Abstract
This paper studies the Orthogonal Milling with Turn Costs. An exact algorithm is proposed based on an Integer Programming formulation of the problem. To our knowledge, this is the first exact algorithm ever proposed for the problem. Besides, a simple heuristic is also presented and an unprecedented experimentation involving these two algorithms and an existing approximation algorithm is carried out. We report and analyze the results obtained in these tests. Our benchmark instances are made public to allow for future comparisons.
This research was partially supported by cnpq (Conselho Nacional de Desenvolvimento CientÃfico e Tecnológico) – grants #301732/2007-8, #473867/2010-9, fapesp (Fundação de Amparo à Pesquisa do Estado de São Paulo) – grant #07/52015-0, and a grant from faepex/unicamp.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arkin, E.M., Bender, M.A., Demaine, E., Fekete, S.P., Mitchell, J.S.B., Sethia, S.: Optimal covering tours with turn costs. In: Proc. 13th ACM-SIAM Symposium on Discrete Algorithms, pp. 138–147 (2001)
Demaine, E.D., Mitchell, J.S.B., O’Rourke, J.: The open problems project. http://maven.smith.edu/~orourke/TOPP (page visited in January, 2011)
Arkin, E., Bender, M., Demaine, E., Fekete, S., Mitchell, J., Sethia, S.: Optimal covering tours with turn costs. SIAM Journal on Computing 35(3), 531–566 (2005)
Clossey, J., Laporte, G., Soriano, P.: Solving arc routing problems with turn penalties. Journal of the Operational Research Society 52, 433–439 (2001)
Benavent, E., Soler, D.: The directed rural postman problem with turn penalties. Transportation Science 30(4), 408–418 (1999)
Grötschel, M., Lovász, L., Schrijver, A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2), 169–197 (1981)
Ben-Arieh, D., Gutin, G., Penn, M., Yeo, A., Zverovitch, A.: Transformations of generalized ATSP into ATSP. Operations Research Letters 31(5), 357–365 (2003)
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Elsevier Science, New York (1976)
Resende, M.G., Ribeiro, C.C.: Greedy randomized adaptive search procedures: Advances, hybridizations, and applications. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics. International Series in Operations Research and Management Science, vol. 146, pp. 283–319. Springer, US (2010)
Kolmogorov, V.: Blossom V: A new implementation of a minimum cost perfect matching algorithm. Mathematical Programming Computation 1(1), 43–67 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Assis, I.R., de Souza, C.C. (2011). Experimental Evaluation of Algorithms for the Orthogonal Milling Problem with Turn Costs. In: Pardalos, P.M., Rebennack, S. (eds) Experimental Algorithms. SEA 2011. Lecture Notes in Computer Science, vol 6630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20662-7_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-20662-7_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20661-0
Online ISBN: 978-3-642-20662-7
eBook Packages: Computer ScienceComputer Science (R0)