Search results for: grey wolf optimization algorithm

Authors: Cheng-Hong Yang, Yu-Huei Cheng, Hsueh-Wei Chang, Li-Yeh Chuang

Abstract:

Before performing polymerase chain reactions (PCR), a feasible primer set is required. Many primer design methods have been proposed for design a feasible primer set. However, the majority of these methods require a relatively long time to obtain an optimal solution since large quantities of template DNA need to be analyzed. Furthermore, the designed primer sets usually do not provide a specific PCR product. In recent years, evolutionary computation has been applied to PCR primer design and yielded promising results. In this paper, a particle swarm optimization (PSO) algorithm is proposed to solve primer design problems associated with providing a specific product for PCR experiments. A test set of the gene CYP1A1, associated with a heightened lung cancer risk was analyzed and the comparison of accuracy and running time with the genetic algorithm (GA) and memetic algorithm (MA) was performed. A comparison of results indicated that the proposed PSO method for primer design finds optimal or near-optimal primer sets and effective PCR products in a relatively short time.

Keywords: polymerase chain reaction (PCR), primer design, evolutionary computation, particle swarm optimization (PSO).

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Authors: M. Senthil Arumugam, M.V.C. Rao

Abstract:

This paper presents a novel two-phase hybrid optimization algorithm with hybrid genetic operators to solve the optimal control problem of a single stage hybrid manufacturing system. The proposed hybrid real coded genetic algorithm (HRCGA) is developed in such a way that a simple real coded GA acts as a base level search, which makes a quick decision to direct the search towards the optimal region, and a local search method is next employed to do fine tuning. The hybrid genetic operators involved in the proposed algorithm improve both the quality of the solution and convergence speed. The phase–1 uses conventional real coded genetic algorithm (RCGA), while optimisation by direct search and systematic reduction of the size of search region is employed in the phase – 2. A typical numerical example of an optimal control problem with the number of jobs varying from 10 to 50 is included to illustrate the efficacy of the proposed algorithm. Several statistical analyses are done to compare the validity of the proposed algorithm with the conventional RCGA and PSO techniques. Hypothesis t – test and analysis of variance (ANOVA) test are also carried out to validate the effectiveness of the proposed algorithm. The results clearly demonstrate that the proposed algorithm not only improves the quality but also is more efficient in converging to the optimal value faster. They can outperform the conventional real coded GA (RCGA) and the efficient particle swarm optimisation (PSO) algorithm in quality of the optimal solution and also in terms of convergence to the actual optimum value.

Keywords: Hybrid systems, optimal control, real coded genetic algorithm (RCGA), Particle swarm optimization (PSO), Hybrid real coded GA (HRCGA), and Hybrid genetic operators.

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Authors: M. R. Ghasemi, A. Ehsani

Abstract:

In this paper, the optimum weight and cost of a laminated composite plate is seeked, while it undergoes the heaviest load prior to a complete failure. Various failure criteria are defined for such structures in the literature. In this work, the Tsai-Hill theory is used as the failure criterion. The theory of analysis was based on the Classical Lamination Theory (CLT). A newly type of Genetic Algorithm (GA) as an optimization technique with a direct use of real variables was employed. Yet, since the optimization via GAs is a long process, and the major time is consumed through the analysis, Radial Basis Function Neural Networks (RBFNN) was employed in predicting the output from the analysis. Thus, the process of optimization will be carried out through a hybrid neuro-GA environment, and the procedure will be carried out until a predicted optimum solution is achieved.

Keywords: Composite Laminates, GA, Multi-objectiveOptimisation, Neural Networks, RBFNN.

