Search results for: vector optimization

Authors: Stephen Kirkup

Abstract:

This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: boundary element method, Laplace’s equation, vector calculus, simulation, education

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Authors: Abdelsalam A. Ahmed

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Fast speed drives for Permanent Magnet Synchronous Motor (PMSM) is a crucial performance for the electric traction systems. In this paper, PMSM is drived with a Model-based Predictive Control (MPC) technique. Fast speed tracking is achieved through optimization of the DC source utilization using MPC. The technique is based on predicting the optimum voltage vector applied to the driver. Control technique is investigated by comparing to the cascaded PI control based on Space Vector Pulse Width Modulation (SVPWM). MPC and SVPWM-based FOC are implemented with the TMS320F2812 DSP and its power driver circuits. The designed MPC for a PMSM drive is experimentally validated on a laboratory test bench. The performances are compared with those obtained by a conventional PI-based system in order to highlight the improvements, especially regarding speed tracking response.

Keywords: permanent magnet synchronous motor, model-based predictive control, DC source utilization, cascaded PI control, space vector pulse width modulation, TMS320F2812 DSP

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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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Authors: Ahmed Abdolkhalig, Rastko Zivanovic

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This paper evaluates the Total Vector Error of an estimated Phasor as define in IEEE C37.118 standard within different medium access in Local Area Networks (LAN). Three different LAN models (CSMA/CD, CSMA/AMP, and Switched Ethernet) are evaluated. The Total Vector Error of the estimated Phasor has been evaluated for the effect of Nodes Number under the standardized network Band-width values defined in IEC 61850-9-2 communication standard (i.e. 0.1, 1, and 10 Gbps).

Keywords: phasor, local area network, total vector error, IEEE C37.118, IEC 61850

Procedia PDF Downloads 297

Authors: Aldan A. Sapargaliyev, Yerbol A. Sapargaliyev

Abstract:

Since the invention, the electric machine (EM) can be defined as oEM – one-vector electric machine, as it works due to one-vector inductive coupling with use of one-vector electromagnet. The disadvantages of oEM are large size and limited efficiency at low and medium power applications. This paper describes multi-vector electric machine (mEM) based on multi-vector inductive coupling, which is characterized by the increased surface area of ​​the inductive coupling per EM volume, with a reduced share of inefficient and energy-consuming part of the winding, in comparison with oEM’s. Particularly, it is considered, calculated and compared the performance of three different electrical motors and their power at the same volumes and rotor frequencies. It is also presented the result of calculation of correlation between power density and volume for oEM and mEM. The method of multi-vector inductive coupling enables mEM to possess 1.5-4.0 greater density of power per volume and significantly higher efficiency, in comparison with today’s oEM, especially in low and medium power applications. mEM has distinct advantages, when used in transport vehicles such as electric cars and aircrafts.

Keywords: electric machine, electric motor, electromagnet, efficiency of electric motor

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Authors: Serges Mendomo Meye, Li Guowei, Shen Zhenzhong, Gan Lei, Xu Liqun

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Given the limitations of the original whale optimization algorithm (WAO) in local optimum and low convergence accuracy in truss structure optimization problems, based on the fundamental whale algorithm, an improved whale optimization algorithm (SWAO) based on information entropy is proposed. The information entropy itself is an uncertain measure. It is used to control the range of whale searches in path selection. It can overcome the shortcomings of the basic whale optimization algorithm (WAO) and can improve the global convergence speed of the algorithm. Taking truss structure as the optimization research object, the mathematical model of truss structure optimization is established; the cross-sectional area of truss is taken as the design variable; the objective function is the weight of truss structure; and an improved whale optimization algorithm (SWAO) is used for optimization design, which provides a new idea and means for its application in large and complex engineering structure optimization design.

Keywords: information entropy, structural optimization, truss structure, whale algorithm

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Authors: Ramin Javadzadeh

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The particle swarm optimization are Meta heuristic optimization method, which are used for clustering and pattern recognition applications are abundantly. These algorithms in multimodal optimization problems are more efficient than genetic algorithms. A major drawback in these algorithms is their slow convergence to global optimum and their weak stability can be considered in various running of these algorithms. In this paper, improved Particle swarm optimization is introduced for the first time to overcome its problems. The fuzzy cellular automata is used for improving the algorithm efficiently. The credibility of the proposed approach is evaluated by simulations, and it is shown that the proposed approach achieves better results can be achieved compared to the Particle swarm optimization algorithms.

