Search results for: real-time optimization
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1883

Search results for: real-time optimization

1883 An Integrated Framework for the Realtime Investigation of State Space Exploration

Authors: Jörg Lassig, Stefanie Thiem

Abstract:

The objective of this paper is the introduction to a unified optimization framework for research and education. The OPTILIB framework implements different general purpose algorithms for combinatorial optimization and minimum search on standard continuous test functions. The preferences of this library are the straightforward integration of new optimization algorithms and problems as well as the visualization of the optimization process of different methods exploring the search space exclusively or for the real time visualization of different methods in parallel. Further the usage of several implemented methods is presented on the basis of two use cases, where the focus is especially on the algorithm visualization. First it is demonstrated how different methods can be compared conveniently using OPTILIB on the example of different iterative improvement schemes for the TRAVELING SALESMAN PROBLEM. A second study emphasizes how the framework can be used to find global minima in the continuous domain.

Keywords: Global Optimization Heuristics, Particle Swarm Optimization, Ensemble Based Threshold Accepting, Ruin and Recreate

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1882 Modeling and Analysis of Adaptive Buffer Sharing Scheme for Consecutive Packet Loss Reduction in Broadband Networks

Authors: Sakshi Kausha, R.K Sharma

Abstract:

High speed networks provide realtime variable bit rate service with diversified traffic flow characteristics and quality requirements. The variable bit rate traffic has stringent delay and packet loss requirements. The burstiness of the correlated traffic makes dynamic buffer management highly desirable to satisfy the Quality of Service (QoS) requirements. This paper presents an algorithm for optimization of adaptive buffer allocation scheme for traffic based on loss of consecutive packets in data-stream and buffer occupancy level. Buffer is designed to allow the input traffic to be partitioned into different priority classes and based on the input traffic behavior it controls the threshold dynamically. This algorithm allows input packets to enter into buffer if its occupancy level is less than the threshold value for priority of that packet. The threshold is dynamically varied in runtime based on packet loss behavior. The simulation is run for two priority classes of the input traffic – realtime and non-realtime classes. The simulation results show that Adaptive Partial Buffer Sharing (ADPBS) has better performance than Static Partial Buffer Sharing (SPBS) and First In First Out (FIFO) queue under the same traffic conditions.

Keywords: Buffer Management, Consecutive packet loss, Quality-of-Service, Priority based packet discarding, partial buffersharing.

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1881 Real-Time Visualization Using GPU-Accelerated Filtering of LiDAR Data

Authors: Sašo Pečnik, Borut Žalik

Abstract:

This paper presents a real-time visualization technique and filtering of classified LiDAR point clouds. The visualization is capable of displaying filtered information organized in layers by the classification attribute saved within LiDAR datasets. We explain the used data structure and data management, which enables real-time presentation of layered LiDAR data. Real-time visualization is achieved with LOD optimization based on the distance from the observer without loss of quality. The filtering process is done in two steps and is entirely executed on the GPU and implemented using programmable shaders.

Keywords: Filtering, graphics, level-of-details, LiDAR, realtime visualization.

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1880 A Short Reflection on the Strengths and Weaknesses of Simulation Optimization

Authors: P. Vazan, P. Tanuska

Abstract:

The paper provides the basic overview of simulation optimization. The procedure of its practical using is demonstrated on the real example in simulator Witness. The simulation optimization is presented as a good tool for solving many problems in real praxis especially in production systems. The authors also characterize their own experiences and they mention the strengths and weakness of simulation optimization.

Keywords: discrete event simulation, simulation optimization, Witness

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1879 System Identification with General Dynamic Neural Networks and Network Pruning

Authors: Christian Endisch, Christoph Hackl, Dierk Schröder

Abstract:

This paper presents an exact pruning algorithm with adaptive pruning interval for general dynamic neural networks (GDNN). GDNNs are artificial neural networks with internal dynamics. All layers have feedback connections with time delays to the same and to all other layers. The structure of the plant is unknown, so the identification process is started with a larger network architecture than necessary. During parameter optimization with the Levenberg- Marquardt (LM) algorithm irrelevant weights of the dynamic neural network are deleted in order to find a model for the plant as simple as possible. The weights to be pruned are found by direct evaluation of the training data within a sliding time window. The influence of pruning on the identification system depends on the network architecture at pruning time and the selected weight to be deleted. As the architecture of the model is changed drastically during the identification and pruning process, it is suggested to adapt the pruning interval online. Two system identification examples show the architecture selection ability of the proposed pruning approach.