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Authors: H. Shayeghi, M. Mahdavi, A. Kazemi

Abstract:

Transmission network expansion planning (TNEP) is a basic part of power system planning that determines where, when and how many new transmission lines should be added to the network. Up till now, various methods have been presented to solve the static transmission network expansion planning (STNEP) problem. But in all of these methods, transmission expansion planning considering network adequacy restriction has not been investigated. Thus, in this paper, STNEP problem is being studied considering network adequacy restriction using discrete particle swarm optimization (DPSO) algorithm. The goal of this paper is obtaining a configuration for network expansion with lowest expansion cost and a specific adequacy. The proposed idea has been tested on the Garvers network and compared with the decimal codification genetic algorithm (DCGA). The results show that the network will possess maximum efficiency economically. Also, it is shown that precision and convergence speed of the proposed DPSO based method for the solution of the STNEP problem is more than DCGA approach.

Keywords: DPSO algorithm, Adequacy restriction, STNEP.

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Authors: Alireza Keshmiri, Shahriar Bagheri, Nan Wu

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This research presents an analytical model for the development of an energy harvester with piezoelectric rings stacked at the boundary of the structure based on the Adomian decomposition method. The model is applied to geometrically non-uniform beams to derive the steady-state dynamic response of the structure subjected to base motion excitation and efficiently harvest the subsequent vibrational energy. The in-plane polarization of the piezoelectric rings is employed to enhance the electrical power output. A parametric study for the proposed energy harvester with various design parameters is done to prepare the dataset required for optimization. Finally, simulation-based optimization technique helps to find the optimum structural design with maximum efficiency. To solve the optimization problem, an artificial neural network is first trained to replace the simulation model, and then, a genetic algorithm is employed to find the optimized design variables. Higher geometrical non-uniformity and length of the beam lowers the structure natural frequency and generates a larger power output.

Keywords: Piezoelectricity, energy harvesting, simulation-based optimization, artificial neural network, genetic algorithm.

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Authors: Tahseen Al-Shaikhli, Halim Ceylan, Jonathan Weaver, Osman Nuri Çelik, Onur Gungor Sahin

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A concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. Furthermore, the objectives are to control the coordination problem which mainly depends on offset selection, and to estimate the uniform delay based on the offset choice at each signalized intersection. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show that the derived model minimizes the total uniform delay to almost half compared to conventional models; the mathematical objective function is robust; the algorithm convergence time is fast.

Keywords: Area traffic control, differential evolution, offset variable, sinusoidal periodic function, traffic flow, uniform delay.

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Authors: Saeed Sedighizadeh, Abbas Mansoori, Mohammad Reza Pirestani, Davoud Sedighizadeh

Abstract:

The usual method of river flow diversion involves construction of tunnels and cofferdams. Given the fact that the cost of diversion works could be as high as 10-20% of the total dam construction cost, due attention should be paid to optimum design of the diversion works. The cost of diversion works depends, on factors, such as: the tunnel dimensions and the intended tunneling support measures during and after excavation; quality and characterizes of the rock through which the tunnel should be excavated; the dimensions of the upstream (and downstream) cofferdams; and the magnitude of river flood the system is designed to divert. In this paper by use of the cost of unit prices for tunnel excavation, tunnel lining, tunnel support (rock bolt + shotcrete) and cofferdam fill the cost function was determined. The function is then minimized by the aid of PSO Algorithm (particle swarm optimization). It is found that the optimum diameter and the total diversion cost are directly related to the river flood discharge (Q). It has also shown that in addition to optimum diameter design discharge (Q), river length, tunnel length, is mainly a function of the ratios (not the absolute values) of the unit prices and does not depend on the overall price levels in the respective country. The results of optimization use in some of the case study lead us to significant changes in the cost.

Keywords: Diversion Tunnel, Optimization, PSO Algorithm

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Authors: C. Chitra, P. Subbaraj

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The shortest path routing problem is a multiobjective nonlinear optimization problem with constraints. This problem has been addressed by considering Quality of service parameters, delay and cost objectives separately or as a weighted sum of both objectives. Multiobjective evolutionary algorithms can find multiple pareto-optimal solutions in one single run and this ability makes them attractive for solving problems with multiple and conflicting objectives. This paper uses an elitist multiobjective evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA), for solving the dynamic shortest path routing problem in computer networks. A priority-based encoding scheme is proposed for population initialization. Elitism ensures that the best solution does not deteriorate in the next generations. Results for a sample test network have been presented to demonstrate the capabilities of the proposed approach to generate well-distributed pareto-optimal solutions of dynamic routing problem in one single run. The results obtained by NSGA are compared with single objective weighting factor method for which Genetic Algorithm (GA) was applied.

