ORIGINAL_ARTICLE
Haar Matrix Equations for Solving Time-Variant Linear-Quadratic Optimal Control Problems
In this paper, Haar wavelets are performed for solving continuous time-variant linear-quadratic optimal control problems. Firstly, using necessary conditions for optimality, the problem is changed into a two-boundary value problem (TBVP). Next, Haar wavelets are applied for converting the TBVP, as a system of differential equations, in to a system of matrix algebraic equations, as Haar matrix equations using Kronecker product. Then the error analysis of the proposed method is presented. Some numerical examples are given to demonstrate the efficiency of the method. The solutions converge as the number of approximate terms increase.
https://mathco.journals.pnu.ac.ir/article_5726_39c990da2be15864978cbf6bbbeb5534.pdf
2017-12-01
1
14
Time-variant linear-quadratic optimal control problems
Matrix algebraic equation
Haar wavelet
Saeed
Nezhadhosein
s_nezhadhossin@yahoo.com
1
Department of Applied Mathematics, Payame Noor University, Tehran, 193953697, Iran
LEAD_AUTHOR
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1
Betts J.T. (2010). ``Practical Methods for Optimal Control and Estimation Using Nonlinear
2
Programming", Society for Industrial and Applied Mathematics.
3
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Kirk D.E. (2004). ``Optimal Control Theory: An Introduction", Dover Publications.
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Srinivasan B., Palanki S., Bonvin D. (2003). ``Dynamic optimization of batch processes:
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I. characterization of the nominal solution'', Computers Chemical Engineering,
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27, 1, 1-26.
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bibitem{Binder2001}%4
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Binder T., Blank L., Dahmen W., Marquardt W. (2001). ``Iterative algorithms for multiscale
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state estimation", part 1: Concepts, Journal of Optimization Theory and
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Applications, 111, 3, 501--527.
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Schlegel M., Stockmann K., Binder T., Marquardt W. (2005). ``Dynamic optimization
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using adaptive control vector parameterization", Computers Chemical Engineering,
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29, 8, 1731--1751.
17
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CHEN W.L., SHIH Y.P. (1978). ``Analysis and optimal control of time-varying linear
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systems via walsh functions", International Journal of Control, 27, 6,
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917--932.
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Wang X.T. (2007). ``Numerical solutions of optimal control for time delay systems
23
by hybrid of block-pulse functions and legendre polynomials", Applied Mathematics
24
and Computation, 184, 2, 849--856.
25
bibitem{Hsiaovariational}%8
26
Hsiao C.H. (2004). ``Haar wavelet direct method for solving variational problems",
27
Mathematics and Computers in Simulation, 64, 5, 569--585.
28
bibitem{Legendre2012}%9
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El-Kady M. (2012). ``Efficient reconstructed legendre algorithm for solving linearquadratic
30
optimal control problems", Applied Mathematics Letters, 25, 7,
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1034--1040.
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bibitem{Kafash2012}%10
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Kafash B., Delavarkhalafi A., Karbassi S.M. (2012). ``Application of chebyshev polynomials to derive efficient algorithms for the
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solution of optimal control problems", Scientia Iranica, 19, 3, 795-- 805.
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Kosmol P., Pavon M. (2001). ``Solving optimal control problems by means of general
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lagrange functionals", Automatica, 37, 6, 907--913.
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Razzaghi M., Tahai A., Arabshahi A. (1989). ``Solution of linear two-point boundary
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value problems via fourier series and application to optimal control of linear
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systems", Journal of the Franklin Institute, 326, 4, 523--533.
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Aziz I., ul Islam S., Khan F. (2014). ``A new method based on haar wavelet for the
44
numerical solution of two-dimensional nonlinear integral equations", Journal
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of Computational and Applied Mathematics, 272, 0, 70--80.
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Kaur H., Mittal R., Mishra V. (2014). ``Haar wavelet solutions of nonlinear oscillator
48
equations", Applied Mathematical Modelling.
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Hsiao C.H., Wang W.J. (1998). ``State analysis and optimal control of linear timevarying
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systems via haar wavelets", Optimal Control Applications and Methods,
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19, 6, 423--433.
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Dai R., Cochran J.E., (2009). ``Wavelet collocation method for optimal control problems",
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Journal of Optimization Theory and Applications, 143, 2, 265--278.
