Search results for: Heuristic Methods
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4124

Search results for: Heuristic Methods

3944 Analysis of Green Wood Preservation Chemicals

Authors: Aitor Barbero-López, Soumaya Chibily, Gerhard Scheepers, Thomas Grahn, Martti Venäläinen, Antti Haapala

Abstract:

Wood decay is addressed continuously within the wood industry through use and development of wood preservatives. The increasing awareness on the negative effects of many chemicals towards the environment is causing political restrictions in their use and creating more urgent need for research on green alternatives. This paper discusses some of the possible natural extracts for wood preserving applications and compares the analytical methods available for testing their behavior and efficiency against decay fungi. The results indicate that natural extracts have interesting chemical constituents that delay fungal growth but vary in efficiency depending on the chemical concentration and substrate used. Results also suggest that presence and redistribution of preservatives in wood during exposure trials can be assessed by spectral imaging methods although standardized methods are not available. This study concludes that, in addition to the many standard methods available, there is a need to develop new faster methods for screening potential preservative formulation while maintaining the comparability and relevance of results.

Keywords: Analytics, methods, preservatives, wood decay.

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3943 The Application of Homotopy Method In Solving Electrical Circuit Design Problem

Authors: Talib Hashim Hasan

Abstract:

This paper describes simple implementation of homotopy (also called continuation) algorithm for determining the proper resistance of the resistor to dissipate energy at a specified rate of an electric circuit. Homotopy algorithm can be considered as a developing of the classical methods in numerical computing such as Newton-Raphson and fixed point methods. In homoptopy methods, an embedding parameter is used to control the convergence. The method purposed in this work utilizes a special homotopy called Newton homotopy. Numerical example solved in MATLAB is given to show the effectiveness of the purposed method

Keywords: electrical circuit homotopy, methods, MATLAB, Newton homotopy

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3942 Preconditioned Generalized Accelerated Overrelaxation Methods for Solving Certain Nonsingular Linear System

Authors: Deyu Sun, Guangbin Wang

Abstract:

In this paper, we present preconditioned generalized accelerated overrelaxation (GAOR) methods for solving certain nonsingular linear system. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned GAOR methods converge faster than the GAOR method whenever the GAOR method is convergent. Finally, we give two numerical examples to confirm our theoretical results.

Keywords: Preconditioned, GAOR method, linear system, convergence, comparison.

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3941 Applications for Accounting of Inherited Object-Oriented Class Members

Authors: Jehad Al Dallal

Abstract:

A class in an Object-Oriented (OO) system is the basic unit of design, and it encapsulates a set of attributes and methods. In OO systems, instead of redefining the attributes and methods that are included in other classes, a class can inherit these attributes and methods and only implement its unique attributes and methods, which results in reducing code redundancy and improving code testability and maintainability. Such mechanism is called Class Inheritance. However, some software engineering applications may require accounting for all the inherited class members (i.e., attributes and methods). This paper explains how to account for inherited class members and discusses the software engineering applications that require such consideration.

Keywords: Object-oriented design, inheritance, internal quality attribute, external quality attribute, class flattening.

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3940 Self-Organization-Based Approach for Embedded Real-Time System Design

Authors: S. S. Bendib, L. W. Mouss, S. Kalla

Abstract:

This paper proposes a self-organization-based approach for real-time systems design. The addressed issue is the mapping of an application onto an architecture of heterogeneous processors while optimizing both makespan and reliability. Since this problem is NP-hard, a heuristic algorithm is used to obtain efficiently approximate solutions. The proposed approach takes into consideration the quality as well as the diversity of solutions. Indeed, an alternate treatment of the two objectives allows to produce solutions of good quality while a self-organization approach based on the neighborhood structure is used to reorganize solutions and consequently to enhance their diversity. Produced solutions make different compromises between the makespan and the reliability giving the user the possibility to select the solution suited to his (her) needs.

Keywords: Embedded real-time systems design, makespan, reliability, self-organization, compromises.