Keywords: cellular automata, cellular learning automata, local search, optimization, particle swarm optimization

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Authors: María L. Jalón, Feargal Brennan

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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, temporal variability, wave energy

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Authors: Liudmyla Koliechkina, Olena Dvirna

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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, Pareto solutions, partial permutation set, structural graph

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Authors: Kang-Mo Jung

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Least squares support vector machine (LS-SVM) is a penalized regression which considers both fitting and generalization ability of a model. However, the squared loss function is very sensitive to even single outlier. We proposed a weighted absolute deviation loss function for the robustness of the estimates in least absolute deviation support vector machine. The proposed estimates can be obtained by a quadratic programming algorithm. Numerical experiments on simulated datasets show that the proposed algorithm is competitive in view of robustness to outliers.

Keywords: least absolute deviation, quadratic programming, robustness, support vector machine, weight

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Authors: Songul Cinaroglu

Abstract:

Machine learning regression methods are recommended as an alternative to classical regression methods in the existence of variables which are difficult to model. Data for health expenditure is typically non-normal and have a heavily skewed distribution. This study aims to compare machine learning regression methods by hyperparameter tuning to predict health expenditure per capita. A multiple regression model was conducted and performance results of Lasso Regression, Random Forest Regression and Support Vector Machine Regression recorded when different hyperparameters are assigned. Lambda (λ) value for Lasso Regression, number of trees for Random Forest Regression, epsilon (ε) value for Support Vector Regression was determined as hyperparameters. Study results performed by using 'k' fold cross validation changed from 5 to 50, indicate the difference between machine learning regression results in terms of R², RMSE and MAE values that are statistically significant (p < 0.001). Study results reveal that Random Forest Regression (R² ˃ 0.7500, RMSE ≤ 0.6000 ve MAE ≤ 0.4000) outperforms other machine learning regression methods. It is highly advisable to use machine learning regression methods for modelling health expenditures.

Keywords: machine learning, lasso regression, random forest regression, support vector regression, hyperparameter tuning, health expenditure

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Authors: R. M. Rizk-Allah

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This paper presents co-evolutionary fruit fly optimization algorithm based on firefly algorithm (CFOA-FA) for solving unconstrained optimization problems. The proposed algorithm integrates the merits of fruit fly optimization algorithm (FOA), firefly algorithm (FA) and elite strategy to refine the performance of classical FOA. Moreover, co-evolutionary mechanism is performed by applying FA procedures to ensure the diversity of the swarm. Finally, the proposed algorithm CFOA- FA is tested on several benchmark problems from the usual literature and the numerical results have demonstrated the superiority of the proposed algorithm for finding the global optimal solution.

Keywords: firefly algorithm, fruit fly optimization algorithm, unconstrained optimization problems

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Authors: Amir Hossein Hejazi, Nima Amjady

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In recent years, due to environmental issues traditional energy sources had been replaced by renewable ones. Wind energy as the fastest growing renewable energy shares a considerable percent of energy in power electricity markets. With this fast growth of wind energy worldwide, owners and operators of wind farms, transmission system operators, and energy traders need reliable and secure forecasts of wind energy production. In this paper, a new forecasting strategy is proposed for short-term wind power prediction based on Echo State Networks (ESN). The forecast engine utilizes state-of-the-art training process including dynamical reservoir with high capability to learn complex dynamics of wind power or wind vector signals. The study becomes more interesting by incorporating prediction of wind direction into forecast strategy. The Big Bang-Big Crunch (BB-BC) evolutionary optimization algorithm is adopted for adjusting free parameters of ESN-based forecaster. The proposed method is tested by real-world hourly data to show the efficiency of the forecasting engine for prediction of both wind vector and wind power output of aggregated wind power production.

Keywords: wind power forecasting, echo state network, big bang-big crunch, evolutionary optimization algorithm

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Authors: H. Hotait, X. Chiementin, L. Rasolofondraibe

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This paper presents a continuous work to detect the abnormal state in the rolling bearing by studying the vibration signature analysis and calculation of the remaining useful life. To achieve these aims, two methods; the first method is the classification to detect the degradation state by the AOM-OPTICS (Acousto-Optic Modulator) method. The second one is the prediction of the degradation state using least-squares support vector regression and then compared with the linear degradation model. An experimental investigation on ball-bearing was conducted to see the effectiveness of the used method by applying the acquired vibration signals. The proposed model for predicting the state of bearing gives us accurate results with the experimental and numerical data.

