Search results for: quadratic convex function.

Authors: Tayeb Lardjane, Rabah Messaci

Abstract:

We consider a network of two M/M/1 parallel queues having the same poisonnian arrival stream with rate λ. Upon his arrival to the system a customer heads to the shortest queue and stays until being served. If the two queues have the same length, an arriving customer chooses one of the two queues with the same probability. Each duration of service in the two queues is an exponential random variable with rate μ and no jockeying is permitted between the two queues. A new numerical method, based on linear programming and convex optimization, is performed for the computation of the steady state solution of the system.

Keywords: Steady state solution, matrix formulation, convex set, shortest queue, linear programming.

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Authors: Chung To Kong, Siu Ming Yiu

Abstract:

Rubik's cube was invented in 1974. Since then, speedcubers all over the world try their best to break the world record again and again. The newest record is 3.47 seconds. There are many factors that affect the timing including turns per second (tps), algorithm, finger trick, and hardware of the cube. In this paper, the lower bound of the cube solving time will be discussed using convex optimization. Extended analysis of the world records will be used to understand how to improve the timing. With the understanding of each part of the solving step, the paper suggests a list of speed improvement technique. Based on the analysis of the world record, there is a high possibility that the 3 seconds mark will be broken soon.

Keywords: Rubik’s cube, convex optimization, speed cubing, CFOP.

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Authors: Amir Azizi, Amir Yazid b. Ali, Loh Wei Ping, Mohsen Mohammadzadeh

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Uncertainties of a serial production line affect on the production throughput. The uncertainties cannot be prevented in a real production line. However the uncertain conditions can be controlled by a robust prediction model. Thus, a hybrid model including autoregressive integrated moving average (ARIMA) and multiple polynomial regression, is proposed to model the nonlinear relationship of production uncertainties with throughput. The uncertainties under consideration of this study are demand, breaktime, scrap, and lead-time. The nonlinear relationship of production uncertainties with throughput are examined in the form of quadratic and cubic regression models, where the adjusted R-squared for quadratic and cubic regressions was 98.3% and 98.2%. We optimized the multiple quadratic regression (MQR) by considering the time series trend of the uncertainties using ARIMA model. Finally the hybrid model of ARIMA and MQR is formulated by better adjusted R-squared, which is 98.9%.

Keywords: ARIMA, multiple polynomial regression, production throughput, uncertainties

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Authors: R. K. Saxena, Ravi Saxena

Abstract:

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

Keywords: Fox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

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Authors: Ellips Masehian, Golnaz Habibi

Abstract:

This paper presents a novel algorithm for path planning of mobile robots in known 3D environments using Binary Integer Programming (BIP). In this approach the problem of path planning is formulated as a BIP with variables taken from 3D Delaunay Triangulation of the Free Configuration Space and solved to obtain an optimal channel made of connected tetrahedrons. The 3D channel is then partitioned into convex fragments which are used to build safe and short paths within from Start to Goal. The algorithm is simple, complete, does not suffer from local minima, and is applicable to different workspaces with convex and concave polyhedral obstacles. The noticeable feature of this algorithm is that it is simply extendable to n-D Configuration spaces.

Keywords: 3D C-space, Binary Integer Programming (BIP), Delaunay Tessellation, Robot Motion Planning.

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Authors: Chuanyun Gu

Abstract:

By using fixed point theorems for a class of generalized concave and convex operators, the positive solution of nonlinear fractional differential equation with integral boundary conditions is studied, where n ≥ 3 is an integer, μ is a parameter and 0 ≤ μ < α. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it. Finally, two examples are given to illustrate our results.

Keywords: Fractional differential equation, positive solution, existence and uniqueness, fixed point theorem, generalized concave and convex operator, integral boundary conditions.

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, we investigate dynamics of 2n almost periodic attractors for Cohen-Grossberg neural networks (CGNNs) with variable and distribute time delays. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of CGNNs into 2n compact convex subsets. Then the existence of 2n almost periodic solutions lying in compact convex subsets is attained due to employment of the theory of exponential dichotomy and Schauder-s fixed point theorem. Meanwhile, we derive some new criteria for the networks to converge toward these 2n almost periodic solutions and exponential attracting domains are also given correspondingly.

