Abstract
The Algorithm Selection Problem is concerned with selecting the best algorithm to solve a given problem on a case-by-case basis. It has become especially relevant in the last decade, as researchers are increasingly investigating how to identify the most suitable existing algorithm for solving a problem instead of developing new algorithms. This survey presents an overview of this work focusing on the contributions made in the area of combinatorial search problems, where Algorithm Selection techniques have achieved significant performance improvements. We unify and organise the vast literature according to criteria that determine Algorithm Selection systems in practice. The comprehensive classification of approaches identifies and analyses the different directions from which Algorithm Selection has been approached. This chapter contrasts and compares different methods for solving the problem as well as ways of using these solutions.
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References
Aha, D.W.: Generalizing from case studies: a case study. In: Proceedings of the 9th International Workshop on Machine Learning, pp. 1–10. Morgan Kaufmann Publishers Inc, San Francisco (1992)
Allen, J.A., Minton, S.: Selecting the right heuristic algorithm: runtime performance predictors. In: McCalla, G. (ed.) AI 1996. LNCS, vol. 1081, pp. 41–53. Springer, Heidelberg (1996). doi:10.1007/3-540-61291-2_40
Amadini, R., Gabbrielli, M., Mauro, J.: SUNNY: a lazy portfolio approach for constraint solving. TPLP 14(4–5), 509–524 (2014)
Ansel, J., Chan, C., Wong, Y.L., Olszewski, M., Zhao, Q., Edelman, A., Amarasinghe, S.: PetaBricks: a language and compiler for algorithmic choice. SIGPLAN Not. 44(6), 38–49 (2009)
Ansótegui, C., Sellmann, M., Tierney, K.: A gender-based genetic algorithm for the automatic configuration of algorithms. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 142–157. Springer, Heidelberg (2009). doi:10.1007/978-3-642-04244-7_14
Arbelaez, A., Hamadi, Y., Sebag, M.: Online heuristic selection in constraint programming. In: Symposium on Combinatorial Search (2009)
Armstrong, W., Christen, P., McCreath, E., Rendell, A.P.: Dynamic algorithm selection using reinforcement learning. In: International Workshop on Integrating AI and Data Mining, pp. 18–25, December 2006
Balasubramaniam, D., Gent, I.P., Jefferson, C., Kotthoff, L., Miguel, I., Nightingale, P.: An automated approach to generating efficient constraint solvers. In: 34th International Conference on Software Engineering, pp. 661–671, June 2012
Bauer, E., Kohavi, R.: An empirical comparison of voting classification algorithms: bagging, boosting, and variants. Mach. Learn. 36(1–2), 105–139 (1999)
Beck, J.C., Fox, M.S.: Dynamic problem structure analysis as a basis for constraint-directed scheduling heuristics. Artif. Intell. 117(1), 31–81 (2000)
Beck, J.C., Freuder, E.C.: Simple rules for low-knowledge algorithm selection. In: Régin, J.-C., Rueher, M. (eds.) CPAIOR 2004. LNCS, vol. 3011, pp. 50–64. Springer, Heidelberg (2004). doi:10.1007/978-3-540-24664-0_4
Bhowmick, S., Eijkhout, V., Freund, Y., Fuentes, E., Keyes, D.: Application of machine learning in selecting sparse linear solvers. Technical report, Columbia University (2006)
Bhowmick, S., Toth, B., Raghavan, P.: Towards low-cost, high-accuracy classifiers for linear solver selection. In: Allen, G., Nabrzyski, J., Seidel, E., Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2009. LNCS, vol. 5544, pp. 463–472. Springer, Heidelberg (2009). doi:10.1007/978-3-642-01970-8_45
Borrett, J.E., Tsang, E.P.K.: A context for constraint satisfaction problem formulation selection. Constraints 6(4), 299–327 (2001)
Borrett, J.E., Tsang, E.P.K., Walsh, N.R.: Adaptive constraint satisfaction: The quickest first principle. In: ECAI, pp. 160–164 (1996)
