Abstract
Bin packing is a ubiquitous problem that arises in many practical applications. The motivation for the work presented here comes from the domain of data centre optimisation. In this paper we present a parameterisable benchmark generator for bin packing instances based on the well-known Weibull distribution. Using the shape and scale parameters of this distribution we can generate benchmarks that contain a variety of item size distributions. We show that real-world bin packing benchmarks can be modelled extremely well using our approach. We also study both systematic and heuristic bin packing methods under a variety of Weibull settings. We observe that for all bin capacities, the number of bins required in an optimal solution increases as the Weibull shape parameter increases. However, for each bin capacity, there is a range of Weibull shape settings, corresponding to different item size distributions, for which bin packing is hard for a CP-based method.
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References
Alvim, A.C.F., Ribeiro, C.C., Glover, F., Aloise, D.J.: A hybrid improvement heuristic for the one-dimensional bin packing problem. Journal of Heuristics 10(2), 205–229 (2004)
Boost: free peer-reviewed portable C++ source libraries. Version 1.47.0, http://www.boost.org/
Cambazard, H., O’Sullivan, B.: Propagating the Bin Packing Constraint Using Linear Programming. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 129–136. Springer, Heidelberg (2010)
Carlsson, M., Beldiceanu, N., Martin, J.: A geometric constraint over k-dimensional objects and shapes subject to business rules. In: Stuckey (ed.) [31], pp. 220–234
de Carvalho, J.V.: Exact solution of cutting stock problems using column generation and branch-and-bound. International Transactions in Operational Research 5(1), 35–44 (1998)
Dupuis, J., Schaus, P., Deville, Y.: Consistency check for the bin packing constraint revisited. In: Lodi, et al. (eds.) [15], pp. 117–122
Falkenauer, E.: A hybrid grouping genetic algorithm for bin packing. Journal of Heuristics 2(1), 5–30 (1996)
Gecode: generic constraint development environment. Version 3.7.0, http://www.gecode.org/
Gent, I.P.: Heuristic solution of open bin packing problems. Journal of Heuristics 3(4), 299–304 (1998)
Gent, I.P., Walsh, T.: From approximate to optimal solutions: constructing pruning and propagation rules. In: International Joint Conference on Artifical Intelligence, pp. 1396–1401 (1997)
Grandcolas, S., Pinto, C.: A SAT encoding for multi-dimensional packing problems. In: Lodi, et al. (eds.) [15], pp. 141–146
Hermenier, F., Demassey, S., Lorca, X.: Bin Repacking Scheduling in Virtualized Datacenters. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 27–41. Springer, Heidelberg (2011)
Korf, R.E.: An improved algorithm for optimal bin packing. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence, pp. 1252–1258 (2003)
Labbé, M., Laporte, G., Martello, S.: Upper bounds and algorithms for the maximum cardinality bin packing problem. European Journal of Operational Research 149(3), 490–498 (2003)
Lodi, A., Milano, M., Toth, P. (eds.): CPAIOR 2010. LNCS, vol. 6140. Springer, Heidelberg (2010)
Steenberger, M.R.: Maximum likelihood programming in R, http://www.unc.edu/~monogan/computing/r/MLE_in_R.pdf
Denis, J.-B., Delignette-Muller, M.L., Pouillot, R., Dutang, C.: Use of the package fitdistrplus to specify a distribution from non-censored or censored data (April 2011)
Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. John Wiley & Sons, Inc. (1990)
Martello, S., Toth, P.: Lower bounds and reduction procedures for the bin packing problem. Discrete Appl. Math. 28, 59–70 (1990)
Qu, R., Burke, E., McCollum, B., Merlot, L.T., Lee, S.Y.: A survey of search methodologies and automated approaches for examination timetabling (2006)
Régin, J.-C., Rezgui, M.: Discussion about constraint programming bin packing models. In: Proceedings of the AIDC Workshop (2011)
Rici, V.: Fitting distribution with R (2005)
Schaus, P.: Solving Balancing and Bin-Packing Problems with Constraint Programming. PhD thesis, Université Catholique de Louvain-la-Neuve (2009)
Scholl, A., Klein, R., Jürgens, C.: Bison: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem. Computers & Operations Research 24(7), 627–645 (1997)
Schulte, C., Tack, G., Lagerkvist, M.Z.: Modeling and Programming with Gecode (2012), http://www.gecode.org/doc-latest/MPG.pdf
Schwerin, P., Wäscher, G.: The bin-packing problem: A problem generator and some numerical experiments with FFD packing and MTP. International Transactions in Operational Research 4(5-6), 377–389 (1997)
Schwerin, P., Wäscher, G.: A New Lower Bound for the Bin-Packing Problem and its Integration Into MTP. Martin-Luther-Univ. (1998)
Shaw, P.: A constraint for bin packing. In: Wallace (ed.) [34], pp. 648–662
Simonis, H., O’Sullivan, B.: Search strategies for rectangle packing. In: Stuckey (ed.) [31], pp. 52–66
Simonis, H., O’Sullivan, B.: Almost Square Packing. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 196–209. Springer, Heidelberg (2011)
Stuckey, P.J. (ed.): CP 2008. LNCS, vol. 5202. Springer, Heidelberg (2008)
The R project for statistical computing. Version 1.47.0, http://www.r-project.org/
Vidotto, A.: Online constraint solving and rectangle packing. In: Wallace (ed.) [34], p. 807
Wallace, M. (ed.): CP 2004. LNCS, vol. 3258. Springer, Heidelberg (2004)
Wäscher, G., Gau, T.: Heuristics for the integer one-dimensional cutting stock problem: A computational study. OR Spectrum 18(3), 131–144 (1996)
Weibull, W.: A statistical distribution function of wide applicability. Journal of Appl. Mech.-Transactions 18(3), 293–297 (1951)
Wessa, P.: Free Statistics Software, Office for Research Development and Education, version 1.1.23-r7 (2011), http://www.wessa.net/
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Castiñeiras, I., De Cauwer, M., O’Sullivan, B. (2012). Weibull-Based Benchmarks for Bin Packing. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_17
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DOI: https://doi.org/10.1007/978-3-642-33558-7_17
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