Search results for: Differential Evolution Algorithm Static Synchronous Compensator
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 5200

Search results for: Differential Evolution Algorithm Static Synchronous Compensator

4330 Flow and Heat Transfer over a Shrinking Sheet: A Stability Analysis

Authors: Anuar Ishak

Abstract:

The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, shrinking sheet, stability analysis.

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4329 Sensitivity and Removed THD of a Phase- Cutting Dimmer

Authors: H. Fathabadi

Abstract:

In this paper, we consider a designed and implemented phase-cutting dimmer. In fact, the dimmer is closed loop and a microcontroller calculates and then regulates the firing delay angles of each channel. Depending on the firing angle, the harmonic distortion in the input current will not comply with international standards, such as IEC 61000-3-2 (class C equipments). For solving this problem, eight harmonic compensators have been added to the dimmer. So, the proposed dimmer has a little harmonic distortion in the input current whereas conventional phase-cutting dimmers are not so. Sensitivity and removed THD of the proposed dimmer will be presented.

Keywords: Dimmer, compensator, harmonic, dimming.

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4328 The Evolution of Quality Improvement Methodology in Malaysia-s IT Industry: The Past, Current and Future

Authors: Whee Yen Wong, Kim Yeow Tshai, Chan Wai Lee

Abstract:

There are various approaches to implement quality improvements. Organizations aim for a management standard which is capable of providing customers with quality assurance on their product/service via continuous process improvement. Carefully planned steps are necessary to ensure the right quality improvement methodology (QIM) and business operations are consistent, reliable and truly meet the customers' needs. This paper traces the evolution of QIM in Malaysia-s Information Technology (IT) industry in the past, current and future; and highlights some of the thought of researchers who contributed to the science and practice of quality, and identifies leading methodologies in use today. Some of the misconceptions and mistakes leading to quality system failures will also be examined and discussed. This paper aims to provide a general overview of different types of QIMs available for IT businesses in maximizing business advantages, enhancing product quality, improving process routines and increasing performance earnings.

Keywords: Evolution, Integrating and Aligning, Malaysia's Quality Improvement Methodology, Six Sigma Data Quality Management.

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4327 Design and Simulation of Low Speed Axial Flux Permanent Magnet (AFPM) Machine

Authors: Ahmad Darabi, Hassan Moradi, Hossein Azarinfar

Abstract:

In this paper presented initial design of Low Speed Axial Flux Permanent Magnet (AFPM) Machine with Non-Slotted TORUS topology type by use of certain algorithm (Appendix). Validation of design algorithm studied by means of selected data of an initial prototype machine. Analytically design calculation carried out by means of design algorithm and obtained results compared with results of Finite Element Method (FEM).

Keywords: Axial Flux Permanent Magnet (AFPM) Machine, Design Algorithm, Finite Element Method (FEM), TORUS

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4326 Levenberg-Marquardt Algorithm for Karachi Stock Exchange Share Rates Forecasting

Authors: Syed Muhammad Aqil Burney, Tahseen Ahmed Jilani, C. Ardil

Abstract:

Financial forecasting is an example of signal processing problems. A number of ways to train/learn the network are available. We have used Levenberg-Marquardt algorithm for error back-propagation for weight adjustment. Pre-processing of data has reduced much of the variation at large scale to small scale, reducing the variation of training data.

Keywords: Gradient descent method, jacobian matrix.Levenberg-Marquardt algorithm, quadratic error surfaces,

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4325 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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4324 Adaptive Total Variation Based on Feature Scale

Authors: Jianbo Hu, Hongbao Wang

Abstract:

The widely used Total Variation de-noising algorithm can preserve sharp edge, while removing noise. However, since fixed regularization parameter over entire image, small details and textures are often lost in the process. In this paper, we propose a modified Total Variation algorithm to better preserve smaller-scaled features. This is done by allowing an adaptive regularization parameter to control the amount of de-noising in any region of image, according to relative information of local feature scale. Experimental results demonstrate the efficient of the proposed algorithm. Compared with standard Total Variation, our algorithm can better preserve smaller-scaled features and show better performance.

