Mathematical Models and Optimization in Line Structure Routing: Survey and Advanced Results

Valery I. Struchenkov

Moscow State University of Radio Engineering, Electronics and Automation, Moscow, Russia.

DOI: 10.4236/ijcns.2012.529073                

Abstract

Under study is the optimization problem of line structure (primarily railroad) routing. The improved mathematical models and algorithms of vertical alignment by set versions of the route plan are offered. The problem is solved in some stages in interrelation with other design problems. The original algorithm of descent is given for solving the arising problem of nonlinear programming. Structural features of constraints are used and so it is not required to solve any systems of linear equations.

Keywords

Route; Horizontal and Vertical Alignment; Nonlinear Programming; Objective Function; Reduced Gradient

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	CARD/1, 2012. http://www.card-1.com/en/home/
[2]	Тоpomatic Robur, 2012. http://www.topomatic.ru
[3]	Y. Shafahi and M. J. Shahbazi, “Optimum Railway Alignment,” 2012. http://www.uic.org/cdrom/2001/wcrr2001/pdf/sp/2_1_1/210.pdf
[4]	M. K. Jha, P. M. Schonfeld, J.-C. Yong and E. Kim, “Intelligent Road Design,” WIT Press, Southampton, 2006.
[5]	J. Kurilko and V. Chesheva, “Geonics ZHELDOR- CAD,” CADmaster, Vol. 1, No. 36, 2007.
[6]	V. I. Struchenkov, “Optimization Methods in Applied Problems,” Solon-Press, Moscow, 2009.
[7]	E. S. Wentzel, “Operations Research: Challenges, Principles, Metodologiya,” KnoRus, Moscow, 2010.
[8]	V. S. Mikhalevich, V. I. Bykov and A. N. Sibirko, “The Problem of Designing Optimum Longitudinal Profile of the Road,” Transportation Building, Moscow, 1975.
[9]	Anonym, “The Use of Mathematical Optimization Techniques and Computer Engineering at the Longitudinal Profile of the Railways,” Proceedings of the All-Union Scientific Research Institute of Transport Engineering, Transport, Moscow, Vol. 101, 1977.
[10]	F. Gill and W. Murray, “Numerical Methods for Constrained Optimization,” Mir, Moscow, 1977.
[11]	M. Aoki, “Introduction to Optimization Methods,” Nauka, Moscow, 1977.
[12]	V. I. Struchenkov, “Methods for Optimal Design of Routes of Line Structures,” Proceedings of Artificial Intelligence in Engineering Systems, Vol. 20, Gos.IFTP, Moscow, 1999.
[13]	J. Zoutendijk, “Methods of Feasible Directions,” IL, Moscow, 1963.
[14]	V. I. Struchenkov, A. N. Kozlov and A. S. Yegunov, “Piecewise—Linear Approximation of Planar Curves under Constraints,” Information Technology, Vol. 12, No. 172, 2010.