Bougeret, M., Dutot, P., Goldman, A., Ngoko, Y., Trystram, D.: Combining multiple heuristics on discrete resources. In: IEEE International Symposium on Parallel and Distributed Processing, pp. 1–8. IEEE Computer Society, Washington, DC (2009)
Brazdil, P.B., Soares, C.: A comparison of ranking methods for classification algorithm selection. In: López de Mántaras, R., Plaza, E. (eds.) ECML 2000. LNCS (LNAI), vol. 1810, pp. 63–75. Springer, Heidelberg (2000). doi:10.1007/3-540-45164-1_8
Breiman, L.: Bagging predictors. Mach. Learn. 24(2), 123–140 (1996)
Brewer, E.A.: High-level optimization via automated statistical modeling. In: Proceedings of the 5th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming PPOPP 1995, pp. 80–91. ACM, New York (1995)
Brodley, C.E.: Addressing the selective superiority problem: automatic algorithm/model class selection. In: ICML, pp. 17–24 (1993)
Cahill, E.: Knowledge-based algorithm construction for real-world engineering PDEs. Math. Comput. Simul. 36(4–6), 389–400 (1994)
Carbonell, J., Etzioni, O., Gil, Y., Joseph, R., Knoblock, C., Minton, S., Veloso, M.: PRODIGY: an integrated architecture for planning and learning. SIGART Bull. 2, 51–55 (1991)
Carchrae, T., Beck, J.C.: Low-knowledge algorithm control. In: AAAI, pp. 49–54 (2004)
Carchrae, T., Beck, J.C.: Applying machine learning to Low-knowledge control of optimization algorithms. Comput. Intell. 21(4), 372–387 (2005)
Caseau, Y., Laburthe, F., Silverstein, G.: A meta-heuristic factory for vehicle routing problems. In: Jaffar, J. (ed.) CP 1999. LNCS, vol. 1713, pp. 144–158. Springer, Heidelberg (1999). doi:10.1007/978-3-540-48085-3_11
Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the really hard problems are. In: 12th International Joint Conference on Artificial Intelligence, pp. 331–337. Morgan Kaufmann Publishers Inc, San Francisco, CA, USA (1991)
Cicirello, V.A., Smith, S.F.: The max k-armed bandit: a new model of exploration applied to search heuristic selection. In: Proceedings of the 20th National Conference on Artificial Intelligence, pp. 1355–1361. AAAI Press (2005)
Cook, D.J., Varnell, R.C.: Maximizing the benefits of parallel search using machine learning. In: Proceedings of the 14th National Conference on Artificial Intelligence, pp. 559–564. AAAI Press (1997)
Demmel, J., Dongarra, J., Eijkhout, V., Fuentes, E., Petitet, A., Vuduc, R., Whaley, R.C., Yelick, K.: Self-adapting linear algebra algorithms and software. Proc. IEEE 93(2), 293–312 (2005)
Dietterich, T.G.: Ensemble methods in machine learning. In: Kittler, J., Roli, F. (eds.) MCS 2000. LNCS, vol. 1857, pp. 1–15. Springer, Heidelberg (2000). doi:10.1007/3-540-45014-9_1
Domingos, P.: How to get a free lunch: a simple cost model for machine learning applications. In: AAAI98/ICML98 Workshop on the Methodology of Applying Machine Learning, pp. 1–7. AAAI Press (1998)
Domshlak, C., Karpas, E., Markovitch, S.: To max or not to max: online learning for speeding up optimal planning. In: AAAI (2010)
Elsayed, S.A.M., Michel, L.: Synthesis of search algorithms from high-level CP models. In: Proceedings of the 9th International Workshop on Constraint Modelling and Reformulation, September 2010
Elsayed, S.A.M., Michel, L.: Synthesis of search algorithms from high-level CP models. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 256–270. Springer, Heidelberg (2011). doi:10.1007/978-3-642-23786-7_21
Epstein, S.L., Freuder, E.C.: Collaborative learning for constraint solving. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 46–60. Springer, Heidelberg (2001). doi:10.1007/3-540-45578-7_4
Epstein, S.L., Freuder, E.C., Wallace, R., Morozov, A., Samuels, B.: The adaptive constraint engine. In: Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 525–540. Springer, Heidelberg (2002). doi:10.1007/3-540-46135-3_35
