristine state. The novel method takes advantage of block based watermarking and iterative optimization of threshold for companding which avoids histogram pre and post-processing. Consequently, it reduces the associated overhead usually required in most of the reversible watermarking techniques. As a result, it keeps the distortion small between the marked and the original images. Experimental results show that the proposed method outperforms the existing reversible data hiding schemes reported in the literature.

Keywords: Adaptive Thresholding, Companding Technique, Integer Wavelet Transform, Reversible Watermarking

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Authors: Zuraida Alwadood, Adibah Shuib, Norlida Abd Hamid

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This paper presents the review of past studies concerning mathematical models for rescheduling passenger railway services, as part of delay management in the occurrence of railway disruption. Many past mathematical models highlighted were aimed at minimizing the service delays experienced by passengers during service disruptions. Integer programming (IP) and mixed-integer programming (MIP) models are critically discussed, focusing on the model approach, decision variables, sets and parameters. Some of them have been tested on real-life data of railway companies worldwide, while a few have been validated on fictive data. Based on selected literatures on train rescheduling, this paper is able to assist researchers in the model formulation by providing comprehensive analyses towards the model building. These analyses would be able to help in the development of new approaches in rescheduling strategies or perhaps to enhance the existing rescheduling models and make them more powerful or more applicable with shorter computing time.

Keywords: Mathematical modelling, Mixed-integer programming, Railway rescheduling, Service delays.

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