Keywords: System identification, dynamic neural network, recurrentneural network, GDNN, optimization, Levenberg Marquardt, realtime recurrent learning, network pruning, quasi-online learning.

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1878 Evaluation of Energy-Aware QoS Routing Protocol for Ad Hoc Wireless Sensor Networks

Authors: M.K.Jeya Kumar

Abstract:

Many advanced Routing protocols for wireless sensor networks have been implemented for the effective routing of data. Energy awareness is an essential design issue and almost all of these routing protocols are considered as energy efficient and its ultimate objective is to maximize the whole network lifetime. However, the introductions of video and imaging sensors have posed additional challenges. Transmission of video and imaging data requires both energy and QoS aware routing in order to ensure efficient usage of the sensors and effective access to the gathered measurements. In this paper, the performance of the energy-aware QoS routing Protocol are analyzed in different performance metrics like average lifetime of a node, average delay per packet and network throughput. The parameters considered in this study are end-to-end delay, real time data generation/capture rates, packet drop probability and buffer size. The network throughput for realtime and non-realtime data was also has been analyzed. The simulation has been done in NS2 simulation environment and the simulation results were analyzed with respect to different metrics.

Keywords: Cluster nodes, end-to-end delay, QoS routing, routing protocols, sensor networks, least-cost-path.

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1877 Particle Swarm Optimization with Reduction for Global Optimization Problems

Authors: Michiharu Maeda, Shinya Tsuda

Abstract:

This paper presents an algorithm of particle swarm optimization with reduction for global optimization problems. Particle swarm optimization is an algorithm which refers to the collective motion such as birds or fishes, and a multi-point search algorithm which finds a best solution using multiple particles. Particle swarm optimization is so flexible that it can adapt to a number of optimization problems. When an objective function has a lot of local minimums complicatedly, the particle may fall into a local minimum. For avoiding the local minimum, a number of particles are initially prepared and their positions are updated by particle swarm optimization. Particles sequentially reduce to reach a predetermined number of them grounded in evaluation value and particle swarm optimization continues until the termination condition is met. In order to show the effectiveness of the proposed algorithm, we examine the minimum by using test functions compared to existing algorithms. Furthermore the influence of best value on the initial number of particles for our algorithm is discussed.

Keywords: Particle swarm optimization, Global optimization, Metaheuristics, Reduction.

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1876 Simulated Annealing Application for Structural Optimization

Authors: Farhad Kolahan, M. Hossein Abolbashari, Samaeddin Mohitzadeh

Abstract:

Several methods are available for weight and shape optimization of structures, among which Evolutionary Structural Optimization (ESO) is one of the most widely used methods. In ESO, however, the optimization criterion is completely case-dependent. Moreover, only the improving solutions are accepted during the search. In this paper a Simulated Annealing (SA) algorithm is used for structural optimization problem. This algorithm differs from other random search methods by accepting non-improving solutions. The implementation of SA algorithm is done through reducing the number of finite element analyses (function evaluations). Computational results show that SA can efficiently and effectively solve such optimization problems within short search time.

Keywords: Simulated annealing, Structural optimization, Compliance, C.V. product.

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1875 Reliability-Based Topology Optimization Based on Evolutionary Structural Optimization

Authors: Sang-Rak Kim, Jea-Yong Park, Won-Goo Lee, Jin-Shik Yu, Seog-Young Han

Abstract:

This paper presents a Reliability-Based Topology Optimization (RBTO) based on Evolutionary Structural Optimization (ESO). An actual design involves uncertain conditions such as material property, operational load and dimensional variation. Deterministic Topology Optimization (DTO) is obtained without considering of the uncertainties related to the uncertainty parameters. However, RBTO involves evaluation of probabilistic constraints, which can be done in two different ways, the reliability index approach (RIA) and the performance measure approach (PMA). Limit state function is approximated using Monte Carlo Simulation and Central Composite Design for reliability analysis. ESO, one of the topology optimization techniques, is adopted for topology optimization. Numerical examples are presented to compare the DTO with RBTO.

