Search results for: optimization strategy.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2842

Search results for: optimization strategy.

2752 An Enhanced Particle Swarm Optimization Algorithm for Multiobjective Problems

Authors: Houda Abadlia, Nadia Smairi, Khaled Ghedira

Abstract:

Multiobjective Particle Swarm Optimization (MOPSO) has shown an effective performance for solving test functions and real-world optimization problems. However, this method has a premature convergence problem, which may lead to lack of diversity. In order to improve its performance, this paper presents a hybrid approach which embedded the MOPSO into the island model and integrated a local search technique, Variable Neighborhood Search, to enhance the diversity into the swarm. Experiments on two series of test functions have shown the effectiveness of the proposed approach. A comparison with other evolutionary algorithms shows that the proposed approach presented a good performance in solving multiobjective optimization problems.

Keywords: Particle swarm optimization, migration, variable neighborhood search, multiobjective optimization.

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2751 Ride Control of Passenger Cars with Semi-active Suspension System Using a Linear Quadratic Regulator and Hybrid Optimization Algorithm

Authors: Ali Fellah Jahromi, Wen Fang Xie, Rama B. Bhat

Abstract:

A semi-active control strategy for suspension systems of passenger cars is presented employing Magnetorheological (MR) dampers. The vehicle is modeled with seven DOFs including the, roll pitch and bounce of car body, and the vertical motion of the four tires. In order to design an optimal controller based on the actuator constraints, a Linear-Quadratic Regulator (LQR) is designed. The design procedure of the LQR consists of selecting two weighting matrices to minimize the energy of the control system. This paper presents a hybrid optimization procedure which is a combination of gradient-based and evolutionary algorithms to choose the weighting matrices with regards to the actuator constraint. The optimization algorithm is defined based on maximum comfort and actuator constraints. It is noted that utilizing the present control algorithm may significantly reduce the vibration response of the passenger car, thus, providing a comfortable ride.

Keywords: Full car model, Linear Quadratic Regulator, Sequential Quadratic Programming, Genetic Algorithm

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2750 Reformulations of Big Bang-Big Crunch Algorithm for Discrete Structural Design Optimization

Authors: O. Hasançebi, S. Kazemzadeh Azad

Abstract:

In the present study the efficiency of Big Bang-Big Crunch (BB-BC) algorithm is investigated in discrete structural design optimization. It is shown that a standard version of the BB-BC algorithm is sometimes unable to produce reasonable solutions to problems from discrete structural design optimization. Two reformulations of the algorithm, which are referred to as modified BB-BC (MBB-BC) and exponential BB-BC (EBB-BC), are introduced to enhance the capability of the standard algorithm in locating good solutions for steel truss and frame type structures, respectively. The performances of the proposed algorithms are experimented and compared to its standard version as well as some other algorithms over several practical design examples. In these examples, steel structures are sized for minimum weight subject to stress, stability and displacement limitations according to the provisions of AISC-ASD.

Keywords: Structural optimization, discrete optimization, metaheuristics, big bang-big crunch (BB-BC) algorithm, design optimization of steel trusses and frames.

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2749 Topology Optimization of Structures with Web-Openings

Authors: D. K. Lee, S. M. Shin, J. H. Lee

Abstract:

Topology optimization technique utilizes constant element densities as design parameters. Finally, optimal distribution contours of the material densities between voids (0) and solids (1) in design domain represent the determination of topology. It means that regions with element density values become occupied by solids in design domain, while there are only void phases in regions where no density values exist. Therefore the void regions of topology optimization results provide design information to decide appropriate depositions of web-opening in structure. Contrary to the basic objective of the topology optimization technique which is to obtain optimal topology of structures, this present study proposes a new idea that topology optimization results can be also utilized for decision of proper web-opening’s position. Numerical examples of linear elastostatic structures demonstrate efficiency of methodological design processes using topology optimization in order to determinate the proper deposition of web-openings.

Keywords: Topology optimization, web-opening, structure, element density, material.