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3939 A hybrid Tabu Search Algorithm to Cell Formation Problem and its Variants

Authors: Tai-Hsi Wu, Jinn-Yi Yeh, Chin-Chih Chang

Abstract:

Cell formation is the first step in the design of cellular manufacturing systems. In this study, a general purpose computational scheme employing a hybrid tabu search algorithm as the core is proposed to solve the cell formation problem and its variants. In the proposed scheme, great flexibilities are left to the users. The core solution searching algorithm embedded in the scheme can be easily changed to any other meta-heuristic algorithms, such as the simulated annealing, genetic algorithm, etc., based on the characteristics of the problems to be solved or the preferences the users might have. In addition, several counters are designed to control the timing of conducting intensified solution searching and diversified solution searching strategies interactively.

Keywords: Cell formation problem, Tabu search

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3938 An Analysis of Compression Methods and Implementation of Medical Images in Wireless Network

Authors: C. Rajan, K. Geetha, S. Geetha

Abstract:

The motivation of image compression technique is to reduce the irrelevance and redundancy of the image data in order to store or pass data in an efficient way from one place to another place. There are several types of compression methods available. Without the help of compression technique, the file size is knowingly larger, usually several megabytes, but by doing the compression technique, it is possible to reduce file size up to 10% as of the original without noticeable loss in quality. Image compression can be lossless or lossy. The compression technique can be applied to images, audio, video and text data. This research work mainly concentrates on methods of encoding, DCT, compression methods, security, etc. Different methodologies and network simulations have been analyzed here. Various methods of compression methodologies and its performance metrics has been investigated and presented in a table manner.

Keywords: Image compression techniques, encoding, DCT, lossy compression, lossless compression, JPEG.

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3937 Application of Ant Colony Optimization for Multi-objective Production Problems

Authors: Teerapun Saeheaw, Nivit Charoenchai, Wichai Chattinnawat

Abstract:

This paper proposes a meta-heuristic called Ant Colony Optimization to solve multi-objective production problems. The multi-objective function is to minimize lead time and work in process. The problem is related to the decision variables, i.e.; distance and process time. According to decision criteria, the mathematical model is formulated. In order to solve the model an ant colony optimization approach has been developed. The proposed algorithm is parameterized by the number of ant colonies and the number of pheromone trails. One example is given to illustrate the effectiveness of the proposed model. The proposed formulations; Max-Min Ant system are then used to solve the problem and the results evaluate the performance and efficiency of the proposed algorithm using simulation.

Keywords: Ant colony optimization, multi-objective problems.

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3936 Particle Swarm Optimization for Design of Water Distribution Systems

Authors: A. Vasan

Abstract:

Particle swarm optimization (PSO) technique is applied to design the water distribution pipeline network. A simulation-optimization model is formulated with the objective of minimizing cost and is applied to a benchmark water distribution system optimization problem. The benchmark problem taken for the application of PSO technique to optimize the pipe size of the water distribution network is New York City water supply system problem. The results from the analysis infer that PSO is a potential alternative optimization technique when compared to other heuristic techniques for optimal sizing of water distribution systems.

Keywords: Water distribution systems, Optimization, Particle swarm optimization, Swarm intelligence, New York water supply system.

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3935 Summarizing Data Sets for Data Mining by Using Statistical Methods in Coastal Engineering

Authors: Yunus Doğan, Ahmet Durap

Abstract:

Coastal regions are the one of the most commonly used places by the natural balance and the growing population. In coastal engineering, the most valuable data is wave behaviors. The amount of this data becomes very big because of observations that take place for periods of hours, days and months. In this study, some statistical methods such as the wave spectrum analysis methods and the standard statistical methods have been used. The goal of this study is the discovery profiles of the different coast areas by using these statistical methods, and thus, obtaining an instance based data set from the big data to analysis by using data mining algorithms. In the experimental studies, the six sample data sets about the wave behaviors obtained by 20 minutes of observations from Mersin Bay in Turkey and converted to an instance based form, while different clustering techniques in data mining algorithms were used to discover similar coastal places. Moreover, this study discusses that this summarization approach can be used in other branches collecting big data such as medicine.

