Route optimization using graph theory in the application package

Abstract

The analysis of methods for solving the using graph theory in application packages is represented in this article. For possibility of use of computer algebra system this problem was presented in the form of а mathematical model on the graph. Some versions of the solution of the problem by means of various CAS are in detail considered. Indisputable leaders in in this area are CAS Maple and CAS Mathematica. The solution of this problem by means of CAS Maple is realized by Dijkstra's algorithm, Simulated annealing and Ant colony optimization algorithms. CAS Mathematica has expanded support graphs necessary for solution of the shortest path problem.

Keywords

• graph theory
• mathematical models
• flow networks
• route optimization the shortest path
• transportation expenses