Keywords: CGNNs, almost periodic solution, invariant basins, attracting domains.

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Authors: Roozbeh Molavi, Davood A. Khaburi

Abstract:

The permanent magnet synchronous motor (PMSM) is very useful in many applications. Vector control of PMSM is popular kind of its control. In this paper, at first an optimal vector control for PMSM is designed and then results are compared with conventional vector control. Then, it is assumed that the measurements are noisy and linear quadratic Gaussian (LQG) methodology is used to filter the noises. The results of noisy optimal vector control and filtered optimal vector control are compared to each other. Nonlinearity of PMSM and existence of inverter in its control circuit caused that the system is nonlinear and time-variant. With deriving average model, the system is changed to nonlinear time-invariant and then the nonlinear system is converted to linear system by linearization of model around average values. This model is used to optimize vector control then two optimal vector controls are compared to each other. Simulation results show that the performance and robustness to noise of the control system has been highly improved.

Keywords: Kalman filter, Linear quadratic Gaussian (LQG), Linear quadratic regulator (LQR), Permanent-Magnet synchronousmotor (PMSM).

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Authors: Ning Dong, Bo Yu

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We are concerned with a class of quadratic matrix equations arising from the overdamped mass-spring system. By exploring the structure of coefficient matrices, we propose a fast cyclic reduction algorithm to calculate the extreme solutions of the equation. Numerical experiments show that the proposed algorithm outperforms the original cyclic reduction and the structure-preserving doubling algorithm.

Keywords: Fast algorithm, Cyclic reduction, Overdampedquadratic matrix equation, Structure-preserving doubling algorithm

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Authors: Salah R. Al Zaidee, Ali S. Mahdi

Abstract:

Except for simple problems of statically determinate structures, optimum design problems in structural engineering have implicit objective functions where structural analysis and design are essential within each searching loop. With these implicit functions, the structural engineer is usually enforced to write his/her own computer code for analysis, design, and searching for optimum design among many feasible candidates and cannot take advantage of available software for structural analysis, design, and searching for the optimum solution. The meta-model is a regression model used to transform an implicit objective function into objective one and leads in turn to decouple the structural analysis and design processes from the optimum searching process. With the meta-model, well-known software for structural analysis and design can be used in sequence with optimum searching software. In this paper, the meta-model has been used to develop an explicit objective function for plane steel frames subjected to dead, live, and seismic forces. Frame topology is assumed as predefined based on architectural and functional requirements. Columns and beams sections and different connections details are the main design variables in this study. Columns and beams are grouped to reduce the number of design variables and to make the problem similar to that adopted in engineering practice. Data for the implicit objective function have been generated based on analysis and assessment for many design proposals with CSI SAP software. These data have been used later in SPSS software to develop a pure quadratic nonlinear regression model for the explicit objective function. Good correlations with a coefficient, R², in the range from 0.88 to 0.99 have been noted between the original implicit functions and the corresponding explicit functions generated with meta-model.

Keywords: Meta-modal, objective function, steel frames, seismic analysis, design.

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Authors: Jui-Sheng Lin, Yi-Sung Yang, Meei-Ling Hung, Teh-Lu Liao, Jun-Juh Yan

Abstract:

The global chaos synchronization for a class of time-delayed power systems is investigated via observer-based approach. By employing the concepts of quadratic stability theory and generalized system model, a new sufficient criterion for constructing an observer is deduced. In contrast to the previous works, this paper proposes a theoretical and systematic design procedure to realize chaos synchronization for master-slave power systems. Finally, an illustrative example is given to show the applicability of the obtained scheme.

Keywords: Chaos, Synchronization, Quadratic stability theory, Observer

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Authors: M. Hadi Mashinchi, M. Reza Mashinchi, Siti Mariyam H. J. Shamsuddin

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In this paper a genetic algorithms approach for solving the linear and quadratic fuzzy equations Ãx̃=B̃ and Ãx̃² + B̃x̃=C̃ , where Ã, B̃, C̃ and x̃ are fuzzy numbers is proposed by genetic algorithms. Our genetic based method initially starts with a set of random fuzzy solutions. Then in each generation of genetic algorithms, the solution candidates converge more to better fuzzy solution x̃_b . In this proposed method the final reached x̃_b is not only restricted to fuzzy triangular and it can be fuzzy number.