Ewald, R., Schulz, R., Uhrmacher, A.M.: Selecting simulation algorithm portfolios by genetic algorithms. In: IEEE Workshop on Principles of Advanced and Distributed Simulation PADS 2010, IEEE Computer Society, Washington, DC (2010)
Fawcett, C., Vallati, M., Hutter, F., Hoffmann, J., Hoos, H., Leyton-Brown, K.: Improved features for runtime prediction of domain-independent planners. In: ICAPS (2014)
Fink, E.: Statistical selection among problem-solving methods. Technical report CMU-CS-97-101. Carnegie Mellon University (1997)
Fink, E.: How to solve it automatically: selection among problem-solving methods. In: Proceedings of the 4th International Conference on Artificial Intelligence Planning Systems, pp. 128–136. AAAI Press (1998)
Fukunaga, A.S.: Genetic algorithm portfolios. IEEE Congr. Evol. Comput. 2, 1304–1311 (2000)
Fukunaga, A.S.: Automated discovery of composite SAT variable-selection heuristics. In: 18th National Conference on Artificial Intelligence, pp. 641–648. American Association for Artificial Intelligence, Menlo Park (2002)
Fukunaga, A.S.: Automated discovery of local search heuristics for satisfiability testing. Evol. Comput. 16, 31–61 (2008)
Gagliolo, M., Schmidhuber, J.: A neural network model for inter-problem adaptive online time allocation. In: Duch, W., Kacprzyk, J., Oja, E., Zadrożny, S. (eds.) ICANN 2005. LNCS, vol. 3697, pp. 7–12. Springer, Heidelberg (2005). doi:10.1007/11550907_2
Gagliolo, M., Schmidhuber, J.: Impact of censored sampling on the performance of restart strategies. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 167–181. Springer, Heidelberg (2006). doi:10.1007/11889205_14
Gagliolo, M., Schmidhuber, J.: Learning dynamic algorithm portfolios. Ann. Math. Artif. Intell. 47(3–4), 295–328 (2006)
Gagliolo, M., Schmidhuber, J.: Towards distributed algorithm portfolios. In: Corchado, J.M., Rodríguez, S., Llinas, J., Molina, J.M. (eds.) Advances in Soft Computing. AINSC, vol. 50, pp. 634–643. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85863-8_75
Gagliolo, M., Schmidhuber, J.: Algorithm portfolio selection as a bandit problem with unbounded losses. Ann. Math. Artif. Intell. 61(2), 49–86 (2011)
Gagliolo, M., Zhumatiy, V., Schmidhuber, J.: Adaptive online time allocation to search algorithms. In: Boulicaut, J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) ECML 2004. LNCS (LNAI), vol. 3201, pp. 134–143. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30115-8_15
Garrido, P., Riff, M.: DVRP: a hard dynamic combinatorial optimisation problem tackled by an evolutionary hyper-heuristic. J. Heuristics 16, 795–834 (2010)
Gebruers, C., Guerri, A., Hnich, B., Milano, M.: Making choices using structure at the instance level within a case based reasoning framework. In: CPAIOR, pp. 380–386 (2004)
Gebruers, C., Hnich, B., Bridge, D., Freuder, E.: Using CBR to select solution strategies in constraint programming. In: Proceedings of ICCBR 2005, pp. 222–236 (2005)
Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T., Schneider, M.T., Ziller, S.: A portfolio solver for answer set programming: preliminary report. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS (LNAI), vol. 6645, pp. 352–357. Springer, Heidelberg (2011). doi:10.1007/978-3-642-20895-9_40
Gent, I., Jefferson, C., Kotthoff, L., Miguel, I., Moore, N., Nightingale, P., Petrie, K.: Learning when to use lazy learning in constraint solving. In: 19th European Conference on Artificial Intelligence, pp. 873–878, August 2010
Gent, I., Kotthoff, L., Miguel, I., Nightingale, P.: Machine learning for constraint solver design - a case study for the alldifferent constraint. In: 3rd Workshop on Techniques for implementing Constraint Programming Systems (TRICS), pp. 13–25 (2010)
Gerevini, A.E., Saetti, A., Vallati, M.: An automatically configurable portfolio-based planner with macro-actions: PbP. In: Proceedings of the 19th International Conference on Automated Planning and Scheduling, pp. 350–353 (2009)