Keywords: Evolutionary Structural Optimization, PerformanceMeasure Approach, Reliability-Based Topology Optimization, Reliability Index Approach.

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1874 A Mean–Variance–Skewness Portfolio Optimization Model

Authors: Kostas Metaxiotis

Abstract:

Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: Evolutionary algorithms, portfolio optimization, skewness, stock selection.

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1873 Non-Stationary Stochastic Optimization of an Oscillating Water Column

Authors: María L. Jalón, Feargal Brennan

Abstract:

A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: Non-stationary stochastic optimization, oscillating water column, temporal variability, wave energy.

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1872 Contribution to the Query Optimization in the Object-Oriented Databases

Authors: Minyar Sassi, Amel Grissa-Touzi

Abstract:

Appeared toward 1986, the object-oriented databases management systems had not known successes knew five years after their birth. One of the major difficulties is the query optimization. We propose in this paper a new approach that permits to enrich techniques of query optimization existing in the object-oriented databases. Seen success that knew the query optimization in the relational model, our approach inspires itself of these optimization techniques and enriched it so that they can support the new concepts introduced by the object databases.

Keywords: Query, query optimization, relational databases, object-oriented databases.

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1871 Evaluating and Selecting Optimization Software Packages: A Framework for Business Applications

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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1870 Two-Stage Approach for Solving the Multi-Objective Optimization Problem on Combinatorial Configurations

Authors: Liudmyla Koliechkina, Olena Dvirna

Abstract:

The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: Discrete set, linear combinatorial optimization, multi-objective optimization, multipermutation, Pareto solutions, partial permutation set, permutation, structural graph.

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1869 Application of Soft Computing Methods for Economic Dispatch in Power Systems

Authors: Jagabondhu Hazra, Avinash Sinha

Abstract:

Economic dispatch problem is an optimization problem where objective function is highly non linear, non-convex, non-differentiable and may have multiple local minima. Therefore, classical optimization methods may not converge or get trapped to any local minima. This paper presents a comparative study of four different evolutionary algorithms i.e. genetic algorithm, bacteria foraging optimization, ant colony optimization and particle swarm optimization for solving the economic dispatch problem. All the methods are tested on IEEE 30 bus test system. Simulation results are presented to show the comparative performance of these methods.

Keywords: Ant colony optimization, bacteria foraging optimization, economic dispatch, evolutionary algorithm, genetic algorithm, particle swarm optimization.

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1868 Model of Optimal Centroids Approach for Multivariate Data Classification

Authors: Pham Van Nha, Le Cam Binh

Abstract:

Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: Analysis of optimization, artificial intelligence-based optimization, optimization for learning and data analysis, global optimization.

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1867 Dynamic Mesh Based Airfoil Design Optimization

Authors: Zhu Xiong-feng, Hou Zhong-xi, Guo Zheng, Liu Zhao-Wei

Abstract:

A method of dynamic mesh based airfoil optimization is proposed according to the drawbacks of surrogate model based airfoil optimization. Programs are designed to achieve the dynamic mesh. Boundary condition is add by integrating commercial software Pointwise, meanwhile the CFD calculation is carried out by commercial software Fluent. The data exchange and communication between the software and programs referred above have been accomplished, and the whole optimization process is performed in iSIGHT platform. A simplified airfoil optimization study case is brought out to show that aerodynamic performances of airfoil have been significantly improved, even save massive repeat operations and increase the robustness and credibility of the optimization result. The case above proclaims that dynamic mesh based airfoil optimization is an effective and high efficient method.