Keywords: Fuzzy coefficient, fuzzy equation, genetic algorithms.

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Authors: Abdulrahman S. Alturki, John S. Loomis

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This paper discusses a corner detection algorithm for camera calibration. Calibration is a necessary step in many computer vision and image processing applications. Robust corner detection for an image of a checkerboard is required to determine intrinsic and extrinsic parameters. In this paper, an algorithm for fully automatic and robust X-corner detection is presented. Checkerboard corner points are automatically found in each image without user interaction or any prior information regarding the number of rows or columns. The approach represents each X-corner with a quadratic fitting function. Using the fact that the X-corners are saddle points, the coefficients in the fitting function are used to identify each corner location. The automation of this process greatly simplifies calibration. Our method is robust against noise and different camera orientations. Experimental analysis shows the accuracy of our method using actual images acquired at different camera locations and orientations.

Keywords: Camera Calibration, Corner Detector, Saddle Points, X-Corners.

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Authors: Mohd Amaluddin Yusoff

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In this paper, we consider the design of pulse shaping filter using orthogonal Hermite-Rodriguez basis functions. The pulse shaping filter design problem has been formulated and solved as a quadratic programming problem with linear inequality constraints. Compared with the existing approaches reported in the literature, the use of Hermite-Rodriguez functions offers an effective alternative to solve the constrained filter synthesis problem. This is demonstrated through a numerical example which is concerned with the design of an equalization filter for a digital transmission channel.

Keywords: channel equalization filter, Hermite-Rodriguez, pulseshaping filter, quadratic programming.

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Authors: Shiang-Hwua Yu, Han-Sheng Tseng

Abstract:

This paper presents a novel sinusoidal modulation scheme that features least correlated noise and high linearity. The modulation circuit, which is composed of a quantizer, a resonator, and a comparator, is capable of eliminating correlated modulation noise while doing modulation. The proposed modulation scheme combined with the linear quadratic optimal control is applied to a single-phase voltage source inverter and validated with the experiment results. The experiments show that the inverter supplies stable 60Hz 110V AC power with a total harmonic distortion of less than 1%, under the DC input variation from 190 V to 300 V and the output power variation from 0 to 600 W.

Keywords: Pulse width modulation, feedback dithering, linear quadratic control, inverter.

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Authors: S.C. Swain, S. Panda, A.K. Mohanty, C. Ardil

Abstract:

This paper presents the applications of computational intelligence techniques to economic load dispatch problems. The fuel cost equation of a thermal plant is generally expressed as continuous quadratic equation. In real situations the fuel cost equations can be discontinuous. In view of the above, both continuous and discontinuous fuel cost equations are considered in the present paper. First, genetic algorithm optimization technique is applied to a 6- generator 26-bus test system having continuous fuel cost equations. Results are compared to conventional quadratic programming method to show the superiority of the proposed computational intelligence technique. Further, a 10-generator system each with three fuel options distributed in three areas is considered and particle swarm optimization algorithm is employed to minimize the cost of generation. To show the superiority of the proposed approach, the results are compared with other published methods.

Keywords: Economic Load Dispatch, Continuous Fuel Cost, Quadratic Programming, Real-Coded Genetic Algorithm, Discontinuous Fuel Cost, Particle Swarm Optimization.

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Authors: Anis Gharbi, Mohamed Haouari, Talel Ladhari, Mohamed Ali Rakrouki

Abstract:

We address a complex scheduling problem arising in the wood panel industry with the objective of minimizing a quadratic function of job tardiness. The proposed solution strategy, which is based on an effective genetic algorithm, has been coded and implemented within a major Tunisian company, leader in the wood panel manufacturing. Preliminary experimental results indicate significant decrease of delivery times.

Keywords: Genetic algorithm, heuristic, hybrid flowshop, total weighted squared tardiness.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of exponential stability analysis for recurrent neural networks with time-varying delay.By establishing a suitable augmented LyapunovCKrasovskii function and a novel sufficient condition is obtained to guarantee the exponential stability of the considered system.In order to get a less conservative results of the condition,zero equalities and reciprocally convex approach are employed. The several exponential stability criterion proposed in this paper is simpler and effective. A numerical example is provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Exponential stability , Neural networks, Linear matrix inequality, Lyapunov-Krasovskii, Time-varying.

