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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 4703106, 11 pages
Research Article

A Simulated Annealing Approach for the Train Design Optimization Problem

1Universidad Autónoma del Estado de Morelos, 62209 Cuernavaca, MOR, Mexico
2Instituto de Matemáticas, Universidad Nacional Autónoma de México, 62210 Cuernavaca, MOR, Mexico

Correspondence should be addressed to Federico Alonso-Pecina

Received 10 March 2017; Revised 20 June 2017; Accepted 9 July 2017; Published 10 August 2017

Academic Editor: Jorge Magalhaes-Mendes

Copyright © 2017 Federico Alonso-Pecina and David Romero. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Train Design Optimization Problem regards making optimal decisions on the number and movement of locomotives and crews through a railway network, so as to satisfy requested pick-up and delivery of car blocks at stations. In a mathematical programming formulation, the objective function to minimize is composed of the costs associated with the movement of locomotives and cars, the loading/unloading operations, the number of locomotives, and the crews’ return to their departure stations. The constraints include upper bounds for number of car blocks per locomotive, number of car block swaps, and number of locomotives passing through railroad segments. We propose here a heuristic method to solve this highly combinatorial problem in two steps. The first one finds an initial, feasible solution by means of an ad hoc algorithm. The second step uses the simulated annealing concept to improve the initial solution, followed by a procedure aiming to further reduce the number of needed locomotives. We show that our results are competitive with those found in the literature.