Keywords: Multiobjective optimization, Non-dominated Sorting Genetic Algorithm, Routing, Weighted sum.

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Authors: Abdelhadi Lotfi, Abdelkader Benyettou

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In this work, a training algorithm for probabilistic neural networks (PNN) is presented. The algorithm addresses one of the major drawbacks of PNN, which is the size of the hidden layer in the network. By using a cross-validation training algorithm, the number of hidden neurons is shrunk to a smaller number consisting of the most representative samples of the training set. This is done without affecting the overall architecture of the network. Performance of the network is compared against performance of standard PNN for different databases from the UCI database repository. Results show an important gain in network size and performance.

Keywords: Classification, probabilistic neural networks, network optimization, pattern recognition.

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Authors: Sana Bouzaida, Anis Sakly, Faouzi M'Sahli

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In this paper, a TSK-type Neuro-fuzzy Inference System that combines the features of fuzzy sets and neural networks has been applied for the identification of MIMO systems. The procedure of adapting parameters in TSK model employs a Shuffled Frog Leaping Algorithm (SFLA) which is inspired from the memetic evolution of a group of frogs when seeking for food. To demonstrate the accuracy and effectiveness of the proposed controller, two nonlinear systems have been considered as the MIMO plant, and results have been compared with other learning methods based on Particle Swarm Optimization algorithm (PSO) and Genetic Algorithm (GA).

Keywords: Identification, Shuffled frog Leaping Algorithm (SFLA), TSK-type neuro-fuzzy model.

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Authors: M. R. Alrashidi, M. E. El-Hawary

Abstract:

Environmental awareness and the recent environmental policies have forced many electric utilities to restructure their operational practices to account for their emission impacts. One way to accomplish this is by reformulating the traditional economic dispatch problem such that emission effects are included in the mathematical model. This paper presents a Particle Swarm Optimization (PSO) algorithm to solve the Economic- Emission Dispatch problem (EED) which gained recent attention due to the deregulation of the power industry and strict environmental regulations. The problem is formulated as a multi-objective one with two competing functions, namely economic cost and emission functions, subject to different constraints. The inequality constraints considered are the generating unit capacity limits while the equality constraint is generation-demand balance. A novel equality constraint handling mechanism is proposed in this paper. PSO algorithm is tested on a 30-bus standard test system. Results obtained show that PSO algorithm has a great potential in handling multi-objective optimization problems and is capable of capturing Pareto optimal solution set under different loading conditions.

Keywords: Economic emission dispatch, economic cost dispatch, particle swarm, multi-objective optimization.

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Authors: Chang, Chun-Lang, Liu, Chun-Kai

Abstract:

This study, for its research subjects, uses patients who had undergone total knee replacement surgery from the database of the National Health Insurance Administration. Through the review of literatures and the interviews with physicians, important factors are selected after careful screening. Then using Cross Entropy Method, Genetic Algorithm Logistic Regression, and Particle Swarm Optimization, the weight of each factor is calculated and obtained. In the meantime, Excel VBA and Case Based Reasoning are combined and adopted to evaluate the system. Results show no significant difference found through Genetic Algorithm Logistic Regression and Particle Swarm Optimization with over 97% accuracy in both methods. Both ROC areas are above 0.87. This study can provide critical reference to medical personnel as clinical assessment to effectively enhance medical care quality and efficiency, prevent unnecessary waste, and provide practical advantages to resource allocation to medical institutes.

Keywords: Total knee replacement, Case Based Reasoning, Cross Entropy Method, Genetic Algorithm Logistic Regression, Particle Swarm Optimization.