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bibitem{Wavelet}%17
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Chui C. (1992). ``An Introduction to Wavelets", Academic Press.
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bibitem{Babolian2009}%18
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Babolian E., Shahsavaran A. (2009). ``Numerical solution of nonlinear fredholm integral
60
equations of the second kind using haar wavelets", Journal of Computational
61
and Applied Mathematics, 225, 1, 87--95.
62
ORIGINAL_ARTICLE
Application of Grey System Theory in Rainfall Estimation
Considering the fact that Iran is situated in an arid and semi-arid region, rainfall prediction for the management of water resources is very important and necessary. Researchers have proposed various prediction methods that have been utilized in such areas as water and meteorology, especially water resources management. The present study aimed at predicting rainfall amounts using Grey Prediction Method. It is a novel approach in confrontation with uncertainties in the aquiferous region of Babolrud to serve for the water resources management purposes. Therefore, expressing the concepts of Grey Prediction Methods using the collected data, at a 12-year timeframe of 2006 and 2017, rainfall prediction in 2018 and 2022 were also implemented with three methods GM(1,1), DGM(2,1) and Verhulest models. According to the calculated error and the predictive power, GM(1,1) method is better than other models and was placed within the set of good predictions. Also, we predict that in 2027, there might be a drought. According to the small samples and calculations required in this approach, the method is suggested for rainfall prediction in inexact environments. The authors can use fuzzy grey systems to predict the amount of rainfall in uncertaint environments.
https://mathco.journals.pnu.ac.ir/article_5727_17c516939caa1fdd65c38ca36d074cf4.pdf
2017-12-01
15
32
prediction
Grey system
Water resources management
Rainfall amount
Absolute prediction error
Davood
Darvishi Salookolaei
darvishidavood@yahoo.com
1
Assistant Professor, Department of Mathematics, Payame Noor University, Tehran, Iran.
LEAD_AUTHOR
Sifeng
Liu
sfliu@nuaa.edu.cn
2
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China
AUTHOR
Parvin
Babaei
p.babaeivalohi@gmail.com
3
Master of Science, Department of Mathematics, Payame Noor University, Tehran, Iran.
AUTHOR
bibitem{1} Alvisi S., Franchini M. (2012). ``Grey neural networks for river stage forecasting with uncertainty", Physics and Chemistry of the Earth, 42-44, 108--118.
1
bibitem{2} Box G.E., Jenkins G.M., Reinsel G.C., Ljung G.M. (2015). ``Time Series Analysis: Forecasting and Control", John Wiley & Sons: Hoboken, NJ, USA.
2
bibitem{3} Chuan C. (1997). ``Weather prediction using artificial neural network", Hydrology, 230, 110--119.
3
bibitem{4} Deng J.L. (1982). ``The control problems of grey systems", System Control Letter, 5, 288--294.
4
bibitem{5} Deng J.L. (1989). ``Introduction to grey system theory", The Journal of Grey System, 1(1), 1--24.
5
bibitem{6} Diez J., Deljesus, M. (2017). ``A rainfall analysis and forecasting tool", Environmental Modeling Software, 97, 243--258.
6
bibitem{7} EL-Shafie A., Mukhlisin M., Najah A.A., Taha M.R. (2011). ``Performance of artificial neural network and regression techniques for rainfall-runoff prediction", Physical Sciences, 6(8), 1997--2003.
7
bibitem{8} Kayacan E., Ulutas B., Kaynak O. (2010). ``Grey system theory-based models in time series prediction", Expert Systems with Applications 37, 1784--1789.
8
bibitem{9} Lewis C.D. (1982). ``Industrial and Business Forecasting Methods: A Practical Guide to Exponential Smoothing and Curve Fitting", Butterworth Scientific London, UK.
9
bibitem{DGM} Li J. (2012). ``The optimization DGM(2,1) model and its application", Journal of Grey System, 24(2), 181--186.
10
bibitem{10} Li, C., Cabrera D., Oliveira J.D., etc, (2016). ``Extracting repetitive transients for rotating machinery diagnosis using multiscale clustered grey infogram", Mechanical System on Signal Processing. 76-77, 157--173.
