A numerical method for solving shortest path problems
- 35 Downloads
Chebyshev pseudo-spectral method is one of the most efficient methods for solving continuous-time optimization problems. In this paper, we utilize this method to solve the general form of shortest path problem. Here, the main problem is converted into a nonlinear programming problem and by solving of which, we obtain an approximate shortest path. The feasibility of the nonlinear programming problem and the convergence of the method are given. Finally, some numerical examples are considered to show the efficiency of the presented method over the other methods.
KeywordsShortest path problem Chebyshev pseudo-spectral method Nonlinear programming
Mathematics Subject Classification49M37 49J15 65N35
- 7.Ghaznavi, M., Noori Skandari, M.H.: An efficient pseudo-spectral method for nonsmooth dynamical systems. Iran. J. Sci. Technol. Trans. A Sci. (2016). https://doi.org/10.1007/s40995-016-0040-9
- 12.Ma, Y., Zamirian, M., Yang, Y., Xu, Y., Zhang, J.: Path planning for mobile objects in four-dimension based on particle swarm optimization method with penalty function. Math. Probl. Eng. 2013, 1–9 (2013)Google Scholar
- 18.Otte, M., Correll, N.: C-FOREST: parallel shortest path planning with superlinear speedup. IEEE Robot. Autom. Soc. 29(3), 798–806 (2013)Google Scholar