Keywords: Clustering algorithms, coastal engineering, data mining, data summarization, statistical methods.

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3934 Some Results on Parallel Alternating Methods

Authors: Guangbin Wang, Fuping Tan

Abstract:

In this paper, we investigate two parallel alternating methods for solving the system of linear equations Ax = b and give convergence theorems for the parallel alternating methods when the coefficient matrix is a nonsingular H-matrix. Furthermore, we give one example to show our results.

Keywords: Nonsingular H-matrix, parallel alternating method, convergence.

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3933 Improved Hill Climbing and Simulated Annealing Algorithms for Size Optimization of Trusses

Authors: Morteza Kazemi Torbaghan, Seyed Mehran Kazemi, Rahele Zhiani, Fakhriye Hamed

Abstract:

Truss optimization problem has been vastly studied during the past 30 years and many different methods have been proposed for this problem. Even though most of these methods assume that the design variables are continuously valued, in reality, the design variables of optimization problems such as cross-sectional areas are discretely valued. In this paper, an improved hill climbing and an improved simulated annealing algorithm have been proposed to solve the truss optimization problem with discrete values for crosssectional areas. Obtained results have been compared to other methods in the literature and the comparison represents that the proposed methods can be used more efficiently than other proposed methods

Keywords: Size Optimization of Trusses, Hill Climbing, Simulated Annealing.

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3932 Comparison of Different Methods to Produce Fuzzy Tolerance Relations for Rainfall Data Classification in the Region of Central Greece

Authors: N. Samarinas, C. Evangelides, C. Vrekos

Abstract:

The aim of this paper is the comparison of three different methods, in order to produce fuzzy tolerance relations for rainfall data classification. More specifically, the three methods are correlation coefficient, cosine amplitude and max-min method. The data were obtained from seven rainfall stations in the region of central Greece and refers to 20-year time series of monthly rainfall height average. Three methods were used to express these data as a fuzzy relation. This specific fuzzy tolerance relation is reformed into an equivalence relation with max-min composition for all three methods. From the equivalence relation, the rainfall stations were categorized and classified according to the degree of confidence. The classification shows the similarities among the rainfall stations. Stations with high similarity can be utilized in water resource management scenarios interchangeably or to augment data from one to another. Due to the complexity of calculations, it is important to find out which of the methods is computationally simpler and needs fewer compositions in order to give reliable results.

Keywords: Classification, fuzzy logic, tolerance relations, rainfall data.

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3931 Non-Parametric Histogram-Based Thresholding Methods for Weld Defect Detection in Radiography

Authors: N. Nacereddine, L. Hamami, M. Tridi, N. Oucief

Abstract:

In non destructive testing by radiography, a perfect knowledge of the weld defect shape is an essential step to appreciate the quality of the weld and make decision on its acceptability or rejection. Because of the complex nature of the considered images, and in order that the detected defect region represents the most accurately possible the real defect, the choice of thresholding methods must be done judiciously. In this paper, performance criteria are used to conduct a comparative study of four non parametric histogram thresholding methods for automatic extraction of weld defect in radiographic images.

Keywords: Radiographic images, non parametric methods, histogram thresholding, performance criteria.

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3930 Coding Considerations for Standalone Molecular Dynamics Simulations of Atomistic Structures

Authors: R. O. Ocaya, J. J. Terblans

Abstract:

The laws of Newtonian mechanics allow ab-initio molecular dynamics to model and simulate particle trajectories in material science by defining a differentiable potential function. This paper discusses some considerations for the coding of ab-initio programs for simulation on a standalone computer and illustrates the approach by C language codes in the context of embedded metallic atoms in the face-centred cubic structure. The algorithms use velocity-time integration to determine particle parameter evolution for up to several thousands of particles in a thermodynamical ensemble. Such functions are reusable and can be placed in a redistributable header library file. While there are both commercial and free packages available, their heuristic nature prevents dissection. In addition, developing own codes has the obvious advantage of teaching techniques applicable to new problems.