Keywords: Adaptive, de-noising, feature scale, regularizationparameter, Total Variation.

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4323 A Modified Fuzzy C-Means Algorithm for Natural Data Exploration

Authors: Binu Thomas, Raju G., Sonam Wangmo

Abstract:

In Data mining, Fuzzy clustering algorithms have demonstrated advantage over crisp clustering algorithms in dealing with the challenges posed by large collections of vague and uncertain natural data. This paper reviews concept of fuzzy logic and fuzzy clustering. The classical fuzzy c-means algorithm is presented and its limitations are highlighted. Based on the study of the fuzzy c-means algorithm and its extensions, we propose a modification to the cmeans algorithm to overcome the limitations of it in calculating the new cluster centers and in finding the membership values with natural data. The efficiency of the new modified method is demonstrated on real data collected for Bhutan-s Gross National Happiness (GNH) program.

Keywords: Adaptive fuzzy clustering, clustering, fuzzy logic, fuzzy clustering, c-means.

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4322 A Meta-Heuristic Algorithm for Vertex Covering Problem Based on Gravity

Authors: S. Raja Balachandar, K.Kannan

Abstract:

A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving vertex covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the vertex covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.

Keywords: Vertex covering Problem, Velocity, Gravitational Force, Newton's Law, Meta Heuristic, Combinatorial optimization.

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4321 Algorithm Design and Performance Evaluation of Equivalent CMOS Model

Authors: Parvinder S. Sandhu, Iqbaldeep Kaur, Amit Verma, Inderpreet Kaur, Birinderjit S. Kalyan

Abstract:

This work is a proposed model of CMOS for which the algorithm has been created and then the performance evaluation of this proposition has been done. In this context, another commonly used model called ZSTT (Zero Switching Time Transient) model is chosen to compare all the vital features and the results for the Proposed Equivalent CMOS are promising. In the end, the excerpts of the created algorithm are also included

Keywords: Dual Capacitor Model, ZSTT, CMOS, SPICEMacro-Model.

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4320 A Fuzzy Classifier with Evolutionary Design of Ellipsoidal Decision Regions

Authors: Leehter Yao, Kuei-Song Weng, Cherng-Dir Huang

Abstract:

A fuzzy classifier using multiple ellipsoids approximating decision regions for classification is to be designed in this paper. An algorithm called Gustafson-Kessel algorithm (GKA) with an adaptive distance norm based on covariance matrices of prototype data points is adopted to learn the ellipsoids. GKA is able toadapt the distance norm to the underlying distribution of the prototypedata points except that the sizes of ellipsoids need to be determined a priori. To overcome GKA's inability to determine appropriate size ofellipsoid, the genetic algorithm (GA) is applied to learn the size ofellipsoid. With GA combined with GKA, it will be shown in this paper that the proposed method outperforms the benchmark algorithms as well as algorithms in the field.

Keywords: Ellipsoids, genetic algorithm, classification, fuzzyc-means (FCM)

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4319 A Hybrid CamShift and l1-Minimization Video Tracking Algorithm

Authors: Clark Van Dam, Gagan Mirchandani

Abstract:

The Continuously Adaptive Mean-Shift (CamShift) algorithm, incorporating scene depth information is combined with the l1-minimization sparse representation based method to form a hybrid kernel and state space-based tracking algorithm. We take advantage of the increased efficiency of the former with the robustness to occlusion property of the latter. A simple interchange scheme transfers control between algorithms based upon drift and occlusion likelihood. It is quantified by the projection of target candidates onto a depth map of the 2D scene obtained with a low cost stereo vision webcam. Results are improved tracking in terms of drift over each algorithm individually, in a challenging practical outdoor multiple occlusion test case.