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Authors: I. A. Farhat

Abstract:

The The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: Artificial Immune System (AIS), Dynamic Economic Dispatch (DED).

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Authors: Igor Astrov, Mikhail Pikkov, Rein Paluoja

Abstract:

This paper focuses on a critical component of the situational awareness (SA), the control of autonomous vertical flight for vectored thrust aerial vehicle (VTAV). With the SA strategy, we proposed a linear-quadratic-Gaussian (LQG) flight control procedure for an unmanned helicopter model with vectored thrust configuration. This LQG control for chosen model of VTAV has been verified by simulation of take-off and landing maneuvers using software package Simulink and demonstrated good performance for fast flight stabilization of model, consequently, fast SA with economy in energy can be asserted during search-and-rescue operations.

Keywords: Linear-Quadratic-Gaussian (LQG) controller, situational awareness, vectored thrust aerial vehicle.

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Authors: Ayad Al-Mahturi, Herman Wahid

Abstract:

This paper presents an optimal state feedback controller based on Linear Quadratic Regulator (LQR) for a two-rotor aero-dynamical system (TRAS). TRAS is a highly nonlinear multi-input multi-output (MIMO) system with two degrees of freedom and cross coupling. There are two parameters that define the behavior of LQR controller: state weighting matrix and control weighting matrix. The two parameters influence the performance of LQR. Particle Swarm Optimization (PSO) is proposed to optimally tune weighting matrices of LQR. The major concern of using LQR controller is to stabilize the TRAS by making the beam move quickly and accurately for tracking a trajectory or to reach a desired altitude. The simulation results were carried out in MATLAB/Simulink. The system is decoupled into two single-input single-output (SISO) systems. Comparing the performance of the optimized proportional, integral and derivative (PID) controller provided by INTECO, results depict that LQR controller gives a better performance in terms of both transient and steady state responses when PSO is performed.

Keywords: Linear quadratic regulator, LQR controller, optimal control, particle swarm optimization, PSO, two-rotor aero-dynamical system, TRAS.

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Authors: I. A. Farhat

Abstract:

The dynamic economic dispatch (DED) problem is one of the complex constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand.  Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: Artificial Immune System (AIS), Dynamic Economic Dispatch (DED).

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Authors: Zhihua Yang, Lihua Yang

Abstract:

This paper makes a detailed analysis regarding the definition of the intrinsic mode function and proves that Condition 1 of the intrinsic mode function can really be deduced from Condition 2. Finally, an improved definition of the intrinsic mode function is given.

Keywords: Empirical Mode Decomposition (EMD), Hilbert-Huang transform(HHT), Intrinsic Mode Function(IMF).

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Authors: Marios Poulos, Sozon Papavlasopoulos, V. S. Belesiotis

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In the proposed method for Web page-ranking, a novel theoretic model is introduced and tested by examples of order relationships among IP addresses. Ranking is induced using a convexity feature, which is learned according to these examples using a self-organizing procedure. We consider the problem of selforganizing learning from IP data to be represented by a semi-random convex polygon procedure, in which the vertices correspond to IP addresses. Based on recent developments in our regularization theory for convex polygons and corresponding Euclidean distance based methods for classification, we develop an algorithmic framework for learning ranking functions based on a Computational Geometric Theory. We show that our algorithm is generic, and present experimental results explaining the potential of our approach. In addition, we explain the generality of our approach by showing its possible use as a visualization tool for data obtained from diverse domains, such as Public Administration and Education.

Keywords: Computational Geometry, Education, e-Governance, Semantic Web.

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Authors: T. Mathumathi, S. Ganesh, R. Gunabalan

Abstract:

This work presents an approach for AC load flow based centralized model for congestion management in the forward markets. In this model, transaction maximizes its profit under the limits of transmission line capacities allocated by Independent System Operator (ISO). The voltage and reactive power impact of the system are also incorporated in this model. Genetic algorithm is used to solve centralized congestion management problem for multilateral transactions. Results obtained for centralized model using genetic algorithm is compared with Sequential Quadratic Programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare are given. Simulation results clearly demonstrate the better performance of genetic algorithm over SQP.

