Search results for: Inverse eigenvalue problem.

Authors: Shazia Javed, Noor Atinah Ahmad

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In this paper an efficient incomplete factorization preconditioner is proposed for the Least Mean Squares (LMS) adaptive filter. The proposed preconditioner is approximated from a priori knowledge of the factors of input correlation matrix with an incomplete strategy, motivated by the sparsity patter of the upper triangular factor in the QRD-RLS algorithm. The convergence properties of IPLMS algorithm are comparable with those of transform domain LMS(TDLMS) algorithm. Simulation results show efficiency and robustness of the proposed algorithm with reduced computational complexity.

Keywords: Autocorrelation matrix, Cholesky's factor, eigenvalue spread, Markov input.

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Authors: Arkady Bolotin

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One-way functions are functions that are easy to compute but hard to invert. Their existence is an open conjecture; it would imply the existence of intractable problems (i.e. NP-problems which are not in the P complexity class). If true, the existence of one-way functions would have an impact on the theoretical framework of physics, in particularly, quantum mechanics. Such aspect of one-way functions has never been shown before. In the present work, we put forward the following. We can calculate the microscopic state (say, the particle spin in the z direction) of a macroscopic system (a measuring apparatus registering the particle z-spin) by the system macroscopic state (the apparatus output); let us call this association the function F. The question is: can we compute the function F in the inverse direction? In other words, can we compute the macroscopic state of the system through its microscopic state (the preimage F -1)? In the paper, we assume that the function F is a one-way function. The assumption implies that at the macroscopic level the Schrödinger equation becomes unfeasible to compute. This unfeasibility plays a role of limit of the validity of the linear Schrödinger equation.

Keywords: One-way functions, P versus NP problem, quantummeasurements.

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Authors: Neda Shahidi, Hadi Esmaeilzadeh, Marziye Abdollahi, Caro Lucas

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In this paper, the problem of finding the optimal collision free path for a mobile robot, the path planning problem, is solved using an advanced evolutionary algorithm called memetic algorithm. What is new in this work is a novel representation of solutions for evolutionary algorithms that is efficient, simple and also compatible with memetic algorithm. The new representation makes it possible to solve the problem with a small population and in a few generations. It also makes the genetic operator simple and allows using an efficient local search operator within the evolutionary algorithm. The proposed algorithm is applied to two instances of path planning problem and the results are available.

Keywords: Path planning problem, Memetic Algorithm, Representation.

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Authors: Zhengsheng Wang, Xiangyong Ji, Yong Du

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The projection methods, usually viewed as the methods for computing eigenvalues, can also be used to estimate pseudospectra. This paper proposes a kind of projection methods for computing the pseudospectra of large scale matrices, including orthogonalization projection method and oblique projection method respectively. This possibility may be of practical importance in applications involving large scale highly nonnormal matrices. Numerical algorithms are given and some numerical experiments illustrate the efficiency of the new algorithms.

Keywords: Pseudospectra, eigenvalue, projection method, Arnoldi, IOM(q)

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Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: Coherent covering location problem, efficient frontier, Lagrangian relaxation, data envelopment analysis.

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Authors: Reneiloe Seodigeng, Malwandla Hanabe, Haleden Chiririwa, Hilary Rutto, Tumisang Seodigeng

Abstract:

Neutralisation of acid-mine drainage (AMD) using limestone is cost effective, and good results can be obtained. However, this process has its limitations; it cannot be used for highly acidic water which consists of Fe(III). When Fe(III) reacts with CaCO₃, it results in armoring. Armoring slows the reaction, and additional alkalinity can no longer be generated. Limestone is easily accessible, so this problem can be easily dealt with. Experiments were carried out to evaluate the effect of PVC pipe length on ferric and ferrous ions. It was found that the shorter the pipe length the more these dissolved metals precipitate. The effect of the pipe length on the hydrogen ions was also studied, and it was found that these two have an inverse relationship. Experimental data were further compared with the model prediction data to see if they behave in a similar fashion. The model was able to predict the behaviour of 1.5m and 2 m pipes in ferric and ferrous ion precipitation.

Keywords: Acid mine drainage, neutralization, limestone, modeling.