11
bibitem{11} Li K., Zhang, T. (2018). ``Forecasting Electricity Consumption Using an Improved Grey Prediction Model ", Information, 9, 1--18.
12
bibitem{12} Liu S., Lin L. (2006). ``Grey Information Theory and Practical Applications", Springer, London.
13
bibitem{13} Liu S.F., Forrest J., Yang Y.J. (2012). ``A brief introduction to grey systems theory", Grey System: Theory Application, 2(2), 89--104.
14
bibitem{14} Liu S.F., Lin Y. (2010). ``Grey Systems Theory and Applications ", Springer-Verlag, Berlin Heidelberg, 107--147.
15
bibitem{15} Liu S., Yang Y. and Forrest J. (2017). ``Grey Data Analysis", Springer, Singapore.
16
bibitem{16} Liu S., Yang Y., Xie N., Forrest J. (2016). ``New progress of grey system theory in the new millennium", Grey Systems: Theory and Application, 6(1), 2--31.
17
bibitem{17} Liu S., Zeng B., Liu J., Xie N., Yang Y. (2015). ``Four basic models of GM(1,1) and their suitable sequences", Grey Systems: Theory and Application, 5(2), 141--156.
18
bibitem{18} Miao C., Ashouri H., Hsu K., Sorooshian S., Duan Q. (2015). ``Evaluation of the PERSIANN-CDR daily rainfall estimates in capturing the behavior of extreme precipitation events over china", Journal of Hydrometeorology, 16(3), 1387--1396.
19
bibitem{19} Neiman P., White A., Ralph F., Gottas D., Gutman S. (2009). ``A water vapour flux tool for precipitation forecasting", Proceedings of the Institution of Civil Engineers Water Management, 162, 83--94.
20
bibitem{20} Obukhov A.M. (1971). ``Turbulence in an atmosphere with a non-uniform temperature", Boundary-layer Meteorology, 2(1), 7--29.
21
bibitem{21} Ren J. (2018). ``GM(1,N) method for the prediction of anaerobic digestion system and sensitivity analysis of influential factors", Bioresource Technology, 247, 1258--1261.
22
bibitem{22}Sorooshian S., AghaKouchak A., Arkin P., Eylander J., Foufoula-Georgiou E., Harmon R., et al., (2011). ``Advancing the remote sensing of precipitation", Bulletin of the American Meteorological Society. 92(10), 1271--1272.
23
bibitem{23}Tsai S.B., Xue Y. Zhang J., Chen Q., Liu Y., Zhou J., Dong W. (2017). ``Models for forecasting growth trends in renewable energy", Renewable and Sustainable Energy Reviews, 77, 1169--1178.
24
bibitem{24}Weia B., Xie A., Hu A. (2018). ``Optimal solution for novel grey polynomial prediction model", Applied Mathematical Modelling, 62, 717--727.
25
bibitem{Wen} Wen K. L., Huang Y. F. (2004). ``The development of grey Verhulst toolbox and the analysis of population saturation state in taiwan–fukien'', International Conference on Systems, Man and Cybernetics, Netherlands, 6, 5007--5012.
26
bibitem{25} Wright D., Mantilla R., Peters-Lidard C. (2017). ``A remote sensing-based tool for assessing rainfall-driven hazards", Environmental Modelling and Software. 90, 34--54.
27
bibitem{26} Wu L., Liu S., Fang Z., Xu H. (2015). ``Properties of the GM(1,1) with fractional order accumulation", Applied Mathematics and Computation, 252, 287--293.
28
bibitem{27} Ye R., Lu X., Liu H. (2013). ``Local tomography based on grey model", Neurocomputing, 101(4), 10--17.
29
bibitem{28} Zeng B., Tan Y., Xu H., Quan J., Wang L., Zhou X. (2018). ``Forecasting the electricity consumption of commercial sector in Hong Kong using a novel grey dynamic prediction model", Journal of Grey System, 30(1), 159--174.