Keywords: Congestion management, Genetic algorithm, Sequential quadratic programming.

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Authors: Huaizhi Han, Bingxi Li, Yurong He, Rushan Bie, Zhao Wu

Abstract:

The flow and heat transfer mechanism in convex corrugated tubes have been investigated through numerical simulations in this paper. Two kinds of tube types named as symmetric corrugated tube (SCT) and asymmetric corrugated tube (ACT) are modeled and studied numerically based on the RST model. The predictive capability of RST model is examined in the corrugation wall in order to check the reliability of RST model under the corrugation wall condition. We propose a comparison between the RST modelling the corrugation wall with existing direct numerical simulation of Maaß C and Schumann U [14]. The numerical results pressure coefficient at different profiles between RST and DNS are well matched. The influences of large corrugation tough radii to heat transfer and flow characteristic had been considered. Flow and heat transfer comparison between SCT and ACT had been discussed. The numerical results show that ACT exhibits higher overall heat transfer performance than SCT.

Keywords: Asymmetric corrugated tube, RST, DNS, flow and heat transfer mechanism.

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Authors: Shrawan Kumar, D. K. Lobiyal

Abstract:

In this paper, we propose improved versions of DVHop algorithm as QDV-Hop algorithm and UDV-Hop algorithm for better localization without the need for additional range measurement hardware. The proposed algorithm focuses on third step of DV-Hop, first error terms from estimated distances between unknown node and anchor nodes is separated and then minimized. In the QDV-Hop algorithm, quadratic programming is used to minimize the error to obtain better localization. However, quadratic programming requires a special optimization tool box that increases computational complexity. On the other hand, UDV-Hop algorithm achieves localization accuracy similar to that of QDV-Hop by solving unconstrained optimization problem that results in solving a system of linear equations without much increase in computational complexity. Simulation results show that the performance of our proposed schemes (QDV-Hop and UDV-Hop) is superior to DV-Hop and DV-Hop based algorithms in all considered scenarios.

Keywords: Wireless sensor networks, Error term, DV-Hop algorithm, Localization.

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Authors: Schehrazad Selmane

Abstract:

According to Hermite there exists only a finite number of number fields having a given degree, and a given value of the discriminant, nevertheless this number is not known generally. The determination of a maximum number of number fields of degree 10 having a given discriminant that contain a subfield of degree 5 having a fixed class number, narrow class number and Galois group is the purpose of this work. The constructed lists of the first coincidences of 52 (resp. 50, 40, 48, 22, 6) nonisomorphic number fields with same discriminant of degree 10 of signature (6,2) (resp. (4,3), (8,1), (2,4), (0,5), (10,0)) containing a quintic field. For each field in the lists, we indicate its discriminant, the discriminant of its subfield, a relative polynomial generating the field over its quintic field and its relative discriminant, the corresponding polynomial over Q and its Galois closure are presented with concluding remarks.

Keywords: Discriminant, nonisomorphic fields, quintic fields, relative quadratic extensions.

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Authors: Rashid S. S., Alam M. Z.

Abstract:

A statistical optimization of the saccharification process of EFB was studied. The statistical analysis was done by applying faced centered central composite design (FCCCD) under response surface methodology (RSM). In this investigation, EFB dose, enzyme dose and saccharification period was examined, and the maximum 53.45% (w/w) yield of reducing sugar was found with 4% (w/v) of EFB, 10% (v/v) of enzyme after 120 hours of incubation. It can be calculated that the conversion rate of cellulose content of the substrate is more than 75% (w/w) which can be considered as a remarkable achievement. All the variables, linear, quadratic and interaction coefficient, were found to be highly significant, other than two coefficients, one quadratic and another interaction coefficient. The coefficient of determination (R2) is 0.9898 that confirms a satisfactory data and indicated that approximately 98.98% of the variability in the dependent variable, saccharification of EFB, could be explained by this model.

Keywords: Face centered central composite design (FCCCD), Liquid state bioconversion (LSB), Palm oil mill effluent, Trichoderma reesei RUT C-30.

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Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

Abstract:

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: Fractional model predictive control, fractional order systems, thermal system.

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