Keywords: C-language, molecular dynamics, simulation, embedded atom method.

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3929 The Interaction between Human and Environment on the Perspective of Environmental Ethics

Authors: Mella Ismelina Farma Rahayu

Abstract:

Environmental problems could not be separated from unethical human perspectives and behaviors toward the environment. There is a fundamental error in the philosophy of people’s perspective about human and nature and their relationship with the environment, which in turn will create an inappropriate behavior in relation to the environment. The aim of this study is to investigate and to understand the ethics of the environment in the context of humans interacting with the environment by using the hermeneutic approach. The related theories and concepts collected from literature review are used as data, which were analyzed by using interpretation, critical evaluation, internal coherence, comparisons, and heuristic techniques. As a result of this study, there will be a picture related to the interaction of human and environment in the perspective of environmental ethics, as well as the problems of the value of ecological justice in the interaction of humans and environment. We suggest that the interaction between humans and environment need to be based on environmental ethics, in a spirit of mutual respect between humans and the natural world.

Keywords: The environment, environmental ethics, the interaction, value.

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3928 New Explicit Group Newton's Iterative Methods for the Solutions of Burger's Equation

Authors: Tan K. B., Norhashidah Hj. M. Ali

Abstract:

In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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3927 Computer Aided Assembly Attributes Retrieval Methods for Automated Assembly Sequence Generation

Authors: M. V. A. Raju Bahubalendruni, Bibhuti Bhusan Biswal, B. B. V. L. Deepak

Abstract:

Achieving an appropriate assembly sequence needs deep verification for its physical feasibility. For this purpose, industrial engineers use several assembly predicates; namely, liaison, geometric feasibility, stability and mechanical feasibility. However, testing an assembly sequence for these predicates requires huge assembly information. Extracting such assembly information from an assembled product is a time consuming and highly skillful task with complex reasoning methods. In this paper, computer aided methods are proposed to extract all the necessary assembly information from computer aided design (CAD) environment in order to perform the assembly sequence planning efficiently. These methods use preliminary capabilities of three-dimensional solid modelling and assembly modelling methods used in CAD software considering equilibrium laws of physical bodies.

Keywords: Assembly automation, assembly attributes, assembly sequence generation, computer aided design.

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3926 PSO-based Possibilistic Portfolio Model with Transaction Costs

Authors: Wei Chen, Cui-you Yao, Yue Qiu

Abstract:

This paper deals with a portfolio selection problem based on the possibility theory under the assumption that the returns of assets are LR-type fuzzy numbers. A possibilistic portfolio model with transaction costs is proposed, in which the possibilistic mean value of the return is termed measure of investment return, and the possibilistic variance of the return is termed measure of investment risk. Due to considering transaction costs, the existing traditional optimization algorithms usually fail to find the optimal solution efficiently and heuristic algorithms can be the best method. Therefore, a particle swarm optimization is designed to solve the corresponding optimization problem. At last, a numerical example is given to illustrate our proposed effective means and approaches.

Keywords: Possibility theory, portfolio selection, transaction costs, particle swarm optimization.

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3925 Simulated Annealing and Genetic Algorithm in Telecommunications Network Planning

Authors: Aleksandar Tsenov

Abstract:

The main goal of this work is to propose a way for combined use of two nontraditional algorithms by solving topological problems on telecommunications concentrator networks. The algorithms suggested are the Simulated Annealing algorithm and the Genetic Algorithm. The Algorithm of Simulated Annealing unifies the well known local search algorithms. In addition - Simulated Annealing allows acceptation of moves in the search space witch lead to decisions with higher cost in order to attempt to overcome any local minima obtained. The Genetic Algorithm is a heuristic approach witch is being used in wide areas of optimization works. In the last years this approach is also widely implemented in Telecommunications Networks Planning. In order to solve less or more complex planning problem it is important to find the most appropriate parameters for initializing the function of the algorithm.

Keywords: Concentrator network, genetic algorithm, simulated annealing, UCPL.