30
ORIGINAL_ARTICLE
Two-Level Optimization Problems with Infinite Number of Convex Lower Level Constraints
This paper proposes a new form of optimization problem which is a two-level programming problem with infinitely many lower level constraints. Firstly, we consider some lower level constraint qualifications (CQs) for this problem. Then, under these CQs, we derive formula for estimating the subdifferential of its valued function. Finally, we present some necessary optimality conditions as Fritz-John type for the problem.
https://mathco.journals.pnu.ac.ir/article_5731_e315ece4d1dc99cfd4e6be1448e73889.pdf
2017-12-01
33
44
Two-level programming
Constraint qualification
Optimality conditions
Lower level problem
Nader
Kanzi
nad.kanzi@gmail.com
1
Department of Mathematics, Payame Noor University, P.O. Box. 19395-3697, Tehran, Iran
LEAD_AUTHOR
bibitem{1} Burachik R., Jeyakumar V. (2005). ``Dual condition for the convex subdifferential sum formula with applications", Journal of Convex Analysis, 15, 540-554.
1
bibitem{2} Clarke F. H. (1983). ``Optimization and non-smooth analysis", Wiley-Interscience.
2
bibitem{3} Dinh N., Goberna M. A., Lopez M. A. (2006). ``From linear to convex system: consistency, Farkas' lemma and applications", Journal of Convex Analysis, 13, 279-290.
3
bibitem{4} Dinh N., Goberna M. A., Lopez M. A., Son T. Q. (2007). ``New Farkas-type results with applications to convex infinite programmings", ESIAM: Optimization Calculus Variation, 13, 580-597.
4
bibitem{5} Dinh N., Mordukhovich B. S., Nghia T. T. A. (2010). ``Sub-differentials of value functions and optimality conditions for some class of DC and bilevel infinite and semi-infinite programs", Mathematical Programming, 123, 101-138.
5
bibitem{6} Dinh N., Nghia T. T. A., Vallet G. (2006). ``A closedness condition and its applications to DC programs with convex constraints", Preprint of the Laboratory of Applied Mathematics of Pau 0622.
6
bibitem{7} Dinh N., Vallet G., Nghia T. T. A. (2008). ``Farkas-type results and duality for DC programming with convex constraints", Journal of Convex Analysis, 15, 235-262.
7
8
bibitem{8} Hiriart- Urruty J. B., Lemarechal C. (1991). ``Convex Analysis and Minimization Algorithms, I & II", Springer, Berlin, Heidelberg.
9
bibitem{9} Jeyakumar V., Dinh N., Lee G. M. (2004). ``A new closed cone constraint qualification for convex programs", Applied Mathematics Research Report AMR04/8, School of Mathematics, University of new South Wales, Australia.
10
bibitem{10} Kanzi N. ``Lagrange multiplier rules for non-differentiable DC generalized semi-infinite programming problems", Journal of Global Optimization, (DOI 10.1007/s10898-001-9828-5).
11
bibitem{11} Kanzi N., Nobakhtian S. (2010). ``Optimality conditions for nonsmooth semi-infinite programming", Optimization, 59, 717-727.
12
bibitem{12} Kanzi N., Nobakhtian S. (2010). ``Necessary optimality conditions for nonsmooth generalized semi-infinite programming problems", European Journal of Operational Research, 205, 253-263.
13
bibitem{13} Li W., Nahak C., Singer I. (2000). ``Constraint qualifications in semi-infinite systems of convex inequalities", SIAM Journal of Optimization, 11, 31-52.
14
bibitem{14} Stein O. (2003). ``Bi-level strategies in semi-infinite programming", Kluwer, Boston.
15
ORIGINAL_ARTICLE
Global Asymptotic and Exponential Stability of Tri-Cell Networks with Different Time Delays
In this paper, a bidirectional ring network with three cells and different time delays is presented. To propose this model which is a good extension of three-unit neural networks, coupled cell network theory and neural network theory are applied. In this model, every cell has self-connections without delay but different time delays are assumed in other connections. A suitable Lyapunov function is presented for this model which helps to get sufficient conditions to guarantee asymptotic and exponential stability of the model. Also, these conditions are independent of time delays. Finally, analytical results are confirmed by numerical examples which are stated.
https://mathco.journals.pnu.ac.ir/article_5728_d7d8ad7196d54741fba48dee2dc364e3.pdf
2017-12-01
45
60
Asymptotic stability
Exponential stability
Nonlinear systems
Cell network
Zohreh
Dadi
dadizohreh@gmail.com
1
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran
LEAD_AUTHOR
Farzaneh
Ravanbakhsh
f.ravanbakhsh93@gmail.com
2
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran
AUTHOR
bibitem{R1}
1
Ahmadkhanlou F., Adeli H. (2005). ``Optimum cost design of reinforced concrete slabs using neural dynamics model", Engineering Applications of Artificial Intelligence, 18, 65--72.