Keywords: CamShift, l1-minimization, particle filter, stereo vision, video tracking.

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4318 An Efficient Algorithm for Reliability Lower Bound of Distributed Systems

Authors: Mohamed H. S. Mohamed, Yang Xiao-zong, Liu Hong-wei, Wu Zhi-bo

Abstract:

The reliability of distributed systems and computer networks have been modeled by a probabilistic network or a graph G. Computing the residual connectedness reliability (RCR), denoted by R(G), under the node fault model is very useful, but is an NP-hard problem. Since it may need exponential time of the network size to compute the exact value of R(G), it is important to calculate its tight approximate value, especially its lower bound, at a moderate calculation time. In this paper, we propose an efficient algorithm for reliability lower bound of distributed systems with unreliable nodes. We also applied our algorithm to several typical classes of networks to evaluate the lower bounds and show the effectiveness of our algorithm.

Keywords: Distributed systems, probabilistic network, residual connectedness reliability, lower bound.

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4317 A Novel In-Place Sorting Algorithm with O(n log z) Comparisons and O(n log z) Moves

Authors: Hanan Ahmed-Hosni Mahmoud, Nadia Al-Ghreimil

Abstract:

In-place sorting algorithms play an important role in many fields such as very large database systems, data warehouses, data mining, etc. Such algorithms maximize the size of data that can be processed in main memory without input/output operations. In this paper, a novel in-place sorting algorithm is presented. The algorithm comprises two phases; rearranging the input unsorted array in place, resulting segments that are ordered relative to each other but whose elements are yet to be sorted. The first phase requires linear time, while, in the second phase, elements of each segment are sorted inplace in the order of z log (z), where z is the size of the segment, and O(1) auxiliary storage. The algorithm performs, in the worst case, for an array of size n, an O(n log z) element comparisons and O(n log z) element moves. Further, no auxiliary arithmetic operations with indices are required. Besides these theoretical achievements of this algorithm, it is of practical interest, because of its simplicity. Experimental results also show that it outperforms other in-place sorting algorithms. Finally, the analysis of time and space complexity, and required number of moves are presented, along with the auxiliary storage requirements of the proposed algorithm.

Keywords: Auxiliary storage sorting, in-place sorting, sorting.

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4316 Some Characterizations of Isotropic Curves In the Euclidean Space

Authors: Süha Yılmaz, Melih Turgut

Abstract:

The curves, of which the square of the distance between the two points equal to zero, are called minimal or isotropic curves [4]. In this work, first, necessary and sufficient conditions to be a Pseudo Helix, which is a special case of such curves, are presented. Thereafter, it is proven that an isotropic curve-s position vector and pseudo curvature satisfy a vector differential equation of fourth order. Additionally, In view of solution of mentioned equation, position vector of pseudo helices is obtained.

Keywords: Classical Differential Geometry, Euclidean space, Minimal Curves, Isotropic Curves, Pseudo Helix.

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4315 Orthogonal Regression for Nonparametric Estimation of Errors-in-Variables Models

Authors: Anastasiia Yu. Timofeeva

Abstract:

Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: Grade point average, orthogonal regression, penalized regression spline, locally weighted regression.

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4314 An Iterative Algorithm for KLDA Classifier

Authors: D.N. Zheng, J.X. Wang, Y.N. Zhao, Z.H. Yang

Abstract:

The Linear discriminant analysis (LDA) can be generalized into a nonlinear form - kernel LDA (KLDA) expediently by using the kernel functions. But KLDA is often referred to a general eigenvalue problem in singular case. To avoid this complication, this paper proposes an iterative algorithm for the two-class KLDA. The proposed KLDA is used as a nonlinear discriminant classifier, and the experiments show that it has a comparable performance with SVM.

Keywords: Linear discriminant analysis (LDA), kernel LDA (KLDA), conjugate gradient algorithm, nonlinear discriminant classifier.

