Search results for: Cauchy problem

Authors: C. Bruni, F. Delli Priscoli, G. Koch, I. Marchetti

Abstract:

The Connection Admission Control (CAC) problem is formulated in this paper as a discrete time optimal control problem. The control variables account for the acceptance/ rejection of new connections and forced dropping of in-progress connections. These variables are constrained to meet suitable conditions which account for the QoS requirements (Link Availability, Blocking Probability, Dropping Probability). The performance index evaluates the total throughput. At each discrete time, the problem is solved as an integer-valued linear programming one. The proposed procedure was successfully tested against suitably simulated data.

Keywords: Connection Admission Control, Optimal Control, Integer valued Linear Programming, Quality of Service Requirements, Robust Control.

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Authors: H. Taghvafard, G. H. Erjaee

Abstract:

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Noboru Abe, Yoshinori Amai, Toshinori Nakatake, Sumio Masuda, Kazuaki Yamaguchi

Abstract:

We consider the problem of placing labels of the points on a plane. For each point, its position, the size of its label and a priority are given. Moreover, several candidates of its label positions are prespecified, and each of such label positions is assigned a priority. The objective of our problem is to maximize the total sum of priorities of placed labels and their points. By refining a labeling algorithm that can use these priorities, we propose a new heuristic algorithm which is more suitable for treating the assigned priorities.

Keywords: Map labeling, greedy algorithm, heuristic algorithm, priority.

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Authors: Parvaneh Shabanzadeh, Malik Hj Abu Hassan, Leong Wah June, Maryam Mohagheghtabar

Abstract:

Clustering is one of an interesting data mining topics that can be applied in many fields. Recently, the problem of cluster analysis is formulated as a problem of nonsmooth, nonconvex optimization, and an algorithm for solving the cluster analysis problem based on nonsmooth optimization techniques is developed. This optimization problem has a number of characteristics that make it challenging: it has many local minimum, the optimization variables can be either continuous or categorical, and there are no exact analytical derivatives. In this study we show how to apply a particular class of optimization methods known as pattern search methods to address these challenges. These methods do not explicitly use derivatives, an important feature that has not been addressed in previous studies. Results of numerical experiments are presented which demonstrate the effectiveness of the proposed method.

Keywords: Clustering functions, Non-smooth Optimization, Nonconvex Optimization, Pattern Search Method.

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Authors: Miloš Šeda

Abstract:

In this paper, we deal with the Steiner tree problem (STP) on a graph in which a fuzzy number, instead of a real number, is assigned to each edge. We propose a modification of the shortest paths approximation based on the fuzzy shortest paths (FSP) evaluations. Since a fuzzy min operation using the extension principle leads to nondominated solutions, we propose another approach to solving the FSP using Cheng's centroid point fuzzy ranking method.

Keywords: Steiner tree, single shortest path problem, fuzzyranking, binary heap, priority queue.

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Authors: Y. T. Tsai, Jin H. Huang

Abstract:

The sound pressure level (SPL) of the moving-coil loudspeaker (MCL) is often simulated and analyzed using the lumped parameter model. However, the SPL of a MCL cannot be simulated precisely in the high frequency region, because the value of cone effective area is changed due to the geometry variation in different mode shapes, it is also related to affect the acoustic radiation mass and resistance. Herein, the paper presents the inverse method which has a high ability to measure the value of cone effective area in various frequency points, also can estimate the MCL electroacoustic parameters simultaneously. The proposed inverse method comprises the direct problem, adjoint problem, and sensitivity problem in collaboration with nonlinear conjugate gradient method. Estimated values from the inverse method are validated experimentally which compared with the measured SPL curve result. Results presented in this paper not only improve the accuracy of lumped parameter model but also provide the valuable information on loudspeaker cone design.

Keywords: Inverse problem, cone effective area, loudspeaker, nonlinear conjugate gradient method.

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Authors: Ömer Faruk Baykoç, Ümit Sami Sakalli

Abstract:

In this paper, we propose a fuzzy aggregate production planning (APP) model for blending problem in a brass factory which is the problem of computing optimal amounts of raw materials for the total production of several types of brass in a period. The model has deterministic and imprecise parameters which follows triangular possibility distributions. The brass casting APP model can not always be solved by using common approaches used in the literature. Therefore a mathematical model is presented for solving this problem. In the proposed model, the Lai and Hwang-s fuzzy ranking concept is relaxed by using one constraint instead of three constraints. An application of the brass casting APP model in a brass factory shows that the proposed model successfully solves the multi-blend problem in casting process and determines the optimal raw material purchasing policies.

Keywords: Aggregate production planning, Blending, brasscasting, possibilistic programming.