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3924 A New Routing Algorithm: MIRAD

Authors: Amir Gholami Pastaki, Ali Reza Sahab, Seyed Mehdi Sadeghi

Abstract:

LSP routing is among the prominent issues in MPLS networks traffic engineering. The objective of this routing is to increase number of the accepted requests while guaranteeing the quality of service (QoS). Requested bandwidth is the most important QoS criterion that is considered in literatures, and a various number of heuristic algorithms have been presented with that regards. Many of these algorithms prevent flows through bottlenecks of the network in order to perform load balancing, which impedes optimum operation of the network. Here, a modern routing algorithm is proposed as MIRAD: having a little information of the network topology, links residual bandwidth, and any knowledge of the prospective requests it provides every request with a maximum bandwidth as well as minimum end-to-end delay via uniform load distribution across the network. Simulation results of the proposed algorithm show a better efficiency in comparison with similar algorithms.

Keywords: new generation networks, QoS, traffic engineering, MPLS, QoS based routing, LSP

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3923 Performance Evaluation of Energy Efficient Communication Protocol for Mobile Ad Hoc Networks

Authors: Toshihiko Sasama, Kentaro Kishida, Kazunori Sugahara, Hiroshi Masuyama

Abstract:

A mobile ad hoc network is a network of mobile nodes without any notion of centralized administration. In such a network, each mobile node behaves not only as a host which runs applications but also as a router to forward packets on behalf of others. Clustering has been applied to routing protocols to achieve efficient communications. A CH network expresses the connected relationship among cluster-heads. This paper discusses the methods for constructing a CH network, and produces the following results: (1) The required running costs of 3 traditional methods for constructing a CH network are not so different from each other in the static circumstance, or in the dynamic circumstance. Their running costs in the static circumstance do not differ from their costs in the dynamic circumstance. Meanwhile, although the routing costs required for the above 3 methods are not so different in the static circumstance, the costs are considerably different from each other in the dynamic circumstance. Their routing costs in the static circumstance are also very different from their costs in the dynamic circumstance, and the former is one tenths of the latter. The routing cost in the dynamic circumstance is mostly the cost for re-routing. (2) On the strength of the above results, we discuss new 2 methods regarding whether they are tolerable or not in the dynamic circumstance, that is, whether the times of re-routing are small or not. These new methods are revised methods that are based on the traditional methods. We recommended the method which produces the smallest routing cost in the dynamic circumstance, therefore producing the smallest total cost.

Keywords: cluster, mobile ad hoc network, re-routing cost, simulation

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3922 Some Results on Parallel Alternating Two-stage Methods

Authors: Guangbin Wang, Xue Li

Abstract:

In this paper, we present parallel alternating two-stage methods for solving linear system Ax=b, where A is a symmetric positive definite matrix. And we give some convergence results of these methods for nonsingular linear system.

Keywords: alternating two-stage, convergence, linear system, parallel.

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3921 Fine-Grained Sentiment Analysis: Recent Progress

Authors: Jie Liu, Xudong Luo, Pingping Lin, Yifan Fan

Abstract:

Facebook, Twitter, Weibo, and other social media and significant e-commerce sites generate a massive amount of online texts, which can be used to analyse people’s opinions or sentiments for better decision-making. So, sentiment analysis, especially the fine-grained sentiment analysis, is a very active research topic. In this paper, we survey various methods for fine-grained sentiment analysis, including traditional sentiment lexicon-based methods, ma-chine learning-based methods, and deep learning-based methods in aspect/target/attribute-based sentiment analysis tasks. Besides, we discuss their advantages and problems worthy of careful studies in the future.

Keywords: sentiment analysis, fine-grained, machine learning, deep learning

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3920 Critical Analysis of Decision Making Experience with a Machine Learning Approach in Playing Ayo Game

Authors: Ibidapo O. Akinyemi, Ezekiel F. Adebiyi, Harrison O. D. Longe

Abstract:

The major goal in defining and examining game scenarios is to find good strategies as solutions to the game. A plausible solution is a recommendation to the players on how to play the game, which is represented as strategies guided by the various choices available to the players. These choices invariably compel the players (decision makers) to execute an action following some conscious tactics. In this paper, we proposed a refinement-based heuristic as a machine learning technique for human-like decision making in playing Ayo game. The result showed that our machine learning technique is more adaptable and more responsive in making decision than human intelligence. The technique has the advantage that a search is astutely conducted in a shallow horizon game tree. Our simulation was tested against Awale shareware and an appealing result was obtained.

