Modelling of Curvature of the Railway Track Geometrical Layout Using Particle Swarm Optimization

Katarzyna Małgorzata Palikowska


A method of railway track geometrical layout design, based on an application of cubic C-Bezier curves for describing the layout curvature is presented in the article. The control points of a cubic C-Bezier curve are obtained in an optimization process carried out using Particle Swarm Optimization algorithm. The optimization criteria are based on the evaluation of the dynamic interactions and satisfaction of geometrical design requirements.


Particle Swarm Optimization algorithm, cubic C-Bezier curve, curvature of the railway track layout, dynamic interactions, transition curve

Full Text:



Baykal, O. : On concept of lateral change of acceleration, Journal of Surveying Engineering, 122(3) 1996, 132-141.

Baykal, O, Tarı E, Coşkun Z, Şahin M, A New Transition Curve Joining Two Straight Lines, Journal of Transportation Engineering, ASCE, 123(5),337-345, 1997.

Cai H., Wang G.: A new method in highway route design: joining circular arcs by a single C-Bezier curve with shape parameter. Journal of Zhejiang University Science A 2009, 10(4).

Dahlquist, G., Björck, A. Numerical methods, Prentice-Hall 1974.

Delint I, Siti M., Aida A.: Particle Swarm Optimization for NURBS curve fitting. Proceedings of the 2009 Sixth International Conference on Computer Graphics, Imaging and Visualization, pp. 259-263. DOI 10.1109/CGIV.2009.64

Habib Z., Sakai M.: G2 Pythagorean hodograph quintic transition between two circles with shape control. Computer Aided Geometric Design 2007, nr 24.

Habib Z., Sakai M.: On PH quantic spirals joining two circles with one circle inside the other. Computer-Aided Design 2007, nr 39.

Ifeachor, E., Jervis, B. : Digital Signal Processing. A Practical Approach, Addison-Wesley, 1998.

Kennedy J., Eberhart R.: Swarm intelligence, Morgan Kaufmann Publishers, San Francisco, 2001.

Koc W.: Elements of the theory of track design (in Polish), Gdansk University of Technology Publishing, Gdansk 2004.

Koc, W., Mieloszyk, E.: Comparative analysis of selected transition curves using dynamic model, Archives of Civil Engineering, 33(2) 1987, 239-261.

Koc W., Palikowska K.: Dynamic properties evaluation of the selected methods of joining route segments with different curvature (in Polish), XVI International Scientific Conference "Science, Industry and Transport Computer Support Systems − TransComp", Zakopane 2012.

Koc W., Palikowska K.: Analysis of the curvature modeling methods –Bezier curves against the analytical method (in Polish). Scientific-Technical Papers SITK, 3(99), s. 225-237, Cracow 2012.

Mieloszyk, E., Koc, W.: General dynamic method for determining transition curve equations, Rail International-Schienen der Welt, 10 1991, 32-40.

Palikowska K.: Design of railway track geometrical layout using evolution programming, PhD Thesis (in Polish), Gdansk University of Technology, 2002.

Salmon S., Baudin M., Cornet A.: Particle Swarm Optimization Toolbox, 2012,

Tari, E.: The new generation transition curves. ARI 54(1), Istanbul Technical University 2003.

Tasci, L., Kuloglu N.: Investigation of a new transition curve. The Baltic Journal of Road and Bridge Engineering 6(1) 2001: 23−29. DOI: 10.3846/bjrbe.2011.04

Zhang J.: C-curves: an extension of cubic curves. Computer Aided Geometric Design 13(3) 1996:199-217, DOI: 10.1016/0167-8396(95)00022-4.


  • There are currently no refbacks.