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Authors: Zhenyu Zhao, Lei You

Abstract:

The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: D.Venkatesan, K.Kannan, S. Raja Balachandar

Abstract:

In this paper a new Genetic Algorithm based on a heuristic operator and Centre of Mass selection operator (CMGA) is designed for the unbounded knapsack problem(UKP), which is NP-Hard combinatorial optimization problem. The proposed genetic algorithm is based on a heuristic operator, which utilizes problem specific knowledge. This center of mass operator when combined with other Genetic Operators forms a competitive algorithm to the existing ones. Computational results show that the proposed algorithm is capable of obtaining high quality solutions for problems of standard randomly generated knapsack instances. Comparative study of CMGA with simple GA in terms of results for unbounded knapsack instances of size up to 200 show the superiority of CMGA. Thus CMGA is an efficient tool of solving UKP and this algorithm is competitive with other Genetic Algorithms also.

Keywords: Genetic Algorithm, Unbounded Knapsack Problem, Combinatorial Optimization, Meta-Heuristic, Center of Mass

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Authors: Behrouz Afshar Nadjafi

Abstract:

Extensive research has been devoted to economic production quantity (EPQ) problem. However, no attention has been paid to problems where production period length is constrained. In this paper, we address the problem of deciding the optimal production quantity and the number of minor setups within each cycle, in which, production period length is constrained but a minor setup is possible for pass the constraint. A mathematical model is developed and Iterated Local Search (ILS) is proposed to solve this problem. Finally, solution procedure illustrated with a numerical example and results are analyzed.

Keywords: EPQ, Inventory control, minor setup, ILS.

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Authors: Mustafa Resa Becan

Abstract:

The performance of a type of fuzzy sliding mode control is researched by considering the nonlinear characteristic of a missile-target interception problem to obtain a robust interception process. The variable boundary layer by using fuzzy logic is proposed to reduce the chattering around the switching surface then is applied to the interception model which was derived. The performances of the sliding mode control with constant and fuzzy boundary layer are compared at the end of the study and the results are evaluated.

Keywords: Sliding mode control, fuzzy, boundary layer, interception problem.

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Authors: F. Rezaie Moghaddam, J. Amani, T. Rezaie Moghaddam

Abstract:

Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.

Keywords: Heat conduction, Cellular automata, convergencerate, discrete system.

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Authors: P. Shunmugapriya, S. Kanmani, P. Jude Fredieric, U. Vignesh, J. Reman Justin, K. Vivek

Abstract:

Vehicle Routing Problem (VRP) is a complex combinatorial optimization problem and it is quite difficult to find an optimal solution consisting of a set of routes for vehicles whose total cost is minimum. Evolutionary and swarm intelligent (SI) algorithms play a vital role in solving optimization problems. While the SI algorithms perform search, the diversity between the solutions they exploit is very important. This is because of the need to avoid early convergence and to get an appropriate balance between the exploration and exploitation. Therefore, it is important to check how far the solutions are diverse. In this paper, we measure the similarity between solutions, which ABC exploits while optimizing VRP. The similar solutions found are discarded at the end of the iteration and only unique solutions are passed on to the next iteration. The bees of discarded solutions become scouts and they start searching for new solutions. This process is continued and results show that the solution is optimized at lesser number of iterations but with the overhead of computing similarity in all the iterations. The problem instance from Solomon benchmarked dataset has been used for evaluating the presented methodology.

Keywords: ABC algorithm, vehicle routing problem, optimization, Jaccard’s similarity measure.

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Authors: Hsuan-Ku Liu, Ming Long Liu

Abstract:

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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Authors: G. M. Komaki, S. Mobin, E. Teymourian, S. Sheikh

Abstract:

This paper addresses minimizing the makespan of the distributed permutation flow shop scheduling problem. In this problem, there are several parallel identical factories or flowshops each with series of similar machines. Each job should be allocated to one of the factories and all of the operations of the jobs should be performed in the allocated factory. This problem has recently gained attention and due to NP-Hard nature of the problem, metaheuristic algorithms have been proposed to tackle it. Majority of the proposed algorithms require large computational time which is the main drawback. In this study, a general variable neighborhood search algorithm (GVNS) is proposed where several time-saving schemes have been incorporated into it. Also, the GVNS uses the sophisticated method to change the shaking procedure or perturbation depending on the progress of the incumbent solution to prevent stagnation of the search. The performance of the proposed algorithm is compared to the state-of-the-art algorithms based on standard benchmark instances.

Keywords: Distributed permutation flow shop, scheduling, makespan, general variable neighborhood search algorithm.

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

Abstract:

Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: Ground surface relief, method of integral equations, numerical method.