Keywords: unmanned air vehicles, dynamic mesh, airfoil optimization, CFD, genetic algorithm

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1866 Query Optimization Techniques for XML Databases

Authors: Su Cheng Haw, G. S. V. Radha Krishna Rao

Abstract:

Over the past few years, XML (eXtensible Mark-up Language) has emerged as the standard for information representation and data exchange over the Internet. This paper provides a kick-start for new researches venturing in XML databases field. We survey the storage representation for XML document, review the XML query processing and optimization techniques with respect to the particular storage instance. Various optimization technologies have been developed to solve the query retrieval and updating problems. Towards the later year, most researchers proposed hybrid optimization techniques. Hybrid system opens the possibility of covering each technology-s weakness by its strengths. This paper reviews the advantages and limitations of optimization techniques.

Keywords: indexing, labeling scheme, query optimization, XML storage.

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1865 IBFO_PSO: Evaluating the Performance of Bio-Inspired Integrated Bacterial Foraging Optimization Algorithm and Particle Swarm Optimization Algorithm in MANET Routing

Authors: K. Geetha, P. Thangaraj, C. Rasi Priya, C. Rajan, S. Geetha

Abstract:

This paper presents the performance of Integrated Bacterial Foraging Optimization and Particle Swarm Optimization (IBFO_PSO) technique in MANET routing. The BFO is a bio-inspired algorithm, which simulates the foraging behavior of bacteria. It is effectively applied in improving the routing performance in MANET. In results, it is proved that the PSO integrated with BFO reduces routing delay, energy consumption and communication overhead.

Keywords: Ant Colony Optimization, Bacterial Foraging Optimization, Hybrid Routing Intelligent Algorithm, Naturally inspired algorithms, Particle Swarm Optimization.

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1864 Bandwidth Estimation Algorithms for the Dynamic Adaptation of Voice Codec

Authors: Davide Pierattoni, Ivan Macor, Pier Luca Montessoro

Abstract:

In the recent years multimedia traffic and in particular VoIP services are growing dramatically. We present a new algorithm to control the resource utilization and to optimize the voice codec selection during SIP call setup on behalf of the traffic condition estimated on the network path. The most suitable methodologies and the tools that perform realtime evaluation of the available bandwidth on a network path have been integrated with our proposed algorithm: this selects the best codec for a VoIP call in function of the instantaneous available bandwidth on the path. The algorithm does not require any explicit feedback from the network, and this makes it easily deployable over the Internet. We have also performed intensive tests on real network scenarios with a software prototype, verifying the algorithm efficiency with different network topologies and traffic patterns between two SIP PBXs. The promising results obtained during the experimental validation of the algorithm are now the basis for the extension towards a larger set of multimedia services and the integration of our methodology with existing PBX appliances.

Keywords: Integrated voice-data communication, computernetwork performance, resource optimization.

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1863 A Novel Design Approach for Mechatronic Systems Based On Multidisciplinary Design Optimization

Authors: Didier Casner, Jean Renaud, Remy Houssin, Dominique Knittel

Abstract:

In this paper, a novel approach for the multidisciplinary design optimization (MDO) of complex mechatronic systems. This approach, which is a part of a global project aiming to include the MDO aspect inside an innovative design process. As a first step, the paper considers the MDO as a redesign approach which is limited to the parametric optimization. After defining and introducing the different keywords, the proposed method which is based on the V-Model which is commonly used in mechatronics.

Keywords: mechatronics, Multidisciplinary Design Optimization (MDO), multiobjective optimization, engineering design.

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1862 An Optimization of Orbital Transfer for Spacecrafts with Finite-thrust Based on Legendre Pseudospectral Method

Authors: Yanan Yang, Zhigang Wang, Xiang Chen

Abstract:

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System-s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transform the optimal control problem into a constrained parameter optimization problem. The developed novel optimization algorithm can be used to solve similar optimization problems of spacecraft finite-thrust orbital transfer. The results of a numerical simulation verified the validity of the proposed optimization method. The simulation results reveal that pseudospectral optimization method is a promising method for real-time trajectory optimization and provides good accuracy and fast convergence.