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4313 A New Approach for Image Segmentation using Pillar-Kmeans Algorithm

Authors: Ali Ridho Barakbah, Yasushi Kiyoki

Abstract:

This paper presents a new approach for image segmentation by applying Pillar-Kmeans algorithm. This segmentation process includes a new mechanism for clustering the elements of high-resolution images in order to improve precision and reduce computation time. The system applies K-means clustering to the image segmentation after optimized by Pillar Algorithm. The Pillar algorithm considers the pillars- placement which should be located as far as possible from each other to withstand against the pressure distribution of a roof, as identical to the number of centroids amongst the data distribution. This algorithm is able to optimize the K-means clustering for image segmentation in aspects of precision and computation time. It designates the initial centroids- positions by calculating the accumulated distance metric between each data point and all previous centroids, and then selects data points which have the maximum distance as new initial centroids. This algorithm distributes all initial centroids according to the maximum accumulated distance metric. This paper evaluates the proposed approach for image segmentation by comparing with K-means and Gaussian Mixture Model algorithm and involving RGB, HSV, HSL and CIELAB color spaces. The experimental results clarify the effectiveness of our approach to improve the segmentation quality in aspects of precision and computational time.

Keywords: Image segmentation, K-means clustering, Pillaralgorithm, color spaces.

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4312 Research on Static and Dynamic Behavior of New Combination of Aluminum Honeycomb Panel and Rod Single-layer Latticed Shell

Authors: Xu Chen, Zhao Caiqi

Abstract:

In addition to the advantages of light weight, resistant corrosion and ease of processing, aluminum is also applied to the long-span spatial structures. However, the elastic modulus of aluminum is lower than that of the steel. This paper combines the high performance aluminum honeycomb panel with the aluminum latticed shell, forming a new panel-and-rod composite shell structure. Through comparative analysis between the static and dynamic performance, the conclusion that the structure of composite shell is noticeably superior to the structure combined before.

Keywords: Combination of aluminum honeycomb panel and rod latticed shell, dynamic performance, response spectrum analysis, seismic properties.

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4311 Approximation Algorithm for the Shortest Approximate Common Superstring Problem

Authors: A.S. Rebaï, M. Elloumi

Abstract:

The Shortest Approximate Common Superstring (SACS) problem is : Given a set of strings f={w1, w2, ... , wn}, where no wi is an approximate substring of wj, i ≠ j, find a shortest string Sa, such that, every string of f is an approximate substring of Sa. When the number of the strings n>2, the SACS problem becomes NP-complete. In this paper, we present a greedy approximation SACS algorithm. Our algorithm is a 1/2-approximation for the SACS problem. It is of complexity O(n2*(l2+log(n))) in computing time, where n is the number of the strings and l is the length of a string. Our SACS algorithm is based on computation of the Length of the Approximate Longest Overlap (LALO).

Keywords: Shortest approximate common superstring, approximation algorithms, strings overlaps, complexities.

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4310 Parallel Branch and Bound Model Using Logarithmic Sampling (PBLS) for Symmetric Traveling Salesman Problem

Authors: Sheikh Muhammad Azam, Masood-ur-Rehman, Adnan Khalid Bhatti, Nadeem Daudpota

Abstract:

Very Large and/or computationally complex optimization problems sometimes require parallel or highperformance computing for achieving a reasonable time for computation. One of the most popular and most complicate problems of this family is “Traveling Salesman Problem". In this paper we have introduced a Branch & Bound based algorithm for the solution of such complicated problems. The main focus of the algorithm is to solve the “symmetric traveling salesman problem". We reviewed some of already available algorithms and felt that there is need of new algorithm which should give optimal solution or near to the optimal solution. On the basis of the use of logarithmic sampling, it was found that the proposed algorithm produced a relatively optimal solution for the problem and results excellent performance as compared with the traditional algorithms of this series.