Keywords: bearings, automatization, optimization, prognosis, classification, defect detection

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Authors: Pham Van Nha, Le Cam Binh

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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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Authors: Rikson Gultom

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Hate Speech and Abusive language on social media is difficult to detect, usually, it is detected after it becomes viral in cyberspace, of course, it is too late for prevention. An early detection system that has a fairly good accuracy is needed so that it can reduce conflicts that occur in society caused by postings on social media that attack individuals, groups, and governments in Indonesia. The purpose of this study is to find an early detection model on Twitter social media using machine learning that has high accuracy from several machine learning methods studied. In this study, the support vector machine (SVM), Naïve Bayes (NB), and Random Forest Decision Tree (RFDT) methods were compared with the Support Vector machine with genetic algorithm (SVM-GA), Nave Bayes with genetic algorithm (NB-GA), and Random Forest Decision Tree with Genetic Algorithm (RFDT-GA). The study produced a comparison table for the accuracy of the hate speech and abusive language detection model, and presented it in the form of a graph of the accuracy of the six algorithms developed based on the Indonesian-language Twitter dataset, and concluded the best model with the highest accuracy.

Keywords: abusive language, hate speech, machine learning, optimization, social media

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Authors: Sait Ali Uymaz, Gülay Tezel

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This paper presents the comparison results on the performance of the Cuckoo Search (CS) algorithm for constrained optimization problems. For constraint handling, CS algorithm uses penalty method. CS algorithm is tested on thirteen well-known test problems and the results obtained are compared to Particle Swarm Optimization (PSO) algorithm. Mean, best, median and worst values were employed for the analyses of performance.

Keywords: cuckoo search, particle swarm optimization, constrained optimization problems, penalty method

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Authors: R. O. Osaseri, A. R. Usiobaifo

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The power transformer which is responsible for the voltage transformation is of great relevance in the power system and oil-immerse transformer is widely used all over the world. A prompt and proper maintenance of the transformer is of utmost importance. The dissolved gasses content in power transformer, oil is of enormous importance in detecting incipient fault of the transformer. There is a need for accurate prediction of the incipient fault in transformer oil in order to facilitate the prompt maintenance and reducing the cost and error minimization. Study on fault prediction and diagnostic has been the center of many researchers and many previous works have been reported on the use of artificial intelligence to predict incipient failure of transformer faults. In this study machine learning technique was employed by using gradient decent algorithms and Support Vector Machine (SVM) in predicting incipient fault diagnosis of transformer. The method focuses on creating a system that improves its performance on previous result and historical data. The system design approach is basically in two phases; training and testing phase. The gradient decent algorithm is trained with a training dataset while the learned algorithm is applied to a set of new data. This two dataset is used to prove the accuracy of the proposed model. In this study a transformer fault diagnostic model based on Support Vector Machine (SVM) and gradient decent algorithms has been presented with a satisfactory diagnostic capability with high percentage in predicting incipient failure of transformer faults than existing diagnostic methods.

Keywords: diagnostic model, gradient decent, machine learning, support vector machine (SVM), transformer fault

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Authors: Aasheesh Raturi, Vimal Kothiyal, P. D. Semalty

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We studied mechanical properties of Eucalyptus tereticornis using FT-NIR spectroscopy. Firstly, spectra were pre-processed to eliminate useless information. Then, prediction model was constructed by partial least squares regression. To study the influence of pre-processing on prediction of mechanical properties for NIR analysis of wood samples, we applied various pretreatment methods like straight line subtraction, constant offset elimination, vector-normalization, min-max normalization, multiple scattering. Correction, first derivative, second derivatives and their combination with other treatment such as First derivative + straight line subtraction, First derivative+ vector normalization and First derivative+ multiplicative scattering correction. The data processing methods in combination of preprocessing with different NIR regions, RMSECV, RMSEP and optimum factors/rank were obtained by optimization process of model development. More than 350 combinations were obtained during optimization process. More than one pre-processing method gave good calibration/cross-validation and prediction/test models, but only the best calibration/cross-validation and prediction/test models are reported here. The results show that one can safely use NIR region between 4000 to 7500 cm-1 with straight line subtraction, constant offset elimination, first derivative and second derivative preprocessing method which were found to be most appropriate for models development.

Keywords: FT-NIR, mechanical properties, pre-processing, PLS

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Authors: A. Djahbar, E. Bounadja, A. Zegaoui, H. Allouache

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In this paper, vector control of a series-connected two-machine drive system fed by a single inverter (CSI/VSI) is presented. The two stator windings of both machines are connected in series while the rotors may be connected to different loads, are called series-connected two-machine drive. Appropriate phase transposition is introduced while connecting the series stator winding to obtain decoupled control the two-machines. The dynamic decoupling of each machine from the group is obtained using the vector control algorithm. The independent control is demonstrated by analyzing the characteristics of torque and speed of each machine obtained via simulation under vector control scheme. The viability of the control techniques is proved using analytically and simulation approach.

