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The Scientific World Journal
Volume 2014, Article ID 871242, 12 pages
Research Article

Efficient Constraint Handling in Electromagnetism-Like Algorithm for Traveling Salesman Problem with Time Windows

Department of Industrial Engineering, Uludag University, Görükle Campus, 16059 Bursa, Turkey

Received 10 December 2013; Accepted 18 January 2014; Published 27 February 2014

Academic Editors: A. Bartoszewicz and B. Ivorra

Copyright © 2014 Alkın Yurtkuran and Erdal Emel. 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 traveling salesman problem with time windows (TSPTW) is a variant of the traveling salesman problem in which each customer should be visited within a given time window. In this paper, we propose an electromagnetism-like algorithm (EMA) that uses a new constraint handling technique to minimize the travel cost in TSPTW problems. The EMA utilizes the attraction-repulsion mechanism between charged particles in a multidimensional space for global optimization. This paper investigates the problem-specific constraint handling capability of the EMA framework using a new variable bounding strategy, in which real-coded particle’s boundary constraints associated with the corresponding time windows of customers, is introduced and combined with the penalty approach to eliminate infeasibilities regarding time window violations. The performance of the proposed algorithm and the effectiveness of the constraint handling technique have been studied extensively, comparing it to that of state-of-the-art metaheuristics using several sets of benchmark problems reported in the literature. The results of the numerical experiments show that the EMA generates feasible and near-optimal results within shorter computational times compared to the test algorithms.