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Authors: Wang Xingbo

Abstract:

Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: Algorithm, determinant, computation, eigenvalue, time complexity.

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Authors: Ismail El Gayar, Ossama Ismail, Yousri El Gamal

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This paper presented a technique to solve one of the transportation problems that faces us in real life which is the Bus Scheduling Problem. Most of the countries using buses in schools, companies and traveling offices as an example to transfer multiple passengers from many places to specific place and vice versa. This transferring process can cost time and money, so we build a decision support system that can solve this problem. In this paper, a genetic algorithm with the shortest path technique is used to generate a competitive solution to other well-known techniques. It also presents a comparison between our solution and other solutions for this problem.

Keywords: Bus scheduling problem, decision support system, genetic algorithm, operation planning, shortest path, transportation.

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Authors: S.H. Mirtalaie, M.A. Hajabasi

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In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.

Keywords: Free vibration, laminated composite beam, material coupling, state space.

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Authors: Omid S. Fard, Akbar H. Borzabadi

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In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.

Keywords: Optimal control, Integer programming, Genetic algorithm, Discrete approximation, 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: G. V. Novikov, V. S. Sivozhelezov, S. S. Kolesnikov, K. V. Shaitan

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The study reports about the influence of binding of orthosteric ligands as well as point mutations on the conformational dynamics of β-2-adrenoreceptor. Using molecular dynamics simulation we found that there was a little fraction of active states of the receptor in its apo (ligand free) ensemble corresponded to its constitutive activity. Analysis of MD trajectories indicated that such spontaneous activation of the receptor is accompanied by the motion in intracellular part of its alpha-helices. Thus receptor’s constitutive activity directly results from its conformational dynamics. On the other hand the binding of a full agonist resulted in a significant shift of the initial equilibrium towards its active state. Finally, the binding of the inverse agonist stabilized the receptor in its inactive state. It is likely that the binding of inverse agonists might be a universal way of constitutive activity inhibition in vivo. Our results indicate that ligand binding redistribute pre-existing conformational degrees of freedom (in accordance to the Monod-Wyman-Changeux-Model) of the receptor rather than cause induced fit in it. Therefore, the ensemble of biologically relevant receptor conformations is encoded in its spatial structure, and individual conformations from that ensemble might be used by the cell in conformity with the physiological behavior.

Keywords: Seven-transmembrane receptors, constitutive activity, activation, x-ray crystallography, principal component analysis, molecular dynamics simulation.

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Authors: C. E. Nugraheni, L. Abednego

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This paper introduces a framework based on the collaboration of multi agent and hyper-heuristics to find a solution of the real single machine production problem. There are many techniques used to solve this problem. Each of it has its own advantages and disadvantages. By the collaboration of multi agent system and hyper-heuristics, we can get more optimal solution. The hyper-heuristics approach operates on a search space of heuristics rather than directly on a search space of solutions. The proposed framework consists of some agents, i.e. problem agent, trainer agent, algorithm agent (GPHH, GAHH, and SAHH), optimizer agent, and solver agent. Some low level heuristics used in this paper are MRT, SPT, LPT, EDD, LDD, and MON

Keywords: Hyper-heuristics, multi-agent systems, scheduling problem.

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Authors: Alyaa M. Younes, Nermine Harraz, Mohammad H. Elwany

Abstract:

Lithium ion batteries are currently used for many applications including satellites, electric vehicles and mobile electronics. Their ability to store relatively large amount of energy in a limited space make them most appropriate for critical applications. Evaluation of the life of these batteries and their reliability becomes crucial to the systems they support. Reliability of Li-Ion batteries has been mainly considered based on its lifetime. However, another important factor that can be considered critical in many applications such as in electric vehicles is the cycle duration. The present work presents the results of an experimental investigation on the degradation behavior of a Laptop Li-ion battery (type TKV2V) and the effect of applied load on the battery cycle time. The reliability was evaluated using an accelerated life test. Least squares linear regression with median rank estimation was used to estimate the Weibull distribution parameters needed for the reliability functions estimation. The probability density function, failure rate and reliability function under each of the applied loads were evaluated and compared. An inverse power model is introduced that can predict cycle time at any stress level given.