2
bibitem{R2} Amari S.I., Cichocki A. (1998). ``Adaptive blind signal processing-neural network approaches", Proceedings of the IEEE, 86, 2026--2048.
3
bibitem{ZD} Dadi Z. (2017). ``Dynamics of two-cell systems with discrete delays", Advances in Computational Mathematics, 43:3, 653--676.
4
bibitem{G2} Golubitsky M., Pivato M., Stewart I. (2004). ``Interior symmetry and local bifurcation in coupled cell networks", Dynamical Systems, 19:4, 389--407.
5
bibitem{G3} Golubitsky M., Stewart I. (2006). ``Nonlinear dynamics of networks: the groupoid formalism", Bulletin of the American Mathematical Society, 43, 305--364.
6
bibitem{G} Golubitsky M., Stewart I., Buono P.L., Collins J.J. (1998). ``A modular network for legged locomotion", Physica D, 115, 56--72.
7
bibitem{G4} Golubitsky M., Stewart I., T"{o}r"{o}k A. (2005). ``Patterns of synchrony in coupled cell networks with multiple arrows", SIAM Journal on Applied Dynamical Systems, 4:1, 78--100.
8
bibitem{R3} Guo S., Huang L. (2003). ``Hopf bifurcating periodic orbits in a ring of neurons with delays", Physica D, 183, 19--44.
9
bibitem{dj} Javidmanesh E., Dadi Z., Afsharnezhad Z., Effati S. (2014). ``Global stability analysis and existence of periodic solutions in an eight-neuron BAM neural network model with delays", Journal of Intelligent and Fuzzy Systems, 27:1, 391--406.
10
bibitem{R4} Jiang F., Shen J., Li X. (2013) ``The LMI method for stationary oscillation of interval neural networks with three neuron activations under impulsive effects", Nonlinear Analysis: Real World Applications, 14:3, 1404--1416.
11
bibitem{R5} Kwon O.M., Kwon J.W., Kim S.H. (2011). ``New results on stability criteria for neural networks with time-varying delays", Chinese Physics B, 20:5, 050505.
12
bibitem{R6} Kwon O.M., Park M., Lee S.M., Park J.H., Cha E.J. (2013). ``Stability for neural networks with time-varying delay via some new approaches",
13
IEEE Transactions on Neural Networks and Learning Systems, 24:2, 181--193.
14
bibitem{R7} Li H., Liao X., Li C., Huang H., Li C. (2011). ``Edge detection of noisy images based on cellular neural networks", Communications in Nonlinear Science and Numerical Simulations, 16:9, 3746--3759.
15
bibitem{R9} Luo R., Xu H., Wang W.S., Sun J., Xu W. (2016). ``A weak condition for global stability of delayed neural networks", Journal of Industrial and Management Optimization, 12:2, 505--514.
16
bibitem{R10} Shen Y., Wang J. (2012). ``Robustness analysis of global exponential stability of recurrent networks in the presence of time delays and random disturbances", IEEE Transactions on Neural Networks and Learning Systems, 23:1, 87--96.
17
bibitem{R11} Shu Y., Liu X., Liu Y. (2016). ``Stability and passivity analysis for uncertain discrete-time neural networks with time-varying delay", Neurocomputing, 173:3, 1706--1714.
18
bibitem{R12} Song Y., Han M., Wei J. (2005). ``Stability and Hopf bifurcation on a simplified BAM neural network with delays", Physica D: Nonlinear Phenomena, 200, 185--204.
19
bibitem{R13} Tian J., Xie X. (2010). ``New asymptotic stability criteria for neural networks with time varying delay", Physics Letters A, 374:7, 938--943.
20
bibitem{S} Stewart I., Golubitsky M., Pivato M. (2003). ``Symmetry groupoids and patterns of synchrony in coupled cell networks", SIAM Journal on Applied Dynamical Systems, 2:4, 606--646.
21
bibitem{R15} Wei J., Li M.Y. (2004). ``Global existence of periodic solutions in a tri-neuron network model with delays", Physica D, 198, 106--119.