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Authors: Shengbiao Wu, Weihua Cao, Min Wu, Can Liu

Abstract:

This paper presents an intelligent tuning method of microwave filter based on complex neural network and improved space mapping. The tuning process consists of two stages: the initial tuning and the fine tuning. At the beginning of the tuning, the return loss of the filter is transferred to the passband via the error of phase. During the fine tuning, the phase shift caused by the transmission line and the higher order mode is removed by the curve fitting. Then, an Cauchy method based on the admittance parameter (Y-parameter) is used to extract the coupling matrix. The influence of the resonant cavity loss is eliminated during the parameter extraction process. By using processed data pairs (the amount of screw variation and the variation of the coupling matrix), a tuning model is established by the complex neural network. In view of the improved space mapping algorithm, the mapping relationship between the actual model and the ideal model is established, and the amplitude and direction of the tuning is constantly updated. Finally, the tuning experiment of the eight order coaxial cavity filter shows that the proposed method has a good effect in tuning time and tuning precision.

Keywords: Microwave filter, scattering parameter (s-parameter), coupling matrix, intelligent tuning.

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Authors: M. S. Annie Christi

Abstract:

Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Keywords: Best candidates method, centroid ranking technique, robust ranking technique, transportation problem, fuzzy transportation problem.

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Authors: A. M. Nazari, B. Sepehrian, M. Jabari

Abstract:

In this paper we study the inverse eigenvalue problem for symmetric special matrices and introduce sufficient conditions for obtaining nonnegative matrices. We get the HROU algorithm from [1] and introduce some extension of this algorithm. If we have some eigenvectors and associated eigenvalues of a matrix, then by this extension we can find the symmetric matrix that its eigenvalue and eigenvectors are given. At last we study the special cases and get some remarkable results.

Keywords: Householder matrix, nonnegative matrix, Inverse eigenvalue problem.

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Authors: F. Sokhanvar, A. B. Khoshnevis

Abstract:

In the present work steady inviscid hypersonic flows are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the surface distribution of pressure is obtained.

Keywords: Hypersonic flow, Inverse problem method

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Authors: V. Tereshchenko, D. Taran

Abstract:

In this paper we propose a new approach to constructing the Delaunay Triangulation and the optimum algorithm for the case of multidimensional spaces (d ≥ 2). Analysing the modern state, it is possible to draw a conclusion, that the ideas for the existing effective algorithms developed for the case of d ≥ 2 are not simple to generalize on a multidimensional case, without the loss of efficiency. We offer for the solving this problem an effective algorithm that satisfies all the given requirements. But theoretical complexity of the problem it is impossible to improve as the Worst - Case Optimality for algorithms of solving such a problem is proved.

Keywords: Delaunay triangulation, multidimensional space, Voronoi Diagram, optimal algorithm.

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Authors: Waleed Abohamad, Amr Arisha

Abstract:

Owing the fact that optimization of business process is a crucial requirement to navigate, survive and even thrive in today-s volatile business environment, this paper presents a framework for selecting a best-fit optimization package for solving complex business problems. Complexity level of the problem and/or using incorrect optimization software can lead to biased solutions of the optimization problem. Accordingly, the proposed framework identifies a number of relevant factors (e.g. decision variables, objective functions, and modeling approach) to be considered during the evaluation and selection process. Application domain, problem specifications, and available accredited optimization approaches are also to be regarded. A recommendation of one or two optimization software is the output of the framework which is believed to provide the best results of the underlying problem. In addition to a set of guidelines and recommendations on how managers can conduct an effective optimization exercise is discussed.

Keywords: Complex Business Problems, Optimization, Selection Criteria, Software Evaluation.

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Authors: Nadaniela Egidi, Pierluigi Maponi

Abstract:

The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts and its two-dimensional formulation is a Fredholm integral equation of second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e. Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem.

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Authors: Jihyung Kim, Taejin Kim, Sungho Park, Jun-Dong Cho

Abstract:

In this paper, we address the problem of reducing the switching activity (SA) in on-chip buses through the use of a bus binding technique in high-level synthesis. While many binding techniques to reduce the SA exist, we present yet another technique for further reducing the switching activity. Our proposed method combines bus binding and data sequence reordering to explore a wider solution space. The problem is formulated as a multiple traveling salesman problem and solved using simulated annealing technique. The experimental results revealed that a binding solution obtained with the proposed method reduces 5.6-27.2% (18.0% on average) and 2.6-12.7% (6.8% on average) of the switching activity when compared with conventional binding-only and hybrid binding-encoding methods, respectively.

Keywords: low power, bus binding, switching activity, multiple traveling salesman problem, data sequence reordering

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

Abstract:

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

Keywords: Multiobjective evolutionary optimization, geneticalgorithms, shortest paths.