Keywords: drives, inverter, multi-phase induction machine, vector control

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Authors: Usoro Anthony E., Udoh Emediong

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Diagonal Vector Autoregressive Models are special classes of the general vector autoregressive models identified under certain conditions, where parameters are restricted to the diagonal elements in the coefficient matrices. Variance, autocovariance, and autocorrelation properties of the upper and lower diagonal VAR models are derived. The new set of VAR models is verified with empirical data and is found to perform favourably with the general VAR models. The advantage of the diagonal models over the existing models is that the new models are parsimonious, given the reduction in the interactive coefficients of the general VAR models.

Keywords: VAR models, diagonal VAR models, variance, autocovariance, autocorrelations

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Authors: Takahiro Hino, Michiharu Maeda

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Particle swarm optimization (PSO) is an optimization approach that achieves the social model of bird flocking and fish schooling. PSO works in continuous space and can solve continuous optimization problem with high quality. Set-based particle swarm optimization (SPSO) functions in discrete space by using a set. SPSO can solve combinatorial optimization problem with high quality and is successful to apply to the large-scale problem. In this paper, we present an algorithm of SPSO with status memory to decide the position based on the previous position for solving traveling salesman problem (TSP). In order to show the effectiveness of our approach. We examine SPSOSM for TSP compared to the existing algorithms.

Keywords: combinatorial optimization problems, particle swarm optimization, set-based particle swarm optimization, traveling salesman problem

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Authors: Jamilatuzzahro, Rezzy Eko Caraka

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The yield curve is the plot of the yield to maturity of zero-coupon bonds against maturity. In practice, the yield curve is not observed but must be extracted from observed bond prices for a set of (usually) incomplete maturities. There exist many methodologies and theory to analyze of yield curve. We use two methods (the Nelson-Siegel Method, the Svensson Method, and the SVR method) in order to construct and compare our zero-coupon yield curves. The objectives of this research were: (i) to study the adequacy of NSS model and SVR to Indonesian government bonds data, (ii) to choose the best optimization or estimation method for NSS model and SVR. To obtain that objective, this research was done by the following steps: data preparation, cleaning or filtering data, modeling, and model evaluation.

Keywords: support vector regression, Nelson-Siegel-Svensson, yield curve, Indonesian government

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Authors: Karchung, S. Ruangsinchaiwanich

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This paper presents open-loop vector control method of induction motor with space vector pulse width modulation (SVPWM) technique. Normally, the closed loop speed control is preferred and is believed to be more accurate. However, it requires a position sensor to track the rotor position which is not desirable to use it for certain workspace applications. This paper exhibits the performance of three-phase induction motor with the simplest control algorithm without the use of a position sensor nor an estimation block to estimate rotor position for sensorless control. The motor stator currents are measured and are transformed to synchronously rotating (d-q-axis) frame by use of Clarke and Park transformation. The actual control happens in this frame where the measured currents are compared with the reference currents. The error signal is fed to a conventional PI controller, and the corrected d-q voltage is generated. The controller outputs are transformed back to three phase voltages and are fed to SVPWM block which generates PWM signal for the voltage source inverter. The open loop vector control model along with SVPWM algorithm is modeled in MATLAB/Simulink software and is experimented and validated in TMS320F28335 DSP board.

Keywords: electric drive, induction motor, open-loop vector control, space vector pulse width modulation technique

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Authors: Ronak Khosravi, Mahmood Abbasi Layegh, Siamak Haghipour, Avin Esmaili

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In this paper, a study on classification of musical woodwind instruments using a small set of features selected from a broad range of extracted ones by the sequential forward selection method was carried out. Firstly, we extract 42 features for each record in the music database of 402 sound files belonging to five different groups of Flutes (end blown and internal duct), Single –reed, Double –reed (exposed and capped), Triple reed and Quadruple reed. Then, the sequential forward selection method is adopted to choose the best feature set in order to achieve very high classification accuracy. Two different classification techniques of support vector machines and relevance vector machines have been tested out and an accuracy of up to 96% can be achieved by using 21 time, frequency and coefficient features and relevance vector machine with the Gaussian kernel function.