22
bibitem{R16} Wei J.J., Velarde M.G. (2004). ``Bifurcation analysis and existence of periodic solutions in a simple neural network with delays", Chaos, 143, 940--953.
23
bibitem{R17}Yan X.P. (2006). ``Hopf bifurcation and stability for a delayed tri-neuron network model", Journal of Computational and Applied Mathematics, 196, 579--595.
24
bibitem{R8} Yiping L., Lemmert R., Volkmann P. (2001). ``Bifurcation of periodic solution in a three-unit neural network with delay", Acta Mathematicae Applicatae Sinica, 17:3, 375--381.
25
bibitem{R18}Yuan Y. (2007). ``Dynamics in a delayed-neural network", Chaos, Solitons and Fractals, 33:2, 443--454.
26
bibitem{R19} Zeng Z., Huang D.S., Wang Z. (2008). ``Pattern memory analysis based on stability theory of cellular neural networks", Applied Mathematical Modelling, 32:1, 112--121.
27
bibitem{R20} Zeng Z., Wang J. (2007). ``Analysis and design of associative memories based on recurrent neural networks with linear saturation activation functions and time-varying delays", Neural computation, 19:8, 2149--2182.
28
bibitem{R21} Zheng M., Mao Z., Li K., Fei M. (2016). ``Quadratic separation framework for stability analysis of a class of systems with time delays",
29
Neurocomputing, 174, 466--474.
30
bibitem{R22} Zheng C.D., Shan QH, Wang Z. (2012). ``Novel stability criterion for cellular neural networks: an improved Gu's discretized LKF approach", Journal of the Franklin Institute, 349:1, 25--41.
31
bibitem{R23} Zou S., Huang L., Wang Y. (2010). ``Bifurcation of a three-unit neural network", Applied Mathematics and Computation, 217:2, 904--917.
32
ORIGINAL_ARTICLE
Optimal Shape Design for a Cooling Pin Fin Connection Profil
A shape optimization problem of cooling fins for computer parts and integrated circuits is modeled and solved in this paper. The main purpose is to determine the shape of a two-dimensional pin fin, which leads to the maximum amount of removed heat. To do this, the shape optimization problem is defined as maximizing the norm of the Nusselt number distribution at the boundary of the pin fin's connection profile. The governing differential equations are solved in solid and fluid phases separately. In order to formulate the optimization problem with finite dimensions, the shapes of the profiles are parameterized with cubic polynomials. Due to the lack of an explicit relation between the objective function and the geometric parameters, an approximate modeling method is used for the optimization process. The proposed method starts with three initial points. Then, the governing differential equations are solved for each of the profiles related to the initial points. The new step in this iterative process involves calculations based on a polynomial interpolation within the resulting Nusselt number norms. A numerical example is given to show the implementation and accuracy of the method.
https://mathco.journals.pnu.ac.ir/article_5729_87708eb61cfd12941c88d00dc22a3b3c.pdf
2017-12-01
61
76
Approximation
Heat Transfer
Optimization
Shape Optimization
Seyed Hamed
Hashemi Mehne
hmehne@ari.ac.ir
1
Assistant Professor of Aerospace Research Institute, Tehran, 14665-834, Iran.
LEAD_AUTHOR
Khodayar
Javadi
kjavadi@sharif.edu
2
Department of Aerospace Engineering, Sharif University of Technology
AUTHOR
bibitem{1} Hamadneh N., Khan W. A., Sathasivam S., Ong H. C. (2013). ``Design Optimization of Pin Fin Geometry Using Particle Swarm Optimization Algorithm", Plos One, 8, 1-9.
1
bibitem{2} Dede E. M., Joshi S. N., Zhou F. (2015). ``Topology Optimization'', Journal of Mechanical Design, 137, 111403 (2015).
2
bibitem{3} Klass Haertel J. H., Engelbrecht K., Lazarov B. S., Sig-mund O. (2015). ``Topology Optimization of Thermal Heat Sinks", Proc. of COMSOL conference 2015, Grenoble, France, 1–6.
3
bibitem{4} Kayhani M. H., Norouzi M., Delouei A. A. (2012). ``Analytical investigation of orthotropic unsteady heat transfer in compo-site pin fins", Modares Mechanical Engineering, 11, 21–32 (in Persian).