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Authors: Fatemeh Dadkhah, Hossein Ali Akbarpour

Abstract:

This paper considers a scheduling problem in flexible flow shops environment with the aim of minimizing two important criteria including makespan and cumulative tardiness of jobs. Since the proposed problem is known as an Np-hard problem in literature, we have to develop a meta-heuristic to solve it. We considered general structure of Genetic Algorithm (GA) and developed a new version of that based on Data Envelopment Analysis (DEA). Two objective functions assumed as two different inputs for each Decision Making Unit (DMU). In this paper we focused on efficiency score of DMUs and efficient frontier concept in DEA technique. After introducing the method we defined two different scenarios with considering two types of mutation operator. Also we provided an experimental design with some computational results to show the performance of algorithm. The results show that the algorithm implements in a reasonable time.

Keywords: Data envelopment analysis, Efficiency, Flexible flow shops, Genetic algorithm

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Authors: A.M. Al-Fahed Nuseirat, R. Abu-Zitar

Abstract:

In this paper the design of maximally flat linear phase finite impulse response (FIR) filters is considered. The problem is handled with totally two different approaches. The first one is completely deterministic numerical approach where the problem is formulated as a Linear Complementarity Problem (LCP). The other one is based on a combination of Markov Random Fields (MRF's) approach with messy genetic algorithm (MGA). Markov Random Fields (MRFs) are a class of probabilistic models that have been applied for many years to the analysis of visual patterns or textures. Our objective is to establish MRFs as an interesting approach to modeling messy genetic algorithms. We establish a theoretical result that every genetic algorithm problem can be characterized in terms of a MRF model. This allows us to construct an explicit probabilistic model of the MGA fitness function and introduce the Ising MGA. Experimentations done with Ising MGA are less costly than those done with standard MGA since much less computations are involved. The least computations of all is for the LCP. Results of the LCP, random search, random seeded search, MGA, and Ising MGA are discussed.

Keywords: Filter design, FIR digital filters, LCP, Ising model, MGA, Ising MGA.

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Authors: Min Kyung An

Abstract:

In this paper, we study the data collection problem in Wireless Sensor Networks (WSNs) adopting the two interference models: The graph model and the more realistic physical interference model known as Signal-to-Interference-Noise-Ratio (SINR). The main issue of the problem is to compute schedules with the minimum number of timeslots, that is, to compute the minimum latency schedules, such that data from every node can be collected without any collision or interference to a sink node. While existing works studied the problem with unit-sized and unbounded-sized message models, we investigate the problem with the bounded-sized message model, and introduce a constant factor approximation algorithm. To the best known of our knowledge, our result is the first result of the data collection problem with bounded-sized model in both interference models.

Keywords: Data collection, collision-free, interference-free, physical interference model, SINR, approximation, bounded-sized message model, wireless sensor networks, WSN.

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Authors: Mian Tahir Aftab, Muhammad Umer, Riaz Ahmad

Abstract:

This article proposes an Ant Colony Optimization (ACO) metaheuristic to minimize total makespan for scheduling a set of jobs and assign workers for uniformly related parallel machines. An algorithm based on ACO has been developed and coded on a computer program Matlab®, to solve this problem. The paper explains various steps to apply Ant Colony approach to the problem of minimizing makespan for the worker assignment & jobs scheduling problem in a parallel machine model and is aimed at evaluating the strength of ACO as compared to other conventional approaches. One data set containing 100 problems (12 Jobs, 03 machines and 10 workers) which is available on internet, has been taken and solved through this ACO algorithm. The results of our ACO based algorithm has shown drastically improved results, especially, in terms of negligible computational effort of CPU, to reach the optimal solution. In our case, the time taken to solve all 100 problems is even lesser than the average time taken to solve one problem in the data set by other conventional approaches like GA algorithm and SPT-A/LMC heuristics.

Keywords: Ant Colony Optimization (ACO), Genetic algorithms (GA), Makespan, SPT-A/LMC heuristic.

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Authors: Jui P. Hung, Hsia C. Chang, Yuan L. Lai

Abstract:

Introduction applicability of high-speed cutting stock problem (CSP) is presented in this paper. Due to the orders continued coming in from various on-line ways for a professional cutting company, to stay competitive, such a business has to focus on sustained production at high levels. In others words, operators have to keep the machine running to stay ahead of the pack. Therefore, the continuous stock cutting problem with setup is proposed to minimize the cutting time and pattern changing time to meet the on-line given demand. In this paper, a novel method is proposed to solve the problem directly by using cutting patterns directly. A major advantage of the proposed method in series on-line production is that the system can adjust the cutting plan according to the floating orders. Examples with multiple items are demonstrated. The results show considerable efficiency and reliability in high-speed cutting of CSP.

Keywords: Cutting stock, Optimization, Heuristics

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