Keywords: Accelerated life test, inverse power law, lithium ion battery, reliability evaluation, Weibull distribution.

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Authors: Yong-Quan Zhou, Deng-Xu He, Zheng Nong

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In this paper two models using a functional network were employed to solving classification problem. Functional networks are generalized neural networks, which permit the specification of their initial topology using knowledge about the problem at hand. In this case, and after analyzing the available data and their relations, we systematically discuss a numerical analysis method used for functional network, and apply two functional network models to solving XOR problem. The XOR problem that cannot be solved with two-layered neural network can be solved by two-layered functional network, which reveals a potent computational power of functional networks, and the performance of the proposed model was validated using classification problems.

Keywords: Functional network, neural network, XOR problem, classification, numerical analysis method.

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Authors: Atilla Bayram

Abstract:

This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: Computed force control method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss.

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Authors: M. Erol Genevois, D. Celik, H. Z. Ulukan

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Automated Teller Machines (ATMs) can be considered among one of the most important service facilities in the banking industry. The investment in ATMs and the impact on the banking industry is growing steadily in every part of the world. The banks take into consideration many factors like safety, convenience, visibility, and cost in order to determine the optimum locations of ATMs. Today, ATMs are not only available in bank branches but also at retail locations. Another important factor is the cash management in ATMs. A cash demand model for every ATM is needed in order to have an efficient cash management system. This forecasting model is based on historical cash demand data which is highly related to the ATMs location. So, the location and the cash management problem should be considered together. This paper provides a general review on studies, efforts and development in ATMs location and cash management problem.

Keywords: ATM location problem, cash management problem, ATM cash replenishment problem, literature review in ATMs.

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Authors: M. Polanský

Abstract:

This paper introduces a new method called ARPDC (Advanced Robust Parallel Distributed Compensation) for automatic control of nonlinear systems. This method improves a quality of robust control by interpolating of robust and optimal controller. The weight of each controller is determined by an original criteria function for model validity and disturbance appreciation. ARPDC method is based on nonlinear Takagi-Sugeno (T-S) fuzzy systems and Parallel Distributed Compensation (PDC) control scheme. The relaxed stability conditions of ARPDC control of nominal system have been derived. The advantages of presented method are demonstrated on the inverse pendulum benchmark problem. From comparison between three different controllers (robust, optimal and ARPDC) follows, that ARPDC control is almost optimal with the robustness close to the robust controller. The results indicate that ARPDC algorithm can be a good alternative not only for a robust control, but in some cases also to an adaptive control of nonlinear systems.

Keywords: Robust control, optimal control, Takagi–Sugeno (TS) fuzzy models, linear matrix inequality (LMI), observer, Advanced Robust Parallel Distributed Compensation (ARPDC).

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Authors: B. Özlük, A. Karaaslan

Abstract:

This study has been conducted as a supplementary and relationship seeking study with the purpose of measuring the tendency and success of support among peers amid nursing students studying at university in solving interpersonal problems. The population of the study (N:279) is comprised of nursing students who are studying at one state and one private university in the province of Konya, while its sample is comprised of 231 nursing students who agreed to take part in the study voluntarily. As a result of this study, it has been determined that the peer support and interpersonal problem solving characteristics among students were at medium levels and that the interpersonal problem solving skills of students studying in the third year were higher than those of first and second year students. While the interpersonal problem solving characteristics of students who are aged 20 and over were found to be higher, no difference could be determined in terms of the interpersonal problem solving skills and tendencies among students, based on their gender and where they reside. A positive – to a medium degree – and significant relationship was determined between peer support and interpersonal problem solving skills, and it is possible to say that as peer support increases, so do the skills and tendencies to solve problems.

Keywords: Interpersonal problem, nursing students, peer support, problem solving.

