Abstract
This paper proposes a new method for solving the Machine Reassignment Problem in a very short computational time. The problem has been proposed by Google as subject of the Challenge ROADEF/EURO 2012. The Machine Reassignment Problem consists in looking for a reassignment of processes to machines in order to minimize a complex objective function, subject to a rich set of constraints including multidimensional resource, conflict and dependency constraints. In this study, a cooperative search approach is presented for machine reassignment. This approach uses two components: Adaptive Variable Neighbourhood Search and Simulated Annealing based Hyper-Heuristic, running in parallel on two threads and exchanging solutions. Both algorithms employ a rich set of heuristics and a learning mechanism to select the best neighborhood/move type during the search process. The cooperation mechanism acts as a multiple restart which gets triggered whenever a new better solution is achieved by a thread and then shared with the other thread. Computational results on the Challenge instances as well as instances of a Generalized Assignment-like problem are given to show the relevance of the chosen methods and the high benefits of cooperation.
Similar content being viewed by others
Notes
FMR is open source and is distributed under GPL, see http://www.lipn.fr/~butelle/s26.tgz.
For more detailed results and information see http://challenge.roadef.org/2012/en/results.php.
References
Bai, R., Blazewicz, J., Burke, E. K., Kendall, G., & McCollum, B. (2012). A simulated annealing hyper-heuristic methodology for flexible decision support. 4OR: A Quarterly Journal of Operations Research, 10(1), 43–66.
Bai, R., & Kendall, G. (2005). An investigation of automated planograms using a simulated annealing based hyper-heuristic. In T. Ibaraki, K. Nonobe & M. Yagiura (Eds.), Metaheuristics: Progress as real problem solvers (pp. 87–108). New York: Springer.
Bilgin, B., Özcan, E., & Korkmaz, E. E. (2006). An experimental study on hyper-heuristics and exam timetabling. In Practice and theory of automated timetabling VI, 6th international conference, PATAT, Brno, Czech Republic, Revised selected papers (pp. 394–412). doi:10.1007/978-3-540-77345-0_25.
Burke, E. K., Gendreau, M., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., et al. (2013). Hyper-heuristics: A survey of the state of the art. Journal of the Operational Research Society, 64(12), 1695–1724.
Burke, E. K., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., & Woodward, J. R. (2010). A classification of hyper-heuristic approaches. In M. Gendreau & J. -Y. Potvin (Eds.), Handbook of metaheuristics (pp. 449–468). New York: Springer.
Burke, E. K., Kendall, G., Misir, M., & Özcan, E. (2012). Monte carlo hyper-heuristics for examination timetabling. Annals of Operations Research, 196(1), 73–90.
Caprara, A., & Toth, P. (2001). Lower bounds and algorithms for the 2-dimensional vector packing problem. Discrete Applied Mathematics, 111(3), 231–262.
Cattrysse, D. G., & Van Wassenhove, L. N. (1992). A survey of algorithms for the generalized assignment problem. European Journal of Operational Research, 60(3), 260–272.
Chen, Y., Das, A., Qin, W., Sivasubramaniam, A., Wang, Q., & Gautam, N. (2005). Managing server energy and operational costs in hosting centers. In Proceedings of the ACM international conference on measurement and modeling of computer systems (SIGMETRICS) (pp. 303–314). doi:10.1145/1064212.1064253.
Chung, F. R., Garey, M. R., & Johnson, D. S. (1982). On packing two-dimensional bins. SIAM Journal on Algebraic Discrete Methods, 3(1), 66–76. doi:10.1137/0603007.
Cowling, P., Kendall, G., & Soubeiga, E. (2001). A hyperheuristic approach to scheduling a sales summit. In E. K. Burke & W. Erben (Eds.), Practice and theory of automated timetabling III (pp. 176–190). New York: Springer.
Crainic, T. G., & Gendreau, M. (2002). Cooperative parallel tabu search for capacitated network design. Journal of Heuristics, 8(6), 601–627.
Crainic, T. G., Gendreau, M., Hansen, P., & Mladenović, N. (2004). Cooperative parallel variable neighborhood search for the p-median. Journal of Heuristics, 10(3), 293–314.
Dowsland, K. A., Soubeiga, E., & Burke, E. K. (2007). A simulated annealing based hyperheuristic for determining shipper sizes for storage and transportation. European Journal of Operational Research, 179(3), 759–774. doi:10.1016/j.ejor.2005.03.058.
Gavish, B., & Pirkul, H. (1991). Algorithms for the multi-resource generalized assignment problem. Management Science, 37(6), 695–713. doi:10.1287/mnsc.37.6.695.
Han, B. T., Diehr, G., & Cook, J. S. (1994). Multiple-type, two-dimensional bin packing problems: Applications and algorithms. Annals of Operations Research, 50(1), 239–261. doi:10.1007/BF02085642.
Hochbaum, D. S. (1996). Approximation algorithms for NP-hard problems. Boston, MA: PWS Publishing.
James, T., Rego, C., & Glover, F. (2009). A cooperative parallel tabu search algorithm for the quadratic assignment problem. European Journal of Operational Research, 195(3), 810–826.