Keywords: Parallel execution, symmetric traveling salesman problem, branch and bound algorithm, logarithmic sampling.

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4309 A New Method in Detection of Ceramic Tiles Color Defects Using Genetic C-Means Algorithm

Authors: Mahkameh S. Mostafavi

Abstract:

In this paper an algorithm is used to detect the color defects of ceramic tiles. First the image of a normal tile is clustered using GCMA; Genetic C-means Clustering Algorithm; those results in best cluster centers. C-means is a common clustering algorithm which optimizes an objective function, based on a measure between data points and the cluster centers in the data space. Here the objective function describes the mean square error. After finding the best centers, each pixel of the image is assigned to the cluster with closest cluster center. Then, the maximum errors of clusters are computed. For each cluster, max error is the maximum distance between its center and all the pixels which belong to it. After computing errors all the pixels of defected tile image are clustered based on the centers obtained from normal tile image in previous stage. Pixels which their distance from their cluster center is more than the maximum error of that cluster are considered as defected pixels.

Keywords: C-Means algorithm, color spaces, Genetic Algorithm, image clustering.

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4308 An efficient Activity Network Reduction Algorithm based on the Label Correcting Tracing Algorithm

Authors: Weng Ming Chu

Abstract:

When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the non-identical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by Adlakha & Kulkarni [1], many methods and algorithms have been put forward in attempt to resolve this issue, but most have encountered this same large-size network problem. Therefore, in this research, we focus on network reduction through a Series/Parallel combined mechanism. Our suggested algorithm, named the Activity Network Reduction Algorithm (ANRA), can efficiently transfer a large-size network into an S/P Irreducible Network (SPIN). SPIN can enhance stochastic network analysis, as well as serve as the judgment of symmetry for the Graph Theory.

Keywords: Series/Parallel network, Stochastic network, Network reduction, Interdictive Graph, Complexity Index.

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4307 An Enhanced Cryptanalytic Attack on Knapsack Cipher using Genetic Algorithm

Authors: Poonam Garg, Aditya Shastri, D.C. Agarwal

Abstract:

With the exponential growth of networked system and application such as eCommerce, the demand for effective internet security is increasing. Cryptology is the science and study of systems for secret communication. It consists of two complementary fields of study: cryptography and cryptanalysis. The application of genetic algorithms in the cryptanalysis of knapsack ciphers is suggested by Spillman [7]. In order to improve the efficiency of genetic algorithm attack on knapsack cipher, the previously published attack was enhanced and re-implemented with variation of initial assumptions and results are compared with Spillman results. The experimental result of research indicates that the efficiency of genetic algorithm attack on knapsack cipher can be improved with variation of initial assumption.

Keywords: Genetic Algorithm, Knapsack cipher, Key search.

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4306 A Novel Probablistic Strategy for Modeling Photovoltaic Based Distributed Generators

Authors: Engy A. Mohamed, Yasser G. Hegazy

Abstract:

This paper presents a novel algorithm for modeling photovoltaic based distributed generators for the purpose of optimal planning of distribution networks. The proposed algorithm utilizes sequential Monte Carlo method in order to accurately consider the stochastic nature of photovoltaic based distributed generators. The proposed algorithm is implemented in MATLAB environment and the results obtained are presented and discussed.

Keywords: Comulative distribution function, distributed generation, Monte Carlo.

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4305 Magnetic Field Analysis for a Distribution Transformer with Unbalanced Load Conditions by using 3-D Finite Element Method

Authors: P. Meesuk, T. Kulworawanichpong, P. Pao-la-or

Abstract:

This paper proposes a set of quasi-static mathematical model of magnetic fields caused by high voltage conductors of distribution transformer by using a set of second-order partial differential equation. The modification for complex magnetic field analysis and time-harmonic simulation are also utilized. In this research, transformers were study in both balanced and unbalanced loading conditions. Computer-based simulation utilizing the threedimensional finite element method (3-D FEM) is exploited as a tool for visualizing magnetic fields distribution volume a distribution transformer. Finite Element Method (FEM) is one among popular numerical methods that is able to handle problem complexity in various forms. At present, the FEM has been widely applied in most engineering fields. Even for problems of magnetic field distribution, the FEM is able to estimate solutions of Maxwell-s equations governing the power transmission systems. The computer simulation based on the use of the FEM has been developed in MATLAB programming environment.

