Abstract
In non-smooth optimization problems the objective function to minimize or maximize is non-smooth and usually non-convex either, which is a frequent characteristic of real-life optimization problems. In this chapter we discuss the arc routing problem with a non-smooth cost function, and propose a randomized algorithm for solving it. Our approach employs non-uniform probability distributions to add a biased random behavior to the well-known savings heuristic. By doing so, a large set of alternative good solutions can be quickly obtained in a natural way and without complex configuration processes. Since the solution-generation process is based on the criterion of maximizing the savings, it does not need to assume any particular property of the objective function. Therefore, the procedure can be especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregulars solution space, for which the traditional optimization methods -both of exact and approximate nature- may fail to reach their full potential. The results obtained so far suggest that using biased probability distributions to randomize classical heuristics can be successfully applied in non-smooth optimization.
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References
Al-Sultan, K.S.: A tabu search approach to the clustering problem. Pattern Recogn. 28(9), 1443–1451 (1995)
Bagirov, A.M., Yearwood, J.: A new nonsmooh optimization algorithm for minimum sum-of-squares clustering problem. Eur. J. Oper. Res. 170, 578–596 (2006)
Bagirov, A.M, Lai, D.T.H., Palaniswami, M.: A nonsmooth optimization approach to sensor network location. In: Palaniswami, M., Marusic, M., Law, Y.W. (eds) Proceedings of the 2007 International Conference on Intelligent Sensors, Sensor Networks and Information Processing, pp. 727–732 (2007)
Bresina, J.L.: Heuristic-biased srochastic sampling. In: Proceeding of the Thirteenth National Conference on Artificial Intelligence and the Eighth Innovative Applications of Artificial Intelligence Conference, pp. 271–278 (1996)
Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
Chaves, A.A., Lorena, L.A.N.: Clustering search algorithm for the capacitated centered clustering problema. Comput. Oper. Res. 37(3), 552–558 (2010)
Drezner, Z., Hamacher, H. (eds.): Facility Location: Applications and Theory. Springer, New York (2010)
Fleurent, C., Glover, F.: Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS J. Comput. 11(2), 198–204 (1999)
Golden, B.T., Wong, R.T.: Capacitated arc routing problems. Networks 11(3), 215–305 (1981)
Golden, B.T., Dearmon, J.S., Baker, E.K.: Computational experiments with algorithms for a class of routing problems. Comput. Oper. Res. 10(1), 47–59 (1983)
Gonzalez-Martin, S., Juan, A.A., Riera, D., Castella, Q., Perez-Bonilla, A, Muñoz, R.: Development and assessment of the SHARP and RandSHARP algorithms for the arc routing problema. AI Commun. 25(2), 173–189 (2012)
Hamdan, M., El-Hawary, M.E.: Hopfield-genetic approach for solving the routing problem. In: Computer Networks. Proceedings of the 2002 IEEE Canadian Conference on Electrical and Computer Engineering, pp. 823–827 (2002)
Hashimoto, H., Ibaraki, T., Imahori, S., Yagiura, M.: The vehicle routing problema with flexible time Windows and traveling times. Discrete Appl. Math. 154(16), 2271–2290 (2006)
Juan, A.A., Faulin, J., Ferrer, A., Lourenço, H.R., Barrios, B.: MIRHA: multi-start biased randomization of heuristics with adaptive local search for solving non-smooth routing problems. TOP 21, 109–132 (2013)
L’Ecuyer, P.: Random Number Generation in Simulation. Elsevier, Amsterdam (2006)
Laporte, G.: Fifty years of vehicle routing. Transp. Sci. 43(4), 408–413 (2009)
Oonsivilai, A., Srisuruk, W., Marungsri, B., Kulworawanichpong, T.: Tabu search approach to solve routing issues in communication networks. In: World Academy of Science, Engineering and Technology, pp. 1174–1177 (2009)
Ramadurai, V., Sichitiu, M.L.: Localization in wireless sensor networks: a probabilistic approach. In: International Conference on Wireless Networks (ICWN03), pp. 275–281 (2003)
Resende, M.G.C.: Metaheuristic hybridization with greedy randomized adaptive search procedure. In: Chen, S.L., Raghavan, S. (eds.) Handbook of Metaherustics. International Series in Operations Research Management Science, 146(2), pp. 227–264. Kluwer Academic, Dordrecht (2008)
Acknowledgments
The research of the first, third and fourth authors has been partially supported by the Spanish Ministry of Science and Innovation (TRA2010-21644-C03) and by the Ibero-American Programme for Science, Technology and Development (CYTED2010-511RT0419) in the context of the ICSO-HAROSA Programme of the IN3 (http://dpcs.uoc.edu).
The research of the second author has been partially supported by the Spanish Ministry of Science and Technology (MTM2011-29064-C03-01).
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Gonzalez-Martin, S., Ferrer, A., Juan, A.A., Riera, D. (2014). Solving Non-smooth Arc Routing Problems Throughout Biased-Randomized Heuristics. In: de Sousa, J., Rossi, R. (eds) Computer-based Modelling and Optimization in Transportation. Advances in Intelligent Systems and Computing, vol 262. Springer, Cham. https://doi.org/10.1007/978-3-319-04630-3_33
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DOI: https://doi.org/10.1007/978-3-319-04630-3_33
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