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Authors: Amir Farkhonde

Abstract:

The major objective of this study was to devise a method for solving mathematical problems. Three concepts including faculty of understanding, faculty of guess, and free mind or beginner's mind provided the foundation for this method. An explanatory approach along with a hermeneutic process was taken in this study to support the assumption that mathematical knowledge is constantly developing and it seems essential for students to solve math problems on their own using their faculty of understanding (interpretive dialogue) and faculty of guess. For doing so, a kind of movement from the mathematical problem to mathematical knowledge should be adopted for teaching students a new math topic. The research method of this paper is review, descriptive and conception development. This paper first reviews the research findings on the NRICH’S project (NRICH is part of the family of activities in the Millennium Mathematics Project) with the aim that these findings form the theoretical basis of the problem-solving method. Then, the curriculum, the conceptual structure of the new method, how to design the problem and an example of it are discussed. In this way, students are immersed in the story of discovering and understanding the problem formula, and interpretive dialogue with the text continues by following the questions posed by the problem and constantly reconstructing the answer to find a formula or solution to solve the problem.

Keywords: Interpretive dialogue, NRICH, inventing, a method of problem solving.

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Authors: Yepeng Cheng, Yasuhiko Morimoto

Abstract:

Customer relationship analysis is vital for retail stores, especially for supermarkets. The point of sale (POS) systems make it possible to record the daily purchasing behaviors of customers as an identification point of sale (ID-POS) database, which can be used to analyze customer behaviors of a supermarket. The customer value is an indicator based on ID-POS database for detecting the customer loyalty of a store. In general, there are many supermarkets in a city, and other nearby competitor supermarkets significantly affect the customer value of customers of a supermarket. However, it is impossible to get detailed ID-POS databases of competitor supermarkets. This study firstly focused on the customer value and distance between a customer's home and supermarkets in a city, and then constructed the models based on logistic regression analysis to analyze correlations between distance and purchasing behaviors only from a POS database of a supermarket chain. During the modeling process, there are three primary problems existed, including the incomparable problem of customer values, the multicollinearity problem among customer value and distance data, and the number of valid partial regression coefficients. The improved customer value, Huff’s gravity model, and inverse attractiveness frequency are considered to solve these problems. This paper presents three types of models based on these three methods for loyal customer classification and competitors’ influence analysis. In numerical experiments, all types of models are useful for loyal customer classification. The type of model, including all three methods, is the most superior one for evaluating the influence of the other nearby supermarkets on customers' purchasing of a supermarket chain from the viewpoint of valid partial regression coefficients and accuracy.

Keywords: Customer value, Huff's Gravity Model, POS, retailer.

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Authors: W. Wongthatsanekorn, N. Matheekrieangkrai

Abstract:

This research proposes Bee Algorithm (BA) to optimize Ready Mixed Concrete (RMC) truck scheduling problem from single batch plant to multiple construction sites. This problem is considered as an NP-hard constrained combinatorial optimization problem. This paper provides the details of the RMC dispatching process and its related constraints. BA was then developed to minimize total waiting time of RMC trucks while satisfying all constraints. The performance of BA is then evaluated on two benchmark problems (3 and 5construction sites) according to previous researchers. The simulation results of BA are compared in term of efficiency and accuracy with Genetic Algorithm (GA) and all problems show that BA approach outperforms GA in term of efficiency and accuracy to obtain optimal solution. Hence, BA approach could be practically implemented to obtain the best schedule.

Keywords: Bee Colony Optimization, Ready Mixed Concrete Problem.

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Authors: Takayuki Shiina

Abstract:

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: Sanjeeb Kumar Kar

Abstract:

The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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Authors: M. Rezki, A. Belaidi

Abstract:

This paper deals with a method of learning to solve a real problem in biomedical engineering from a technical study of muscle fatigue. Electromyography (EMG) is a technique for evaluating and recording the electrical activity produced by skeletal muscles (viewpoint: anatomical and physiological). EMG is used as a diagnostics tool for identifying neuromuscular diseases, assessing low-back pain and muscle fatigue in general. In order to study the EMG signal for detecting fatigue in a muscle, we have taken a real problem which touches the tramway conductor the handle bar. For the study, we have used a typical autonomous platform in order to get signals at real time. In our case study, we were confronted with complex problem to do our experiments in a tram. This type of problem is recurring among students. To teach our students the method to solve this kind of problem, we built a similar system. Through this study, we realized a lot of objectives such as making the equipment for simulation, the study of detection of muscle fatigue and especially how to manage a study of biomedical looking.