Gomes, C.P., Selman, B.: Algorithm portfolio design: theory vs. practice. In: UAI, pp. 190–197 (1997)
Gomes, C.P., Selman, B.: Practical aspects of algorithm portfolio design. In: Proceedings of 3rd ILOG International Users Meeting (1997)
Gomes, C.P., Selman, B.: Algorithm portfolios. Artif. Intell. 126(1–2), 43–62 (2001)
Gratch, J., DeJong, G.: COMPOSER: a probabilistic solution to the utility problem in speed-up learning. In: AAAI, pp. 235–240 (1992)
Guerri, A., Milano, M.: Learning techniques for automatic algorithm portfolio selection. In: ECAI, pp. 475–479 (2004)
Guo, H.: Algorithm selection for sorting and probabilistic inference: a machine learning-based approach. Ph.D. thesis, Kansas State University (2003)
Guo, H., Hsu, W.H.: A learning-based algorithm selection meta-reasoner for the real-time MPE problem. In: Webb, G.I., Yu, X. (eds.) AI 2004. LNCS (LNAI), vol. 3339, pp. 307–318. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30549-1_28
Haim, S., Walsh, T.: Restart strategy selection using machine learning techniques. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 312–325. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02777-2_30
Hogg, T., Huberman, B.A., Williams, C.P.: Phase transitions and the search problem. Artif. Intell. 81(1–2), 1–15 (1996)
Hong, L., Page, S.E.: Groups of diverse problem solvers can outperform groups of high-ability problem solvers. Proc. Natl. Acad. Sci. U.S.A. 101(46), 16385–16389 (2004)
Hoos, H., Lindauer, M., Schaub, T.: claspfolio 2: Advances in algorithm selection for answer set programming. TPLP 14(4–5), 569–585 (2014)
Hoos, H.H.: Programming by optimization. Commun. ACM 55(2), 70–80 (2012)
Hoos, H.H., Kaminski, R., Lindauer, M., Schaub, T.: aspeed: Solver scheduling via answer set programming. Theory Pract. Logic Program. FirstView 15, 1–26 (2014)
Horvitz, E., Ruan, Y., Gomes, C.P., Kautz, H.A., Selman, B., Chickering, D.M.: A Bayesian approach to tackling hard computational problems. In: Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, pp. 235–244. Morgan Kaufmann Publishers Inc., San Francisco (2001)
Hough, P.D., Williams, P.J.: Modern machine learning for automatic optimization algorithm selection. In: Proceedings of the INFORMS Artificial Intelligence and Data Mining Workshop, November 2006
Howe, A.E., Dahlman, E., Hansen, C., Scheetz, M., Mayrhauser, A.: Exploiting competitive planner performance. In: Biundo, S., Fox, M. (eds.) ECP 1999. LNCS (LNAI), vol. 1809, pp. 62–72. Springer, Heidelberg (2000). doi:10.1007/10720246_5
Huberman, B.A., Lukose, R.M., Hogg, T.: An economics approach to hard computational problems. Science 275(5296), 51–54 (1997)
Hurley, B., Kotthoff, L., Malitsky, Y., O’Sullivan, B.: Proteus: a hierarchical portfolio of solvers and transformations. In: CPAIOR, May 2014
Hutter, F., Hamadi, Y., Hoos, H.H., Leyton-Brown, K.: Performance prediction and automated tuning of randomized and parametric algorithms. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 213–228. Springer, Heidelberg (2006). doi:10.1007/11889205_17
Hutter, F., Hoos, H.H., Leyton-Brown, K.: Sequential model-based optimization for general algorithm configuration. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 507–523. Springer, Heidelberg (2011). doi:10.1007/978-3-642-25566-3_40
Hutter, F., Hoos, H.H., Leyton-Brown, K.: Parallel algorithm configuration. In: Hamadi, Y., Schoenauer, M. (eds.) LION. LNCS, vol. 7219, pp. 55–70. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34413-8_5
Hutter, F., Hoos, H.H., Leyton-Brown, K., Stützle, T.: ParamILS: an automatic algorithm configuration framework. J. Artif. Int. Res. 36(1), 267–306 (2009)
Hutter, F., Hoos, H.H., Stützle, T.: Automatic algorithm configuration based on local search. In: Proceedings of the 22nd National Conference on Artificial Intelligence, pp. 1152–1157. AAAI Press (2007)