Keywords: Distribution Transformer, Magnetic Field, Load Unbalance, 3-D Finite Element Method (3-D FEM)

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4304 Load Modeling for Power Flow and Transient Stability Computer Studies at BAKHTAR Network

Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

A method has been developed for preparing load models for power flow and stability. The load modeling (LOADMOD) computer software transforms data on load class mix, composition, and characteristics into the from required for commonly–used power flow and transient stability simulation programs. Typical default data have been developed for load composition and characteristics. This paper defines LOADMOD software and describes the dynamic and static load modeling techniques used in this software and results of initial testing for BAKHTAR power system.

Keywords: Load Modelling, Static, Power Flow.

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4303 Vision Based People Tracking System

Authors: Boukerch Haroun, Luo Qing Sheng, Li Hua Shi, Boukraa Sebti

Abstract:

In this paper we present the design and the implementation of a target tracking system where the target is set to be a moving person in a video sequence. The system can be applied easily as a vision system for mobile robot. The system is composed of two major parts the first is the detection of the person in the video frame using the SVM learning machine based on the “HOG” descriptors. The second part is the tracking of a moving person it’s done by using a combination of the Kalman filter and a modified version of the Camshift tracking algorithm by adding the target motion feature to the color feature, the experimental results had shown that the new algorithm had overcame the traditional Camshift algorithm in robustness and in case of occlusion.

Keywords: Camshift Algorithm, Computer Vision, Kalman Filter, Object tracking.

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4302 Sensor-Based Motion Planning for a Car-like Robot Based On Bug Family Algorithms

Authors: Dong-Hyung Kim, Ji Yeong Lee, Chang-Soo Han

Abstract:

This paper presents a sensor-based motion planning algorithm for 3-DOF car-like robots with a nonholonomic constraint. Similar to the classic Bug family algorithms, the proposed algorithm enables the car-like robot to navigate in a completely unknown environment using only the range sensor information. The car-like robot uses the local range sensor view to determine the local path so that it moves towards the goal. To guarantee that the robot can approach the goal, the two modes of motion are repeated, termed motion-to-goal and wall-following. The motion-to-goal behavior lets the robot directly move toward the goal, and the wall-following behavior makes the robot circumnavigate the obstacle boundary until it meets the leaving condition. For each behavior, the nonholonomic motion for the car-like robot is planned in terms of the instantaneous turning radius. The proposed algorithm is implemented to the real robot and the experimental results show the performance of proposed algorithm.

Keywords: Motion planning, car-like robot, bug algorithm, autonomous motion planning, nonholonomic constraint.

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4301 Edit Distance Algorithm to Increase Storage Efficiency of Javanese Corpora

Authors: Aji P. Wibawa, Andrew Nafalski, Neil Murray, Wayan F. Mahmudy

Abstract:

Since the one-to-one word translator does not have the facility to translate pragmatic aspects of Javanese, the parallel text alignment model described uses a phrase pair combination. The algorithm aligns the parallel text automatically from the beginning to the end of each sentence. Even though the results of the phrase pair combination outperform the previous algorithm, it is still inefficient. Recording all possible combinations consume more space in the database and time consuming. The original algorithm is modified by applying the edit distance coefficient to improve the data-storage efficiency. As a result, the data-storage consumption is 90% reduced as well as its learning period (42s).

Keywords: edit distance coefficient, Javanese, parallel text alignment, phrase pair combination

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