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2748 Improved Ant Colony Optimization for Solving Reliability Redundancy Allocation Problems

Authors: Phakhapong Thanitakul, Worawat Sa-ngiamvibool, Apinan Aurasopon, Saravuth Pothiya

Abstract:

This paper presents an improved ant colony optimization (IACO) for solving the reliability redundancy allocation problem (RAP) in order to maximize system reliability. To improve the performance of ACO algorithm, two additional techniques, i.e. neighborhood search, and re-initialization process are presented. To show its efficiency and effectiveness, the proposed IACO is applied to solve three RAPs. Additionally, the results of the proposed IACO are compared with those of the conventional heuristic approaches i.e. genetic algorithm (GA), particle swarm optimization (PSO) and ant colony optimization (ACO). The experimental results show that the proposed IACO approach is comparatively capable of obtaining higher quality solution and faster computational time.

Keywords: Ant colony optimization, Heuristic algorithm, Mixed-integer nonlinear programming, Redundancy allocation problem, Reliability optimization.

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2747 Hybrid Optimization of Emission and Economic Dispatch by the Sigmoid Decreasing Inertia Weight Particle Swarm Optimization

Authors: Joko Pitono, Adi Soeprijanto, Takashi Hiyama

Abstract:

This paper present an efficient and reliable technique of optimization which combined fuel cost economic optimization and emission dispatch using the Sigmoid Decreasing Inertia Weight Particle Swarm Optimization algorithm (PSO) to reduce the cost of fuel and pollutants resulting from fuel combustion by keeping the output of generators, bus voltages, shunt capacitors and transformer tap settings within the security boundary. The performance of the proposed algorithm has been demonstrated on IEEE 30-bus system with six generating units. The results clearly show that the proposed algorithm gives better and faster speed convergence then linearly decreasing inertia weight.

Keywords: Optimal Power Flow, Combined Economic Emission Dispatch, Sigmoid decreasing Inertia Weight, Particle Swarm Optimization.

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2746 Application of Hybrid Genetic Algorithm Based on Simulated Annealing in Function Optimization

Authors: Panpan Xu, Shulin Sui, Zongjie Du

Abstract:

Genetic algorithm is widely used in optimization problems for its excellent global search capabilities and highly parallel processing capabilities; but, it converges prematurely and has a poor local optimization capability in actual operation. Simulated annealing algorithm can avoid the search process falling into local optimum. A hybrid genetic algorithm based on simulated annealing is designed by combining the advantages of genetic algorithm and simulated annealing algorithm. The numerical experiment represents the hybrid genetic algorithm can be applied to solve the function optimization problems efficiently.

Keywords: Genetic algorithm, Simulated annealing, Hybrid genetic algorithm, Function optimization.

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2745 A New Tool for Global Optimization Problems- Cuttlefish Algorithm

Authors: Adel Sabry Eesa, Adnan Mohsin Abdulazeez Brifcani, Zeynep Orman

Abstract:

This paper presents a new meta-heuristic bio-inspired optimization algorithm which is called Cuttlefish Algorithm (CFA). The algorithm mimics the mechanism of color changing behavior of the cuttlefish to solve numerical global optimization problems. The colors and patterns of the cuttlefish are produced by reflected light from three different layers of cells. The proposed algorithm considers mainly two processes: reflection and visibility. Reflection process simulates light reflection mechanism used by these layers, while visibility process simulates visibility of matching patterns of the cuttlefish. To show the effectiveness of the algorithm, it is tested with some other popular bio-inspired optimization algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Bees Algorithm (BA) that have been previously proposed in the literature. Simulations and obtained results indicate that the proposed CFA is superior when compared with these algorithms.

Keywords: Cuttlefish Algorithm, bio-inspired algorithms, optimization.

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2744 A Multi-objective Fuzzy Optimization Method of Resource Input Based on Genetic Algorithm

Authors: Tao Zhao, Xin Wang

Abstract:

With the increasing complexity of engineering problems, the traditional, single-objective and deterministic optimization method can not meet people-s requirements. A multi-objective fuzzy optimization model of resource input is built for M chlor-alkali chemical eco-industrial park in this paper. First, the model is changed into the form that can be solved by genetic algorithm using fuzzy theory. And then, a fitness function is constructed for genetic algorithm. Finally, a numerical example is presented to show that the method compared with traditional single-objective optimization method is more practical and efficient.

Keywords: Fitness function, genetic algorithm, multi-objectivefuzzy optimization, satisfaction degree membership function.