Kadioglu, S., Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm selection and scheduling. In: 17th International Conference on Principles and Practice of Constraint Programming, pp. 454–469 (2011)
Kadioglu, S., Malitsky, Y., Sellmann, M., Tierney, K.: ISAC instance-specific algorithm configuration. In: 19th European Conference on Artificial Intelligence, pp. 751–756. IOS Press (2010)
Kamel, M.S., Enright, W.H., Ma, K.S.: ODEXPERT: an expert system to select numerical solvers for initial value ODE systems. ACM Trans. Math. Softw. 19(1), 44–62 (1993)
Kotthoff, L.: Hybrid regression-classification models for algorithm selection. In: 20th European Conference on Artificial Intelligence, pp. 480–485, August 2012
Kotthoff, L.: Algorithm selection for combinatorial search problems: a survey. AI Mag. 35(3), 48–60 (2014)
Kotthoff, L., Gent, I.P., Miguel, I.: An evaluation of machine learning in algorithm selection for search problems. AI Commun. 25(3), 257–270 (2012)
Kotthoff, L., Kerschke, P., Hoos, H., Trautmann, H.: Improving the state of the art in inexact TSP solving using per-instance algorithm selection. In: Dhaenens, C., Jourdan, L., Marmion, M.-E. (eds.) LION 2015. LNCS, vol. 8994, pp. 202–217. Springer, Heidelberg (2015). doi:10.1007/978-3-319-19084-6_18
Kotthoff, L., Miguel, I., Nightingale, P.: Ensemble classification for constraint solver configuration. In: 16th International Conference on Principles and Practices of Constraint Programming, pp. 321–329, September 2010
Kroer, C., Malitsky, Y.: Feature filtering for Instance-Specific algorithm configuration. In: Proceedings of the 23rd International Conference on Tools with Artificial Intelligence (2011)
Kuefler, E., Chen, T.-Y.: On using reinforcement learning to solve sparse linear systems. In: Bubak, M., Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2008. LNCS, vol. 5101, pp. 955–964. Springer, Heidelberg (2008). doi:10.1007/978-3-540-69384-0_100
Lagoudakis, M.G., Littman, M.L.: Algorithm selection using reinforcement learning. In: Proceedings of the 17th International Conference on Machine Learning, pp. 511–518. Morgan Kaufmann Publishers Inc., San Francisco (2000)
Lagoudakis, M.G., Littman, M.L.: Learning to select branching rules in the DPLL procedure for satisfiability. In: LICS/SAT, pp. 344–359 (2001)
Langley, P.: Learning effective search heuristics. In: IJCAI, pp. 419–421 (1983)
Langley, P.: Learning search strategies through discrimination. Int. J. Man-Mach. Stud. 18, 513–541 (1983)
Leite, R., Brazdil, P., Vanschoren, J., Queiros, F.: Using active testing and meta-level information for selection of classification algorithms. In: 3rd PlanLearn Workshop, August 2010
Leyton-Brown, K., Nudelman, E., Shoham, Y.: Learning the empirical hardness of optimization problems: the case of combinatorial auctions. In: Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 556–572. Springer, Heidelberg (2002). doi:10.1007/3-540-46135-3_37
Leyton-Brown, K., Nudelman, E., Shoham, Y.: Empirical hardness models: methodology and a case study on combinatorial auctions. J. ACM 56, 1–52 (2009)
Lindauer, M., Hoos, H., Hutter, F.: From sequential algorithm selection to parallel portfolio selection. In: Dhaenens, C., Jourdan, L., Marmion, M.-E. (eds.) LION 2015. LNCS, vol. 8994, pp. 1–16. Springer, Heidelberg (2015). doi:10.1007/978-3-319-19084-6_1
Lindauer, M., Hoos, H.H., Hutter, F., Schaub, T.: AutoFolio: algorithm configuration for algorithm selection. In: Twenty-Ninth AAAI Workshops on Artificial Intelligence, January 2015
Little, J., Gebruers, C., Bridge, D., Freuder, E.: Capturing constraint programming experience: a case-based approach. In: Modref (2002)
