The minimization of the fuel costs in the train transportation

Abstract

This paper presenting case studies in modern large scale constrained optimization,<br><br>the purpose of which is to illustrate how recent advances in algorithms and modelling<br><br>languages have made it easy to solve difficult optimization problems using of software.<br><br>In this paper we use measure theory technique and iterative dynamic programming<br><br>algorithm for solving of a trajectory optimization problem: how to drive a train so as<br><br>to minimize fuel costs. In the first method, we optimal control problem to using of<br><br>atomic measures change this one to an infinite dimensional linear programming problem<br><br>and then we approximate the latter one to a finite dimensional linear programming<br><br>problem, then by the optimal solution of the final problem we obtain sub-optimal controls<br><br>and then by these controls we obtain the approximate solution of the original<br><br>problem. In the second method, we will using dynamic programming as iteration for<br><br>solving optimal control problem.