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2743 Particle Swarm Optimization with Interval-valued Genotypes and Its Application to Neuroevolution

Authors: Hidehiko Okada

Abstract:

The author proposes an extension of particle swarm optimization (PSO) for solving interval-valued optimization problems and applies the extended PSO to evolutionary training of neural networks (NNs) with interval weights. In the proposed PSO, values in the genotypes are not real numbers but intervals. Experimental results show that interval-valued NNs trained by the proposed method could well approximate hidden target functions despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithms, swarm intelligence, particle swarm optimization, neural network, interval arithmetic.

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2742 Optimization of Quantization in Higher Order Modulations for LDPC-Coded Systems

Authors: M.Sushanth Babu, P.Krishna, U.Venu, M.Ranjith

Abstract:

In this paper, we evaluate the choice of suitable quantization characteristics for both the decoder messages and the received samples in Low Density Parity Check (LDPC) coded systems using M-QAM (Quadrature Amplitude Modulation) schemes. The analysis involves the demapper block that provides initial likelihood values for the decoder, by relating its quantization strategy of the decoder. A mapping strategy refers to the grouping of bits within a codeword, where each m-bit group is used to select a 2m-ary signal in accordance with the signal labels. Further we evaluate the system with mapping strategies like Consecutive-Bit (CB) and Bit-Reliability (BR). A new demapper version, based on approximate expressions, is also presented to yield a low complexity hardware implementation.

Keywords: Low Density parity Check, Mapping, Demapping, Quantization, Quadrature Amplitude Modulation

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2741 Bioprocess Optimization Based On Relevance Vector Regression Models and Evolutionary Programming Technique

Authors: R. Simutis, V. Galvanauskas, D. Levisauskas, J. Repsyte

Abstract:

This paper proposes a bioprocess optimization procedure based on Relevance Vector Regression models and evolutionary programming technique. Relevance Vector Regression scheme allows developing a compact and stable data-based process model avoiding time-consuming modeling expenses. The model building and process optimization procedure could be done in a half-automated way and repeated after every new cultivation run. The proposed technique was tested in a simulated mammalian cell cultivation process. The obtained results are promising and could be attractive for optimization of industrial bioprocesses.

Keywords: Bioprocess optimization, Evolutionary programming, Relevance Vector Regression.

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2740 Migration Aspect in the Realization of the Chinese “Going Out Policy” Strategy

Authors: Nazira B. Boldurukova

Abstract:

The article examines the potential of the Chinese diaspora abroad. Investigate the influence of the highest in the People's Republic of foreign economic strategy of "Going to the outside" on the investment activity of Chinese enterprises abroad, the export of labor.

Keywords: China, migrants, reform, economic strategy, migration policy, huaqiao.

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2739 Personalized Email Marketing Strategy: A Reinforcement Learning Approach

Authors: Lei Zhang, Tingting Xu, Jun He, Zhenyu Yan, Roger Brooks

Abstract:

Email marketing is one of the most important segments of online marketing. Email content is vital to customers. Different customers may have different familiarity with a product, so a successful marketing strategy must personalize email content based on individual customers’ product affinity. In this study, we build our personalized email marketing strategy with three types of emails: nurture, promotion, and conversion. Each type of emails has a different influence on customers. We investigate this difference by analyzing customers’ open rates, click rates and opt-out rates. Feature importance from response models is also analyzed. The goal of the marketing strategy is to improve the click rate on conversion-type emails. To build the personalized strategy, we formulate the problem as a reinforcement learning problem and adopt a Q-learning algorithm with variations. The simulation results show that our model-based strategy outperforms the current marketer’s strategy.

Keywords: Email marketing, email content, reinforcement learning, machine learning, Q-learning.

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2738 Nature Inspired Metaheuristic Algorithms for Multilevel Thresholding Image Segmentation - A Survey

Authors: C. Deepika, J. Nithya

Abstract:

Segmentation is one of the essential tasks in image processing. Thresholding is one of the simplest techniques for performing image segmentation. Multilevel thresholding is a simple and effective technique. The primary objective of bi-level or multilevel thresholding for image segmentation is to determine a best thresholding value. To achieve multilevel thresholding various techniques has been proposed. A study of some nature inspired metaheuristic algorithms for multilevel thresholding for image segmentation is conducted. Here, we study about Particle swarm optimization (PSO) algorithm, artificial bee colony optimization (ABC), Ant colony optimization (ACO) algorithm and Cuckoo search (CS) algorithm.