Keywords: Decision making, Machine learning, Strategy, Ayo game.

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3919 An Optimal Steganalysis Based Approach for Embedding Information in Image Cover Media with Security

Authors: Ahlem Fatnassi, Hamza Gharsellaoui, Sadok Bouamama

Abstract:

This paper deals with the study of interest in the fields of Steganography and Steganalysis. Steganography involves hiding information in a cover media to obtain the stego media in such a way that the cover media is perceived not to have any embedded message for its unintended recipients. Steganalysis is the mechanism of detecting the presence of hidden information in the stego media and it can lead to the prevention of disastrous security incidents. In this paper, we provide a critical review of the steganalysis algorithms available to analyze the characteristics of an image stego media against the corresponding cover media and understand the process of embedding the information and its detection. We anticipate that this paper can also give a clear picture of the current trends in steganography so that we can develop and improvise appropriate steganalysis algorithms.

Keywords: Optimization, heuristics and metaheuristics algorithms, embedded systems, low-power consumption, Steganalysis Heuristic approach.

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3918 Affine Combination of Splitting Type Integrators, Implemented with Parallel Computing Methods

Authors: Adrian Alvarez, Diego Rial

Abstract:

In this work we present a family of new convergent type methods splitting high order no negative steps feature that allows your application to irreversible problems. Performing affine combinations consist of results obtained with Trotter Lie integrators of different steps. Some examples where applied symplectic compared with methods, in particular a pair of differential equations semilinear. The number of basic integrations required is comparable with integrators symplectic, but this technique allows the ability to do the math in parallel thus reducing the times of which exemplify exhibiting some implementations with simple schemes for its modularity and scalability process.

Keywords: Lie Trotter integrators, Irreversible Problems, Splitting Methods without negative steps, MPI, HPC.

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3917 EML-Estimation of Multivariate t Copulas with Heuristic Optimization

Authors: Jin Zhang, Wing Lon Ng

Abstract:

In recent years, copulas have become very popular in financial research and actuarial science as they are more flexible in modelling the co-movements and relationships of risk factors as compared to the conventional linear correlation coefficient by Pearson. However, a precise estimation of the copula parameters is vital in order to correctly capture the (possibly nonlinear) dependence structure and joint tail events. In this study, we employ two optimization heuristics, namely Differential Evolution and Threshold Accepting to tackle the parameter estimation of multivariate t distribution models in the EML approach. Since the evolutionary optimizer does not rely on gradient search, the EML approach can be applied to estimation of more complicated copula models such as high-dimensional copulas. Our experimental study shows that the proposed method provides more robust and more accurate estimates as compared to the IFM approach.

Keywords: Copula Models, Student t Copula, Parameter Inference, Differential Evolution, Threshold Accepting.

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3916 Scheduling a Flexible Flow Shops Problem using DEA

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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3915 An Intelligent Optimization Model for Multi-objective Order Allocation Planning

Authors: W. K. Wong, Z. X. Guo, P.Y. Mok

Abstract:

This paper presents a multi-objective order allocation planning problem with the consideration of various real-world production features. A novel hybrid intelligent optimization model, integrating a multi-objective memetic optimization process, a Monte Carlo simulation technique and a heuristic pruning technique, is proposed to handle this problem. Experiments based on industrial data are conducted to validate the proposed model. Results show that (1) the proposed model can effectively solve the investigated problem by providing effective production decision-making solutions, which outperformsan NSGA-II-based optimization process and an industrial method.

Keywords: Multi-objective order allocation planning, Pareto optimization, Memetic algorithm, Mento Carlo simulation

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