Lobjois, L., Lemaître, M.: Branch and bound algorithm selection by performance prediction. In: Proceedings of the 15th National/10th Conference on Artificial Intelligence/Innovative Applications of Artificial Intelligence, pp. 353–358. American Association for Artificial Intelligence, Menlo Park (1998)
Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Non-model-based algorithm portfolios for SAT. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 369–370. Springer, Heidelberg (2011). doi:10.1007/978-3-642-21581-0_33
Malitsky, Y., Sabharwal, A., Samulowitz, H., Sellmann, M.: Algorithm portfolios based on cost-sensitive hierarchical clustering. In: IJCAI, August 2013
Minton, S.: An analytic learning system for specializing heuristics. In: Proceedings of the 13th International Joint Conference on Artifical Intelligence IJCAI 1993, pp. 922–928. Morgan Kaufmann Publishers Inc., San Francisco (1993)
Minton, S.: Integrating heuristics for constraint satisfaction problems: a case study. In: Proceedings of the 11th National Conference on Artificial Intelligence, pp. 120–126. AAAI (1993)
Minton, S.: Automatically configuring constraint satisfaction programs: a case study. Constraints 1, 7–43 (1996)
Musliu, N., Schwengerer, M.: Algorithm selection for the graph coloring problem. In: Nicosia, G., Pardalos, P. (eds.) LION 2013. LNCS, vol. 7997, pp. 389–403. Springer, Heidelberg (2013). doi:10.1007/978-3-642-44973-4_42
Nareyek, A.: Choosing search heuristics by non-stationary reinforcement learning. In: Nareyek, A. (ed.) Metaheuristics: Computer Decision-Making. Applied Optimization, vol. 86, pp. 523–544. Kluwer Academic Publishers, New York (2001)
Nikolić, M., Marić, F., Janičić, P.: Instance-based selection of policies for SAT solvers. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 326–340. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02777-2_31
Nudelman, E., Leyton-Brown, K., Hoos, H.H., Devkar, A., Shoham, Y.: Understanding random SAT: beyond the clauses-to-variables ratio. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 438–452. Springer, Heidelberg (2004). doi:10.1007/978-3-540-30201-8_33
O’Mahony, E., Hebrard, E., Holland, A., Nugent, C., O’Sullivan, B.: Using case-based reasoning in an algorithm portfolio for constraint solving. In: Proceedings of the 19th Irish Conference on Artificial Intelligence and Cognitive Science (2008)
Opitz, D., Maclin, R.: Popular ensemble methods: an empirical study. J. Artif. Intell. Res. 11, 169–198 (1999)
Paparrizou, A., Stergiou, K.: Evaluating simple fully automated heuristics for adaptive constraint propagation. In: ICTAI (2012)
Petrik, M.: Statistically optimal combination of algorithms. In: Local Proceedings of SOFSEM 2005 (2005)
Petrik, M., Zilberstein, S.: Learning parallel portfolios of algorithms. Ann. Math. Artif. Intell. 48(1–2), 85–106 (2006)
Petrovic, S., Qu, R.: Case-based reasoning as a heuristic selector in hyper-heuristic for course timetabling problems. In: KES, pp. 336–340 (2002)
Pfahringer, B., Bensusan, H., Giraud-Carrier, C.G.: Meta-Learning by landmarking various learning algorithms. In: 17th International Conference on Machine Learning ICML 2000, pp. 743–750, Morgan Kaufmann Publishers Inc., San Francisco (2000)
Pulina, L., Tacchella, A.: A multi-engine solver for quantified Boolean formulas. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 574–589. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74970-7_41
Pulina, L., Tacchella, A.: A self-adaptive multi-engine solver for quantified boolean formulas. Constraints 14(1), 80–116 (2009)
Rao, R.B., Gordon, D., Spears, W.: For every generalization action, is there really an equal and opposite reaction? Analysis of the conservation law for generalization performance. In: Proceedings of the 12th International Conference on Machine Learning, pp. 471–479. Morgan Kaufmann (1995)
Rice, J.R.: The algorithm selection problem. Adv. Comput. 15, 65–118 (1976)