Keywords: Ant colony optimization, Artificial bee colony optimization, Cuckoo search algorithm, Image segmentation, Multilevel thresholding, Particle swarm optimization.

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2737 Collaborative Business Strategy of PTT Energy Trading Co. Ltd. for LNG form of Coal Bed Methane in B2B Transaction to Japanese Shareholder, Especially to Electricity and Power Supply Companies

Authors: Shabrina Pritta Radyanti, Harimukti Wandebori

Abstract:

A research study was conducted with an objective to propose a collaborative business strategy of a oil and gas trading company, representing PPT Energy Trading Co., Ltd., with its shareholder, especially electricity and power supply companies for LNG Form of Coal Bed Methane in B2B Transaction. Collaborative business strategy is a strategy to collaborate with other organizations due to have future benefits in both parties, or achieve the business objective through the collaboration of business, its strategy and partners. A structured interview was established to collect the required primary data from the company. Not only interview, but also company’s business plan and annual report were collected and analyzed for the company’s current condition. As the result, this research shows a recommendation to propose a new collaborative strategy with limiting its target market, diversifying product, conducting new business model, and considering other stakeholders.

Keywords: collaborative business strategy, trading company, LNG, coal bed methane

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2736 Sustainability Strategy and Firm Performance in Residential Trade and Industry: A Conceptual Analysis

Authors: Martin Macion

Abstract:

The request for a sustainable development challenges both managers and consumers to rethink habitual practices and activities. While consumers are challenged to develop sustainable consumption patterns, companies are asked to establish managerial systems and structures considering economical, ecological, and social issues. As this is in particular true for housing associations, this paper aims first, at providing an understanding of sustainability strategy in residential trade and industry (RTI) by identifying relevant facets of this construct and second, at conceptually analyzing the impact of sustainability strategy in RTI on operational efficiency and performance of municipal housing companies. The author develops a model of sustainability strategy in RTI and its effects and further, sheds light in priorities for future research.

Keywords: firm performance, sustainability strategy, residentialtrade and industry

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2735 Evaluation of a Surrogate Based Method for Global Optimization

Authors: David Lindström

Abstract:

We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cyclic parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: Expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon.

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2734 Comparative Study of Ant Colony and Genetic Algorithms for VLSI Circuit Partitioning

Authors: Sandeep Singh Gill, Rajeevan Chandel, Ashwani Chandel

Abstract:

This paper presents a comparative study of Ant Colony and Genetic Algorithms for VLSI circuit bi-partitioning. Ant colony optimization is an optimization method based on behaviour of social insects [27] whereas Genetic algorithm is an evolutionary optimization technique based on Darwinian Theory of natural evolution and its concept of survival of the fittest [19]. Both the methods are stochastic in nature and have been successfully applied to solve many Non Polynomial hard problems. Results obtained show that Genetic algorithms out perform Ant Colony optimization technique when tested on the VLSI circuit bi-partitioning problem.

Keywords: Partitioning, genetic algorithm, ant colony optimization, non-polynomial hard, netlist, mutation.

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2733 Optimized Weight Vector for QoS Aware Web Service Selection Algorithm Using Particle Swarm Optimization

Authors: N. Arulanand, P. M. Ananth

Abstract:

Quality of Service (QoS) attributes as part of the service description is an important factor for service attribute. It is not easy to exactly quantify the weight of each QoS conditions since human judgments based on their preference causes vagueness. As web services selection requires optimization, evolutionary computing based on heuristics to select an optimal solution is adopted. In this work, the evolutionary computing technique Particle Swarm Optimization (PSO) is used for selecting a suitable web services based on the user’s weightage of each QoS values by optimizing the QoS weight vector and thereby finding the best weight vectors for best services that is being selected. Finally the results are compared and analyzed using static inertia weight and deterministic inertia weight of PSO.

Keywords: QoS, Optimization, Particle Swarm Optimization (PSO), weight vector, web services, web service selection.