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Authors: Hidehiko Okada

Abstract:

The author proposes an extension of genetic algorithm (GA) for solving fuzzy-valued optimization problems. In the proposed GA, values in the genotypes are not real numbers but fuzzy numbers. Evolutionary processes in GA are extended so that GA can handle genotype instances with fuzzy numbers. The proposed method is applied to evolving neural networks with fuzzy weights and biases. Experimental results showed that fuzzy neural networks evolved by the fuzzy GA could model hidden target fuzzy functions well despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithm, genetic algorithm, fuzzy number, neural network, neuroevolution.

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Authors: S. Esfandeh, M. Sedighizadeh

Abstract:

Weather systems use enormously complex combinations of numerical tools for study and forecasting. Unfortunately, due to phenomena in the world climate, such as the greenhouse effect, classical models may become insufficient mostly because they lack adaptation. Therefore, the weather forecast problem is matched for heuristic approaches, such as Evolutionary Algorithms. Experimentation with heuristic methods like Particle Swarm Optimization (PSO) algorithm can lead to the development of new insights or promising models that can be fine tuned with more focused techniques. This paper describes a PSO approach for analysis and prediction of data and provides experimental results of the aforementioned method on realworld meteorological time series.

Keywords: Weather, Climate, PSO, Prediction, Meteorological

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Authors: F. Fissou Amigue, S. Ndjakomo Essiane, S. Pérabi Ngoffé, G. Abessolo Ondoa, G. Mengata Mengounou, T. P. Nna Nna

Abstract:

This document proposes a method for determining the optimal point of integration of distributed generation (DG) in distribution grid. Slime mould optimization is applied to determine best node in case of one and two injection point. Problem has been modeled as an optimization problem where the objective is to minimize joule loses and main constraint is to regulate voltage in each point. The proposed method has been implemented in MATLAB and applied in IEEE network 33 and 69 nodes. Comparing results obtained with other algorithms showed that slime mould optimization algorithms (SMOA) have the best reduction of power losses and good amelioration of voltage profile.

Keywords: Optimization, distributed generation, integration, slime mould algorithm.

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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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Authors: M. Farahnakian, M.R. Razfar, S. Elhami-Joosheghan

Abstract:

This paper presents an approach for the determination of the optimal cutting parameters (spindle speed, feed rate, depth of cut and engagement) leading to minimum surface roughness in face milling of high silicon stainless steel by coupling neural network (NN) and Electromagnetism-like Algorithm (EM). In this regard, the advantages of statistical experimental design technique, experimental measurements, artificial neural network, and Electromagnetism-like optimization method are exploited in an integrated manner. To this end, numerous experiments on this stainless steel were conducted to obtain surface roughness values. A predictive model for surface roughness is created by using a back propogation neural network, then the optimization problem was solved by using EM optimization. Additional experiments were performed to validate optimum surface roughness value predicted by EM algorithm. It is clearly seen that a good agreement is observed between the predicted values by EM coupled with feed forward neural network and experimental measurements. The obtained results show that the EM algorithm coupled with back propogation neural network is an efficient and accurate method in approaching the global minimum of surface roughness in face milling.

Keywords: cutting parameters, face milling, surface roughness, artificial neural network, Electromagnetism-like algorithm,

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Authors: Zeshan Ahmad, Matteo Zoppi, Rezia Molfino

Abstract:

The stiffness of the workpiece is very important to reduce the errors in manufacturing process. The high stiffness of the workpiece can be achieved by optimal positioning of fixture elements in the fixture. The minimization of the sum of the nodal deflection normal to the surface is used as objective function in previous research. The deflection in other direction has been neglected. The 3-2-1 fixturing principle is not valid for metal sheets due to its flexible nature. We propose a new fixture layout optimization method N-3-2-1 for metal sheets that uses the strain energy of the finite elements. This method combines the genetic algorithm and finite element analysis. The objective function in this method is to minimize the sum of all the element strain energy. By using the concept of element strain energy, the deformations in all the directions have been considered. Strain energy and stiffness are inversely proportional to each other. So, lower the value of strain energy, higher will be the stiffness. Two different kinds of case studies are presented. The case studies are solved for both objective functions; element strain energy and nodal deflection. The result are compared to verify the propose method.