Rice, J.R., Ramakrishnan, N.: How to get a free lunch (at no cost). Techical report 99–014, Purdue University, April 1999
Roberts, M., Howe, A.E.: Directing a portfolio with learning. In: AAAI 2006 Workshop on Learning for Search (2006)
Roberts, M., Howe, A.E.: Learned models of performance for many planners. In: ICAPS 2007 Workshop AI Planning and Learning (2007)
Roberts, M., Howe, A.E., Wilson, B., des Jardins, M.: What makes planners predictable? In: ICAPS, pp. 288–295 (2008)
Sakkout, H., Wallace, M.G., Richards, E.B.: An instance of adaptive constraint propagation. In: Freuder, E.C. (ed.) CP 1996. LNCS, vol. 1118, pp. 164–178. Springer, Heidelberg (1996). doi:10.1007/3-540-61551-2_73
Samulowitz, H., Memisevic, R.: Learning to solve QBF. In: Proceedings of the 22nd National Conference on Artificial Intelligence, pp. 255–260. AAAI Press (2007)
Sayag, T., Fine, S., Mansour, Y.: Combining multiple heuristics. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 242–253. Springer, Heidelberg (2006). doi:10.1007/11672142_19
Schapire, R.E.: The strength of weak learnability. Mach. Learn. 5(2), 197–227 (1990)
Sillito, J.: Improvements to and estimating the cost of solving constraint satisfaction problems. Master’s thesis, University of Alberta (2000)
Silverthorn, B., Miikkulainen, R.: Latent class models for algorithm portfolio methods. In: Proceedings of the 24th AAAI Conference on Artificial Intelligence (2010)
Smith, T.E., Setliff, D.E.: Knowledge-based constraint-driven software synthesis. In: Knowledge-Based Software Engineering Conference, pp. 18–27, September 1992
Smith-Miles, K., Lopes, L.: Measuring instance difficulty for combinatorial optimization problems. Comput. Oper. Res. 39(5), 875–889 (2012)
Smith-Miles, K.A.: Cross-disciplinary perspectives on meta-learning for algorithm selection. ACM Comput. Surv. 41, 6: 1–6: 25 (2008)
Smith-Miles, K.A.: Towards insightful algorithm selection for optimisation using meta-learning concepts. In: IEEE International Joint Conference on Neural Networks, pp. 4118–4124, June 2008
Soares, C., Brazdil, P.B., Kuba, P.: A meta-learning method to select the kernel width in support vector regression. Mach. Learn. 54(3), 195–209 (2004)
Stergiou, K.: Heuristics for dynamically adapting propagation in constraint satisfaction problems. AI Commun. 22(3), 125–141 (2009)
Stern, D.H., Samulowitz, H., Herbrich, R., Graepel, T., Pulina, L., Tacchella, A.: Collaborative expert portfolio management. In: AAAI, pp. 179–184 (2010)
Streeter, M.J., Golovin, D., Smith, S.F.: Combining multiple heuristics online. In: Proceedings of the 22nd National Conference on Artificial Intelligence, pp. 1197–1203. AAAI Press (2007)
Streeter, M.J., Golovin, D., Smith, S.F.: Restart schedules for ensembles of problem instances. In: Proceedings of the 22nd National Conference on Artificial Intelligence, pp. 1204–1210. AAAI Press (2007)
Streeter, M.J., Smith, S.F.: New techniques for algorithm portfolio design. In: UAI, pp. 519–527 (2008)
Terashima-Marín, H., Ross, P., Valenzuela-Rendón, M.: Evolution of constraint satisfaction strategies in examination timetabling. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 635–642. Morgan Kaufmann (1999)
Tolpin, D., Shimony, S.E.: Rational deployment of CSP heuristics. In: IJCAI, pp. 680–686 (2011)
Tsang, E.P.K., Borrett, J.E., Kwan, A.C.M.: An attempt to map the performance of a range of algorithm and heuristic combinations. In: Proceedings of AISB 1995, pp. 203–216. IOS Press (1995)
Utgoff, P.E.: Perceptron trees: a case study in hybrid concept representations. In: National Conference on Artificial Intelligence, pp. 601–606 (1988)
Vassilevska, V., Williams, R., Woo, S.L.M.: Confronting hardness using a hybrid approach. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms SODA 2006, pp. 1–10. ACM, New York (2006)