Keywords: Finite-thrust, Orbital transfer, Legendre pseudospectral method

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1861 Transmission Lines Loading Enhancement Using ADPSO Approach

Authors: M. Mahdavi, H. Monsef, A. Bagheri

Abstract:

Discrete particle swarm optimization (DPSO) is a powerful stochastic evolutionary algorithm that is used to solve the large-scale, discrete and nonlinear optimization problems. However, it has been observed that standard DPSO algorithm has premature convergence when solving a complex optimization problem like transmission expansion planning (TEP). To resolve this problem an advanced discrete particle swarm optimization (ADPSO) is proposed in this paper. The simulation result shows that optimization of lines loading in transmission expansion planning with ADPSO is better than DPSO from precision view point.

Keywords: ADPSO, TEP problem, Lines loading optimization.

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1860 Mathematical Programming Models for Portfolio Optimization Problem: A Review

Authors: M. Mokhtar, A. Shuib, D. Mohamad

Abstract:

Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: Portfolio optimization, Mathematical programming, Multi-objective programming, Solution approaches.

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1859 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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1858 The Whale Optimization Algorithm and Its Implementation in MATLAB

Authors: S. Adhirai, R. P. Mahapatra, Paramjit Singh

Abstract:

Optimization is an important tool in making decisions and in analysing physical systems. In mathematical terms, an optimization problem is the problem of finding the best solution from among the set of all feasible solutions. The paper discusses the Whale Optimization Algorithm (WOA), and its applications in different fields. The algorithm is tested using MATLAB because of its unique and powerful features. The benchmark functions used in WOA algorithm are grouped as: unimodal (F1-F7), multimodal (F8-F13), and fixed-dimension multimodal (F14-F23). Out of these benchmark functions, we show the experimental results for F7, F11, and F19 for different number of iterations. The search space and objective space for the selected function are drawn, and finally, the best solution as well as the best optimal value of the objective function found by WOA is presented. The algorithmic results demonstrate that the WOA performs better than the state-of-the-art meta-heuristic and conventional algorithms.

Keywords: Optimization, optimal value, objective function, optimization problems, meta-heuristic optimization algorithms, Whale Optimization Algorithm, Implementation, MATLAB.

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1857 Topology Optimization of Aircraft Fuselage Structure

Authors: Muniyasamy Kalanchiam, Baskar Mannai

Abstract:

Topology Optimization is a defined as the method of determining optimal distribution of material for the assumed design space with functionality, loads and boundary conditions [1]. Topology optimization can be used to optimize shape for the purposes of weight reduction, minimizing material requirements or selecting cost effective materials [2]. Topology optimization has been implemented through the use of finite element methods for the analysis, and optimization techniques based on the method of moving asymptotes, genetic algorithms, optimality criteria method, level sets and topological derivatives. Case study of Typical “Fuselage design" is considered for this paper to explain the benefits of Topology Optimization in the design cycle. A cylindrical shell is assumed as the design space and aerospace standard pay loads were applied on the fuselage with wing attachments as constraints. Then topological optimization is done using Finite Element (FE) based software. This optimization results in the structural concept design which satisfies all the design constraints using minimum material.

Keywords: Fuselage, Topology optimization, payloads, designoptimization, Finite Element Analysis.

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1856 Big Bang – Big Crunch Optimization Method in Optimum Design of Complex Composite Laminates

Authors: Pavel Y. Tabakov

Abstract:

An accurate optimal design of laminated composite structures may present considerable difficulties due to the complexity and multi-modality of the functional design space. The Big Bang – Big Crunch (BB-BC) optimization method is a relatively new technique and has already proved to be a valuable tool for structural optimization. In the present study the exceptional efficiency of the method is demonstrated by an example of the lay-up optimization of multilayered anisotropic cylinders based on a three-dimensional elasticity solution. It is shown that, due to its simplicity and speed, the BB-BC is much more efficient for this class of problems when compared to the genetic algorithms.

Keywords: Big Bang – Big Crunch method, optimization, composite laminates, pressure vessel.

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1855 Using Pattern Search Methods for Minimizing Clustering Problems

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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1854 Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems

Authors: Akbar H. Borzabadi, Omid S. Fard

Abstract:

In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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