Keywords: coefficient features, relevance vector machines, spectral features, support vector machines, temporal features

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Authors: Qiuxiao Chen, Yan Hou, Ning Wu

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As there are deficiencies of the classic Douglas-Peucker Algorithm (DPA), such as high risks of deleting key nodes by mistake, high complexity, time consumption and relatively slow execution speed, a new Deletion-Cost Based Compression Algorithm (DCA) for linear vector data was proposed. For each curve — the basic element of linear vector data, all the deletion costs of its middle nodes were calculated, and the minimum deletion cost was compared with the pre-defined threshold. If the former was greater than or equal to the latter, all remaining nodes were reserved and the curve’s compression process was finished. Otherwise, the node with the minimal deletion cost was deleted, its two neighbors' deletion costs were updated, and the same loop on the compressed curve was repeated till the termination. By several comparative experiments using different types of linear vector data, the comparison between DPA and DCA was performed from the aspects of compression quality and computing efficiency. Experiment results showed that DCA outperformed DPA in compression accuracy and execution efficiency as well.

Keywords: Douglas-Peucker algorithm, linear vector data, compression, deletion cost

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Authors: D. Li

Abstract:

Optical thin films are used in a wide variety of optical components and there are many software tools programmed for advancing multilayer thin film design. The available software packages for designing the thin film structure may not provide optimum designs. Normally, almost all current software programs obtain their final designs either from optimizing a starting guess or by technique, which may or may not involve a pseudorandom process, that give different answers every time, depending upon the initial conditions. With the increasing power of personal computers, functional methods in optimization and synthesis of optical multilayer systems have been developed such as DGL Optimization, Simulated Annealing, Genetic Algorithms, Needle Optimization, Inductive Optimization and Flip-Flop Optimization. Among these, DGL Optimization has proved its efficiency in optical thin film designs. The application of the DGL optimization technique to the design of optical coating is presented. A DGL optimization technique is provided, and its main features are discussed. Guidelines on the application of the DGL optimization technique to various types of design problems are given. The innovative global optimization strategies used in a software tool, OnlyFilm, to optimize multilayer thin film designs through different filter designs are outlined. OnlyFilm is a powerful, versatile, and user-friendly thin film software on the market, which combines optimization and synthesis design capabilities with powerful analytical tools for optical thin film designers. It is also the only thin film design software that offers a true global optimization function.

Keywords: optical coatings, optimization, design software, thin film design

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Authors: O. Mohamed Amine, A. Khireddine

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Telecoms operators are always looking to meet their share of the other customers, they try to gain optimum utilization of the deployed equipment and network optimization has become essential. This project consists of optimizing UMTS network, and the study area is an urban area situated in the center of Algiers. It was initially questions to become familiar with the different communication systems (3G) and the optimization technique, its main components, and its fundamental characteristics radios were introduced.

Keywords: UMTS, UTRAN, WCDMA, optimization

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Authors: Surinder Deswal, Mahesh Pal

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The paper investigates the potential of support vector machines based regression approach to model the mass transfer capacity of multiple plunging jets, both vertical (θ = 90°) and inclined (θ = 60°). The data set used in this study consists of four input parameters with a total of eighty eight cases. For testing, tenfold cross validation was used. Correlation coefficient values of 0.971 and 0.981 (root mean square error values of 0.0025 and 0.0020) were achieved by using polynomial and radial basis kernel functions based support vector regression respectively. Results suggest an improved performance by radial basis function in comparison to polynomial kernel based support vector machines. The estimated overall mass transfer coefficient, by both the kernel functions, is in good agreement with actual experimental values (within a scatter of ±15 %); thereby suggesting the utility of support vector machines based regression approach.

Keywords: mass transfer, multiple plunging jets, support vector machines, ecological sciences

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Authors: Vahid Zeighami, Mohsen Ghsemi, Reza Akbari

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In this work, a Multi-Level Artificial Bee Colony (called MLABC) is presented. In MLABC two species are used. The first species employs n colonies in which each of the them optimizes the complete solution vector. The cooperation between these colonies is carried out by exchanging information through a leader colony, which contains a set of elite bees. The second species uses a cooperative approach in which the complete solution vector is divided to k sub-vectors, and each of these sub-vectors is optimized by a a colony. The cooperation between these colonies is carried out by compiling sub-vectors into the complete solution vector. Finally, the cooperation between two species is obtained by exchanging information between them. The proposed algorithm is tested on a set of well known test functions. The results show that MLABC algorithms provide efficiency and robustness to solve numerical functions.

Keywords: artificial bee colony, cooperative, multilevel cooperation, vector

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