Kalender, M., Kheiri, A., Özcan, E., & Burke, E. K. (2013). A greedy gradient-simulated annealing hyper-heuristic. Soft Computing, 17(12), 2279–2292.
Kellerer, H., Pferschy, U., & Pisinger, D. (2004). Knapsack problems. New York: Springer.
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680.
Le Bouthillier, A., & Crainic, T. G. (2005). A cooperative parallel meta-heuristic for the vehicle routing problem with time windows. Computers & Operations Research, 32(7), 1685–1708. doi:10.1016/j.cor.2003.11.023.
Lehre, P., & Özcan, E. (2013). A runtime analysis of simple hyper-heuristics: To mix or not to mix operators. In Proceedings of the 12th ACM workshop on foundations of genetic algorithms (pp. 97–104).
Lodi, A., Martello, S., & Monaci, M. (2002). Two-dimensional packing problems: A survey. European Journal of Operational Research, 141(2), 241–252. doi:10.1016/S0377-2217(02)00123-6.
Martello, S., Pisinger, D., & Vigo, D. (2000). The three-dimensional bin packing problem. Operations Research, 48(2), 256–267. doi:10.1287/opre.48.2.256.12386.
Maruyama, K., Chang, S., & Tang, D. (1977). A general packing algorithm for multidimensional resource requirements. International Journal of Computer & Information Sciences, 6(2), 131–149. doi:10.1007/BF00999302.
Miyazawa, F. K., & Wakabayashi, Y. (2007). Two- and three-dimensional parametric packing. Computers and Operations Research, 34, 2589–2603. doi:10.1016/j.cor.2005.10.001.
Nonobe, K., & Ibaraki, T. (2001). An improved tabu search method for the weighted constraint satisfaction problem. INFOR: Information Systems and Operational Research, 39, 131–151.
Ouelhadj, D., & Petrovic, S. (2008). A cooperative distributed hyper-heuristic framework for scheduling. In IEEE international conference on systems, man and cybernetics (SMC) (pp. 2560–2565). IEEE.
Pentico, D. W. (2007). Assignment problems: A golden anniversary survey. European Journal of Operational Research, 176(2), 774–793. doi:10.1016/j.ejor.2005.09.014.
Pisinger, D., & Ropke, S. (2007). A general heuristic for vehicle routing problems. Computers & Operations Research, 34(8), 2403–2435.
Puchinger, J., & Raidl, G. R. (2007). Models and algorithms for three-stage two-dimensional bin packing. European Journal of Operational Research, 183(3), 1304–1327. doi:10.1016/j.ejor.2005.11.064.
Rattadilok, P., Gaw, A., & Kwan, R. (2005). Distributed choice function hyper-heuristics for timetabling and scheduling. In E. Burke & M. Trick (Eds.), Practice and theory of automated timetabling V, Lecture notes in computer science (Vol. 3616, pp. 51–67). Berlin, Heidelberg: Springer. doi:10.1007/11593577_4.
Romeijn, H. E., & Morales, D. R. (2000). A class of greedy algorithms for the generalized assignment problem. Discrete Applied Mathematics, 103(13), 209–235. doi:10.1016/S0166-218X(99)00224-3.
Ropke, S., & Pisinger, D. (2006). An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science, 40(4), 455–472. doi:10.1287/trsc.1050.0135.
Spieksma, F. C. R. (1994). A branch-and-bound algorithm for the two-dimensional vector packing problem. Computers & Operations Research, 21(1), 19–25. doi:10.1016/0305-0548(94)90059-0.
Vazirani, V. V. (2001). Approximation algorithms. New York: Springer.
Wood, T., Shenoy, P. J., Venkataramani, A., & Yousif, M. S. (2007). Black-box and gray-box strategies for virtual machine migration. In Proceedings of the 4th USENIX conference on Networked systems design and implementation (NSDI’07) (Vol. 7, pp. 229–242).
Yagiura, M., Ibaraki, T., & Glover, F. (2004a). An ejection chain approach for the generalized assignment problem. INFORMS Journal on Computing, 16(2), 133–151. doi:10.1287/ijoc.1030.0036.
Yagiura, M., Ibaraki, T., & Glover, F. (2006). A path relinking approach with ejection chains for the generalized assignment problem. European Journal of Operational Research, 169(2), 548–569. doi:10.1016/j.ejor.2004.08.015.
Yagiura, M., Iwasaki, S., Ibaraki, T., & Glover, F. (2004). A very large-scale neighborhood search algorithm for the multi-resource generalized assignment problem. Discrete Optimization, 1, 87–98. doi:10.1016/j.disopt.2004.03.005.
Yagiura, M., Yamaguchi, T., & Ibaraki, T. (1998). A variable depth search algorithm with branching search for the generalized assignment problem. Optimization Methods and Software, 10, 419–441. doi:10.1080/10556789808805722.
Acknowledgments
The authors wish to thank the two anonymous reviewers for fruitful suggestions which help improve a previous version of this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Butelle, F., Alfandari, L., Coti, C. et al. Fast machine reassignment. Ann Oper Res 242, 133–160 (2016). https://doi.org/10.1007/s10479-015-2082-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-015-2082-3