Keywords: Fixture layout, optimization, fixturing element, genetic algorithm.

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Authors: Refaat M Mohamed, Ayman El-Baz, Aly A. Farag

Abstract:

This paper presents a new approach for the prob-ability density function estimation using the Support Vector Ma-chines (SVM) and the Expectation Maximization (EM) algorithms.In the proposed approach, an advanced algorithm for the SVM den-sity estimation which incorporates the Mean Field theory in the learning process is used. Instead of using ad-hoc values for the para-meters of the kernel function which is used by the SVM algorithm,the proposed approach uses the EM algorithm for an automatic optimization of the kernel. Experimental evaluation using simulated data set shows encouraging results.

Keywords: Density Estimation, SVM, Learning Algorithms, Parameters Estimation.

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Authors: Saeed Vaneshani, Hooshang Jazayeri-Rad

Abstract:

Fuzzy logic control (FLC) systems have been tested in many technical and industrial applications as a useful modeling tool that can handle the uncertainties and nonlinearities of modern control systems. The main drawback of the FLC methodologies in the industrial environment is challenging for selecting the number of optimum tuning parameters. In this paper, a method has been proposed for finding the optimum membership functions of a fuzzy system using particle swarm optimization (PSO) algorithm. A synthetic algorithm combined from fuzzy logic control and PSO algorithm is used to design a controller for a continuous stirred tank reactor (CSTR) with the aim of achieving the accurate and acceptable desired results. To exhibit the effectiveness of proposed algorithm, it is used to optimize the Gaussian membership functions of the fuzzy model of a nonlinear CSTR system as a case study. It is clearly proved that the optimized membership functions (MFs) provided better performance than a fuzzy model for the same system, when the MFs were heuristically defined.

Keywords: continuous stirred tank reactor (CSTR), fuzzy logiccontrol (FLC), membership function(MF), particle swarmoptimization (PSO)

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Authors: Mahmoud M. Othman, Y. G. Hegazy, A. Y. Abdelaziz

Abstract:

This paper proposes a novel heuristic algorithm that aims to determine the best size and location of distributed generators in unbalanced distribution networks. The proposed heuristic algorithm can deal with the planning cases where power loss is to be optimized without violating the system practical constraints. The distributed generation units in the proposed algorithm is modeled as voltage controlled node with the flexibility to be converted to constant power factor node in case of reactive power limit violation. The proposed algorithm is implemented in MATLAB and tested on the IEEE 37 -node feeder. The results obtained show the effectiveness of the proposed algorithm. 

Keywords: Distributed generation, heuristic approach, Optimization, planning.

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Authors: Kehinde K. Agbele, Kehinde Daniel Aruleba, Eniafe F. Ayetiran

Abstract:

When using Information Retrieval Systems (IRS), users often present search queries made of ad-hoc keywords. It is then up to the IRS to obtain a precise representation of the user’s information need and the context of the information. This paper investigates optimization of IRS to individual information needs in order of relevance. The study addressed development of algorithms that optimize the ranking of documents retrieved from IRS. This study discusses and describes a Document Ranking Optimization (DROPT) algorithm for information retrieval (IR) in an Internet-based or designated databases environment. Conversely, as the volume of information available online and in designated databases is growing continuously, ranking algorithms can play a major role in the context of search results. In this paper, a DROPT technique for documents retrieved from a corpus is developed with respect to document index keywords and the query vectors. This is based on calculating the weight (

Keywords: Internet ranking,

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Authors: M. F. Omar, R. A. Salam, R. Abdullah, N. A. Rashid

Abstract:

Proteins or genes that have similar sequences are likely to perform the same function. One of the most widely used techniques for sequence comparison is sequence alignment. Sequence alignment allows mismatches and insertion/deletion, which represents biological mutations. Sequence alignment is usually performed only on two sequences. Multiple sequence alignment, is a natural extension of two-sequence alignment. In multiple sequence alignment, the emphasis is to find optimal alignment for a group of sequences. Several applicable techniques were observed in this research, from traditional method such as dynamic programming to the extend of widely used stochastic optimization method such as Genetic Algorithms (GAs) and Simulated Annealing. A framework with combination of Genetic Algorithm and Simulated Annealing is presented to solve Multiple Sequence Alignment problem. The Genetic Algorithm phase will try to find new region of solution while Simulated Annealing can be considered as an alignment improver for any near optimal solution produced by GAs.

Keywords: Simulated annealing, genetic algorithm, sequence alignment, multiple sequence alignment.

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Authors: S. F. Wong, W. I. Ho, B. Lin, Q. Huang

Abstract:

ERP has been used in many enterprises for management, the accuracy of the production forecasting module is vital to the decision making of the enterprise, and the profit is affected directly. Therefore, enhancing the accuracy of the production forecasting module can also increase the efficiency and profitability. To deal with a lot of data, a suitable, reliable and accurate statistics model is necessary. LSSVM and Grey System are two main models to be studied in this paper, and a case study is used to demonstrate how the combination model is effective to the result of forecasting.

Keywords: ERP, Grey System, LSSVM, production forecasting.

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Authors: Mahmoud M. Othman, Yasser G. Hegazy

Abstract:

This paper proposes a novel heuristic algorithm that aims to determine the best size and location of distributed generators in unbalanced distribution networks. The proposed heuristic algorithm can deal with the planning cases where power loss is to be optimized without violating the system practical constraints. The distributed generation units in the proposed algorithm is modeled as voltage controlled node with the flexibility to be converted to constant power factor node in case of reactive power limit violation. The proposed algorithm is implemented in MATLAB and tested on the IEEE 37 -node feeder. The results obtained show the effectiveness of the proposed algorithm.

Keywords: Distributed generation, heuristic approach, Optimization, planning.

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Authors: N. M. Nawi, R. S. Ransing, M. R. Ransing

Abstract:

The conjugate gradient optimization algorithm is combined with the modified back propagation algorithm to yield a computationally efficient algorithm for training multilayer perceptron (MLP) networks (CGFR/AG). The computational efficiency is enhanced by adaptively modifying initial search direction as described in the following steps: (1) Modification on standard back propagation algorithm by introducing a gain variation term in the activation function, (2) Calculation of the gradient descent of error with respect to the weights and gains values and (3) the determination of a new search direction by using information calculated in step (2). The performance of the proposed method is demonstrated by comparing accuracy and computation time with the conjugate gradient algorithm used in MATLAB neural network toolbox. The results show that the computational efficiency of the proposed method was better than the standard conjugate gradient algorithm.

Keywords: Adaptive gain variation, back-propagation, activation function, conjugate gradient, search direction.

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Authors: Jamal A. Gledan, Othman A. Azzeidani

Abstract:

During the last decade, Libya established a new Geodetic Datum called Libyan Geodetic Datum 2006 (LGD 2006) by using GPS, whereas the ground traversing method was used to establish the last Libyan datum which was called the Europe Libyan Datum 79 (ELD79). The current research paper introduces ELD79 to LGD2006 coordinate transformation technique, the accurate comparison of transformation between multiple regression equations and the three – parameters model (Bursa-Wolf). The results had been obtained show that the overall accuracy of stepwise multi regression equations is better than that can be determined by using Bursa-Wolf transformation model.

Keywords: Geodetic datum, horizontal control points, traditional similarity transformation model, unconventional transformation techniques.

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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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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3ⁿ enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3ⁿ integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

Keywords: Constrained integer problems, enumerative search algorithm, Heuristic algorithm, tunneling algorithm.

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Authors: Chaghoub Soraya, Zhang Xiaoyan

Abstract:

This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: Approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median.

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