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2732 Linear Phase High Pass FIR Filter Design using Improved Particle Swarm Optimization

Authors: Sangeeta Mondal, Vasundhara, Rajib Kar, Durbadal Mandal, S. P. Ghoshal

Abstract:

This paper presents an optimal design of linear phase digital high pass finite impulse response (FIR) filter using Improved Particle Swarm Optimization (IPSO). In the design process, the filter length, pass band and stop band frequencies, feasible pass band and stop band ripple sizes are specified. FIR filter design is a multi-modal optimization problem. An iterative method is introduced to find the optimal solution of FIR filter design problem. Evolutionary algorithms like real code genetic algorithm (RGA), particle swarm optimization (PSO), improved particle swarm optimization (IPSO) have been used in this work for the design of linear phase high pass FIR filter. IPSO is an improved PSO that proposes a new definition for the velocity vector and swarm updating and hence the solution quality is improved. A comparison of simulation results reveals the optimization efficacy of the algorithm over the prevailing optimization techniques for the solution of the multimodal, nondifferentiable, highly non-linear, and constrained FIR filter design problems.

Keywords: FIR Filter, IPSO, GA, PSO, Parks and McClellan Algorithm, Evolutionary Optimization, High Pass Filter

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2731 Tools for Analysis and Optimization of Standalone Green Microgrids

Authors: William Anderson, Kyle Kobold, Oleg Yakimenko

Abstract:

Green microgrids using mostly renewable energy (RE) for generation, are complex systems with inherent nonlinear dynamics. Among a variety of different optimization tools there are only a few ones that adequately consider this complexity. This paper evaluates applicability of two somewhat similar optimization tools tailored for standalone RE microgrids and also assesses a machine learning tool for performance prediction that can enhance the reliability of any chosen optimization tool. It shows that one of these microgrid optimization tools has certain advantages over another and presents a detailed routine of preparing input data to simulate RE microgrid behavior. The paper also shows how neural-network-based predictive modeling can be used to validate and forecast solar power generation based on weather time series data, which improves the overall quality of standalone RE microgrid analysis.

Keywords: Microgrid, renewable energy, complex systems, optimization, predictive modeling, neural networks.

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2730 Thinned Elliptical Cylindrical Antenna Array Synthesis Using Particle Swarm Optimization

Authors: Rajesh Bera, Durbadal Mandal, Rajib Kar, Sakti P. Ghoshal

Abstract:

This paper describes optimal thinning of an Elliptical  Cylindrical Array (ECA) of uniformly excited isotropic antennas  which can generate directive beam with minimum relative Side Lobe  Level (SLL). The Particle Swarm Optimization (PSO) method, which  represents a new approach for optimization problems in  electromagnetic, is used in the optimization process. The PSO is used  to determine the optimal set of ‘ON-OFF’ elements that provides a  radiation pattern with maximum SLL reduction. Optimization is done  without prefixing the value of First Null Beam Width (FNBW). The  variation of SLL with element spacing of thinned array is also  reported. Simulation results show that the number of array elements  can be reduced by more than 50% of the total number of elements in  the array with a simultaneous reduction in SLL to less than -27dB.

 

Keywords: Thinned array, Particle Swarm Optimization, Elliptical Cylindrical Array, Side Lobe Label.

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2729 Cloud Monitoring and Performance Optimization Ensuring High Availability and Security

Authors: Inayat Ur Rehman, Georgia Sakellari

Abstract:

Cloud computing has evolved into a vital technology for businesses, offering scalability, flexibility, and cost-effectiveness. However, maintaining high availability and optimal performance in the cloud is crucial for reliable services. This paper explores the significance of cloud monitoring and performance optimization in sustaining the high availability of cloud-based systems. It discusses diverse monitoring tools, techniques, and best practices for continually assessing the health and performance of cloud resources. The paper also delves into performance optimization strategies, including resource allocation, load balancing, and auto-scaling, to ensure efficient resource utilization and responsiveness. Addressing potential challenges in cloud monitoring and optimization, the paper offers insights into data security and privacy considerations. Through this thorough analysis, the paper aims to underscore the importance of cloud monitoring and performance optimization for ensuring a seamless and highly available cloud computing environment.

Keywords: Cloud computing, cloud monitoring, performance optimization, high availability.