4
bibitem{5} Khan W. A., Culham J. R., Yovanovich M. M. (2005). ``Optimization of Pin-Fin Heat Sinks Using Entropy Generation Minimization", IEEE Transactions on Components and Packaging Technologies, 28, 247-254.
5
bibitem{6} Shaukatullah H., Storr W. R., Hansen B. J., Gaynes M. A. (1996). ``Design and Optimization of Pin Fin Heat Sinks for Low Velocity Applications", SEMI-THERM XII. Proceedings. Twelfth Annual IEEE.
6
bibitem{7} Pakrouh R., Hosseini M.J., Ranjbar A.A., Bahrampoury R. (2015). ``A numerical method for PCM-based pin fin heat sinks optimization", Energy Conversion and Management, 103, 542-552.
7
bibitem{8} Mohammadian S. K., Zhang Y. (2015). ``Thermal management optimization of an air-cooled Li-ion battery module using pin-fin heat sinks for hybrid electric vehicles", Journal of Power Sources, 273, 431-439.
8
bibitem{9} Park S. J., Jang D., Yook S. J., Lee K. S. (2015). ``Optimization of a staggered pin-fin for a radial heat sink under free convection", International Journal of Heat and Mass Transfer, 87, 184-188.
9
bibitem{10} Bhanja D., Kundu B., Mandal P. K. (2013). ``Thermal analysis of porous pin fin used for electronic cooling", Procedia Engineering, 64, 956–965.
10
bibitem{11} Javadi A., Javadi K., Taeibi-Rahni M., Keimasi M. (2002). ``Reynolds Stress Turbulence Models for Prediction of Shear Stress Terms in Cross Flow Film Cooling–Numerical Simulation", ASME Pressure Vessels and Piping Conference, Vancouver, Canada.
11
bibitem{12} Herwig H. (2016). ``What Exactly is the Nusselt Number in Convective Heat Transfer Problems and are There Alternatives?", Entropy, 18, 1-15.
12
bibitem{13} Corm A. R., Scheinberg K., Toint Ph. L. (1997). ``Recent progress in unconstrained nonlinear optimization without derivatives", Mathematical Programming, 79, 397-414.
13
bibitem{14} Corm A. R., Scheinberg K., Toint Ph. L. (1997). ``On the convergence of derivative-free methods for unconstrained optimization", in: A.Iserles, M. Buhmann (Eds.), Approximation Theory and Optimization: Tributes to M.J.D. Powell, Cambridge University Press, Cambridge, UK.
14
bibitem{15} Corm A. R., Scheinberg K., Vicente L. N. (2008). ``Geometry of interpolation sets in derivative free optimization", Mathematical Programming, 111, 141-172.
15
bibitem{16}
16
Patankar S. V. (1980). ``Numerical heat transfer and fluid flow", McGraw-Hill, New York.
17
ORIGINAL_ARTICLE
Optimizing the Static and Dynamic Scheduling problem of Automated Guided Vehicles in Container Terminals
The Minimum Cost Flow (MCF) problem is a well-known problem in the area of network optimisation. To tackle this problem, Network Simplex Algorithm (NSA) is the fastest solution method. NSA has three extensions, namely Network Simplex plus Algorithm (NSA+), Dynamic Network Simplex Algorithm (DNSA) and Dynamic Network Simplex plus Algorithm (DNSA+). The objectives of the research reported in this paper are to simulate and investigate the advantages and disadvantages of NSA compared with those of the three extensions in practical situations. To perform the evaluation, an application of these algorithms to scheduling problem of automated guided vehicles in container terminal is used. In the experiments, the number of iterations, CPU-time required to solve problems, overheads and complexity are considered.
https://mathco.journals.pnu.ac.ir/article_5730_fbbd6925e9091cab1b93c28d72353257.pdf
2017-12-01
77
101
Network Simplex Algorithm
Dynamic Network Simplex Algorithm
Optimization Methods
Dynamic Scheduling
Container Terminals
Hassan
Rashidi
hrashi@gmail.com
1
Department of Mathematics and Computer Science, Allameh Tabataba’i University, Tehran, Iran,
LEAD_AUTHOR
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