Semi-definite programming based   approaches  for real-time tractor  localization  in port container terminals

Wei Huang; Ka-Fai Cedric Yiu; Henry Y. K.  Lau

doi:10.3934/naco.2013.3.665

Article Contents

2013, Volume 3, Issue 4: 665-680. Doi: 10.3934/naco.2013.3.665

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Semi-definite programming based approaches for real-time tractor localization in port container terminals

1.
Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received: February 2013

Revised: October 2013

Published: September 2013

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Abstract

In order to effectively manage and deploy internal tractors in a port container marine terminal, real-time information concerning the location of the tractors is required so that timely scheduling and planning of tractors control and dispatching can be derived. This paper propose a wireless sensor network-based Truck Flow Management System (TFMS) to help tracking the real-time location of internal tractors in a container terminal so as to streamline the management of the terminal operation. Focusing on the real-time localization, the semi-definite programming (SDP) based approaches are employed by introducing the terminal context information, including prior known road constraints and available time-serial data recorded in the network, into the traditional SDP formulation. Experimental results are presented to show that the proposed formulation and treatments to the problem can greatly decrease the estimated errors compared to the traditional formulation.

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Mathematics Subject Classification: Primary: 90C90; Secondary: 90C34.

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References

[1]	A. Y. Alfakih, A. Khandani and H. Wolkowicz, Solving Euclidean distance matrix completion problems via semidefinite programming, Computational optimization and applications, 12 (1999), 13-30.doi: 10.1023/A:1008655427845.
[2]	X. Bai, X. Zheng and X. Sun, A survey on probabilistically constrainted optimization problems, Numerical Algebra, Control and Optimization, 2 (2012), 767-778.doi: 10.3934/naco.2012.2.767.
[3]	P. Biswas, T.C. Liang, K.C. Toh, Y. Ye and T.C. Wang, Semidefinite programming approaches for sensor network localization with noisy distance measurements, IEEE transactions on automation science and engineering, 3 (2006), 360-371.
[4]	P. Biswas, T. C. Liang, T. C. Wang and Y. Ye, Semidefinite programming based algorithms for sensor network localization, ACM Transactions on Sensor Networks, 2 (2006), 188-220.
[5]	P. Biswas, K. C. Toh and Y. Ye, A distributed SDP approach for large-scale noisy anchor-free graph realization with applications to molecular conformation, SIAM Journal on Scientific Computing, 30 (2007), 1251-1277.doi: 10.1137/05062754X.
[6]	P. Biswas and Y. Ye, Semidefinite programming for ad hoc wireless sensor network localization, in "Proceedings of the Third International Symposium on Information Processing in Sensor Networks," New York, 2004, 46-54.
[7]	J.A. Costa, N. Patwari, and A.O. Hero, III, Distributed weighted-multidimensional scaling for node localization in sensor networks, ACM Transactions on Sensor Networks, 2 (2006), 39-64.
[8]	L. Doherty, K. S. J. Pister and L. El Ghaoui, Convex position estimation in wireless sensor networks, in "Proc. IEEE INFOCOM'', Anchorage, (2001), 1655-1663.
[9]	T. Eren, O. K. Goldenberg, W. Whiteley, Y. R. Yang, A. S. Morse, B. D. O. Anderson and P. N. Belhumeur, Rigidity, computation, and randomization in network localization, in "Proceedings of the IEEE INFOCOM'', Washington D.C., (2004), 2673-2684.
[10]	D. Ganesan, B. Krishnamachari, A. Woo, D. Culler, D. Estrin and S. Wicker, "An Empirical Study of Epidemic Algorithms in Large Scale Multihop Wireless Networks," Intel Corporation, 2002.
[11]	M. Gerdts, R. Henrion, D. Homberg and C. Landry, Path planning and collision avoidance for robots, Numerical Algebra, Control and Optimization, 2 (2012), 437-463.doi: 10.3934/naco.2012.2.437.
[12]	A. A. Kannan, G. Mao and B. Vucetic, Simulated annealing based localization in wireless sensor network, in "Proc. IEEE Conf. Local Computer Networks'', Washington DC, 2005, 513-514.
[13]	S. Kim, M. Kojima and H. Waki, Exploiting sparsity in SDP relaxation for sensor network localization, SIAM Journal on Optimization, 20 (2009), 192-215.doi: 10.1137/080713380.
[14]	J. Lofberg, YALMIP: A toolbox for modeling and optimization in MATLAB, in Proc. Int. Symp. CACSD, Taipei, Taiwan, 2004, 284-289.
[15]	K. W. K. Lui, W. K. Ma, H. C. So and F. K. W. Chan, Semi-definite programming algorithms for sensor network node localization with uncertainties in anchor positions and/or propagation speed, IEEE Transactions on Signal Processing, 57 (2009), 752-763.doi: 10.1109/TSP.2008.2007916.
[16]	J. J. Mor and Z. Wu, Global continuation for distance geometry problems, SIAM Journal on Optimization, 7 (1997), 814-836.doi: 10.1137/S1052623495283024.
[17]	E. Niewiadomska-Szynkiewicz and M. Marks, Optimization schemes for wireless sensor network localization, International Journal of Applied Mathematics and Computer Science, 19 (2009), 291-302.
[18]	R. W. Ouyang, A. K. Wong and C. T. Lea, Received signal strength-based wireless localization via semidefinite programming: noncooperative and cooperative schemes, IEEE Transactions on Vehicular Technology, 59 (2010), 1307-1318.
[19]	A. M. C. So and Y. Ye, Theory of semidefinite programming for sensor network localization, Mathematical Programming, 109 (2007), 367-384.doi: 10.1007/s10107-006-0040-1.
[20]	D. Steenken, S. Vos and R. Stahlbock, Container terminal operation and operations research - a classification and literature review, OR Spectrum, 26 (2004), 3-49.doi: 10.1007/s00291-007-0100-9.
[21]	J. F. Sturm, Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones, Optimization Methods and Software, 11 (1999), 625-653.doi: 10.1080/10556789908805766.
[22]	J. Sun, On methods for solving non-linear semidefinite optimization problems, Numerical Algebra, Control and Optimization, 1 (2011), 1-14.doi: 10.3934/naco.2011.1.1.
[23]	K. C. Toh, M. J. Todd and R. H. Tutuncu, SDPT3 - a Matlab software package for semidefinite programming, Optimization Methods and Software, 11 (1999), 545-581.doi: 10.1080/10556789908805762.
[24]	P. Tseng, Second-order cone programming relaxation of sensor network localization, SIAM Journal on Optimization, 18 (2008), 156-185.doi: 10.1137/050640308.
[25]	H. Waki, S. Kim, M. Kojima and M. Muramatsu, Sums of squares and semidefinite programming relaxations for polynomial optimization problems with structured sparsity, SIAM Journal on Optimization, 17 (2006), 218-242.doi: 10.1137/050623802.
[26]	S. Y. Wang and Y. W. Li, Evaluation of intelligent traffic signal control algorithms under realistic landmark-based traffic pattern over the NCTUns network simulator, in "15^th International IEEE Conference on Intelligent Transportation Systems, Anchorage, 2012, 379-384.
[27]	Z. Wang, S. Zheng, S. Boyd and Y. Ye, Further relaxations of the SDP approach to sensor network localization, SIAM Journal on Optimization, 19 (2008), 655-673.doi: 10.1137/060669395.
[28]	S. Zhang, J. Cao, L. Chen and D. Chen, Accurate and energy-efficient range-free localization for mobile sensor networks, IEEE Transactions on Mobile Computing, 9 (2010), 897-910.