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2728 Consumers’ Responses to Non-Traditional Marketing Communication Strategies for Advertising Herbal Products

Authors: Chioma Ifeoma Agbasimelo, Stephen Afam Kenechukwu

Abstract:

The study examined consumers’ responses to non-traditional marketing communication strategies in advertising herbal products. The study identified the following non-traditional marketing communication strategies: (a) trado-instrumental marketing strategy, (b) trado-demonstrative marketing strategy, and (c) trado-iconographic marketing strategy. Anchored on the Black Box Theory, it adopted the survey design of three metropolises (Awka, Onitsha, and Nnewi) in Anambra State, Nigeria. Major findings indicated that among the identified strategies, the trado-instrumental marketing strategy is the most dominant strategy. Other strategies: (b) trado-demonstrative marketing strategy and (c) trado-iconographic marketing strategy, are sparingly used in semi-urban cities. It also found that consumers’ preferences and adoption of non-traditional marketing communication were minimal. Based on the findings, there is a need to create a unified system of integration of both traditional and non-traditional marketing communication strategies due to technology interfaces.

Keywords: Advertising, consumers’ responses, herbal products, non-traditional marketing communication strategies.

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2727 Optimizing the Design of Radial/Axial PMSM and SRM used for Powered Wheel-Chairs

Authors: D. Fodorean, D.C. Popa, F. Jurca, M. Ruba

Abstract:

the paper presents the optimization results for several electrical machines dedicated for powered electric wheel-chairs. The optimization, using the Hook-Jeeves algorithm, was employed based on a design approach which takes into consideration the road conditions. Also, through numerical simulations (based on finite element method), the analytical approach was validated. The optimization approach gave satisfactory results and the best suited variant was chosen for the motorization of the wheel-chair.

Keywords: electrical machines, numerical validation, optimization, electric wheel chair.

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2726 Genetic-Based Planning with Recursive Subgoals

Authors: Han Yu, Dan C. Marinescu, Annie S. Wu, Howard Jay Siegel

Abstract:

In this paper, we introduce an effective strategy for subgoal division and ordering based upon recursive subgoals and combine this strategy with a genetic-based planning approach. This strategy can be applied to domains with conjunctive goals. The main idea is to recursively decompose a goal into a set of serializable subgoals and to specify a strict ordering among the subgoals. Empirical results show that the recursive subgoal strategy reduces the size of the search space and improves the quality of solutions to planning problems.

Keywords: Planning, recursive subgoals, Sliding-tile puzzle, subgoal interaction, genetic algorithms.

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2725 Modeling of Dielectric Heating in Radio- Frequency Applicator Optimized for Uniform Temperature by Means of Genetic Algorithms

Authors: Camelia Petrescu, Lavinia Ferariu

Abstract:

The paper presents an optimization study based on genetic algorithms (GA-s) for a radio-frequency applicator used in heating dielectric band products. The weakly coupled electro-thermal problem is analyzed using 2D-FEM. The design variables in the optimization process are: the voltage of a supplementary “guard" electrode and six geometric parameters of the applicator. Two objective functions are used: temperature uniformity and total active power absorbed by the dielectric. Both mono-objective and multiobjective formulations are implemented in GA optimization.

Keywords: Dielectric heating, genetic algorithms, optimization, RF applicators.

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2724 The Synthetic T2 Quality Control Chart and its Multi-Objective Optimization

Authors: Francisco Aparisi, Marco A. de Luna

Abstract:

In some real applications of Statistical Process Control it is necessary to design a control chart to not detect small process shifts, but keeping a good performance to detect moderate and large shifts in the quality. In this work we develop a new quality control chart, the synthetic T2 control chart, that can be designed to cope with this objective. A multi-objective optimization is carried out employing Genetic Algorithms, finding the Pareto-optimal front of non-dominated solutions for this optimization problem.

Keywords: Multi-objective optimization, Quality Control, SPC, Synthetic T2 control chart.

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2723 Improvement of Gregory's formula using Particle Swarm Optimization

Authors: N. Khelil. L. Djerou , A. Zerarka, M. Batouche

Abstract:

Consider the Gregory integration (G) formula with end corrections where h Δ is the forward difference operator with step size h. In this study we prove that can be optimized by minimizing some of the coefficient k a in the remainder term by particle swarm optimization. Experimental tests prove that can be rendered a powerful formula for library use.

Keywords: Numerical integration, Gregory Formula, Particle Swarm optimization.

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