Keywords: EMG, health platform, conductor’s tram, muscle fatigue.

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Authors: Sameena Tarannum, S. Pranesh

Abstract:

The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.

Keywords: Gravity modulation, Oldroyd-B liquid, triple diffusive convection, Venezian approach.

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Authors: A. I. Augie, Y. Alhassan, U. Z. Magawata

Abstract:

Geophysical investigation was carried out at wacot rice factory Argungu north-western Nigeria, using the 2D electrical resistivity method. The area falls between latitude 12˚44′23ʺN to 12˚44′50ʺN and longitude 4032′18′′E to 4032′39′′E covering a total area of about 1.85 km. Two profiles were carried out with Wenner configuration using resistivity meter (Ohmega). The data obtained from the study area were modeled using RES2DIVN software which gave an automatic interpretation of the apparent resistivity data. The inverse resistivity models of the profiles show the high resistivity values ranging from 208 Ωm to 651 Ωm. These high resistivity values in the overburden were due to dryness and compactness of the strata that lead to consolidation, which is an indication that the area is free from leachate contaminations. However, from the inverse model, there are regions of low resistivity values (1 Ωm to 18 Ωm), these zones were observed and identified as clayey and the most contaminated zones. The regions of low resistivity thereby indicated the leachate plume or the highly leachate concentrated zones due to similar resistivity values in both clayey and leachate. The regions of leachate are mainly from the factory into the surrounding area and its groundwater. The maximum leachate infiltration was found at depths 1 m to 15.9 m (P1) and 6 m to 15.9 m (P2) vertically, as well as distance along the profiles from 67 m to 75 m (P1), 155 m to 180 m (P1), and 115 m to 192 m (P2) laterally.

Keywords: Contaminant, leachate, soil, groundwater, 2D, electrical, resistivity, Argungu.

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Authors: Zuwairie Ibrahim, Yusei Tsuboi, Osamu Ono, Marzuki Khalid

Abstract:

Deoxyribonucleic Acid or DNA computing has emerged as an interdisciplinary field that draws together chemistry, molecular biology, computer science and mathematics. Thus, in this paper, the possibility of DNA-based computing to solve an absolute 1-center problem by molecular manipulations is presented. This is truly the first attempt to solve such a problem by DNA-based computing approach. Since, part of the procedures involve with shortest path computation, research works on DNA computing for shortest path Traveling Salesman Problem, in short, TSP are reviewed. These approaches are studied and only the appropriate one is adapted in designing the computation procedures. This DNA-based computation is designed in such a way that every path is encoded by oligonucleotides and the path-s length is directly proportional to the length of oligonucleotides. Using these properties, gel electrophoresis is performed in order to separate the respective DNA molecules according to their length. One expectation arise from this paper is that it is possible to verify the instance absolute 1-center problem using DNA computing by laboratory experiments.

Keywords: DNA computing, operation research, 1-center problem.

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Authors: Wen-Haw Chen

Abstract:

This paper proposes a method to improve the shortest path problem on a NURBS (Non-uniform rational basis spline) surfaces. It comes from an application of the theory in classic differential geometry on surfaces and can improve the distance problem not only on surfaces but in the Euclidean 3-space R3 .

Keywords: shortest paths, geodesic-like method, NURBS surfaces.

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Authors: Lee Yih Rou, Hishammuddin Asmuni

Abstract:

Flexible Job Shop Problem (FJSP) is an extension of classical Job Shop Problem (JSP). The FJSP extends the routing flexibility of the JSP, i.e assigning machine to an operation. Thus it makes it more difficult than the JSP. In this study, Cooperative Coevolutionary Genetic Algorithm (CCGA) is presented to solve the FJSP. Makespan (time needed to complete all jobs) is used as the performance evaluation for CCGA. In order to test performance and efficiency of our CCGA the benchmark problems are solved. Computational result shows that the proposed CCGA is comparable with other approaches.

Keywords: Co-evolution, Genetic Algorithm (GA), Flexible JobShop Problem(FJSP)

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