Vrakas, D., Tsoumakas, G., Bassiliades, N., Vlahavas, I.: Learning rules for adaptive planning. In: Proceedings of the 13th International Conference on Automated Planning and Scheduling, pp. 82–91 (2003)
Wang, J., Tropper, C.: Optimizing time warp simulation with reinforcement learning techniques. In: Proceedings of the 39th Conference on Winter simulation WSC 2007, pp. 577–584. IEEE Press, Piscataway (2007)
Watson, J.: Empirical modeling and analysis of local search algorithms for the job-shop scheduling problem. Ph.D. thesis, Colorado State University, Fort Collins, CO, USA (2003)
Weerawarana, S., Houstis, E.N., Rice, J.R., Joshi, A., Houstis, C.E.: PYTHIA: a knowledge-based system to select scientific algorithms. ACM Trans. Math. Softw. 22(4), 447–468 (1996)
Wei, W., Li, C.M., Zhang, H.: Switching among non-weighting, clause weighting, and variable weighting in local search for SAT. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 313–326. Springer, Heidelberg (2008). doi:10.1007/978-3-540-85958-1_21
Wilson, D., Leake, D., Bramley, R.: Case-based recommender components for scientific problem-solving environments. In: Proceedings of the 16th International Association for Mathematics and Computers in Simulation World Congress (2000)
Wolpert, D.H.: Stacked generalization. Neural Netw. 5, 241–259 (1992)
Wolpert, D.H.: The supervised learning no-free-lunch theorems. In: Proceedings of the 6th Online World Conference on Soft Computing in Industrial Applications, pp. 25–42 (2001)
Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)
Wu, H., van Beek, P.: On portfolios for backtracking search in the presence of deadlines. In: Proceedings of the 19th IEEE International Conference on Tools with Artificial Intelligence, pp. 231–238. IEEE Computer Society, Washington, DC (2007)
Xu, L., Hoos, H.H., Leyton-Brown, K.: Hierarchical hardness models for SAT. In: CP, pp. 696–711 (2007)
Xu, L., Hoos, H.H., Leyton-Brown, K.: Hydra: automatically configuring algorithms for portfolio-based selection. In: 24th Conference of the Association for the Advancement of Artificial Intelligence (AAAI 2010), pp. 210–216 (2010)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla-07: the design and analysis of an algorithm portfolio for SAT. In: CP, pp. 712–727 (2007)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla: portfolio-based algorithm selection for SAT. J. Artif. Intell. Res. (JAIR) 32, 565–606 (2008)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla2009: an automatic algorithm portfolio for SAT. In: 2009 SAT Competition (2009)
Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: Hydra-MIP: automated algorithm configuration and selection for mixed integer programming. In: RCRA Workshop on Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion at the International Joint Conference on Artificial Intelligence (IJCAI) (2011)
Xu, L., Hutter, F., Hoos, H., Leyton-Brown, K.: Evaluating component solver contributions to portfolio-based algorithm selectors. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 228–241. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31612-8_18
Yu, H., Rauchwerger, L.: An adaptive algorithm selection framework for reduction parallelization. IEEE Trans. Parallel Distrib. Syst. 17(10), 1084–1096 (2006)
Yu, H., Zhang, D., Rauchwerger, L.: An adaptive algorithm selection framework. In: Proceedings of the 13th International Conference on Parallel Architectures and Compilation Techniques, pp. 278–289. IEEE Computer Society, Washington, DC (2004)
Yun, X., Epstein, S.L.: Learning algorithm portfolios for parallel execution. In: Hamadi, Y., Schoenauer, M. (eds.) Proceedings of the 6th International Conference Learning and Intelligent Optimisation LION. LNCS, vol. 7219, pp. 323–338. Springer, Heidelberg (2012)
Acknowledgements
Ian Miguel and Ian Gent provided valuable feedback that helped shape this chapter. We also thank the anonymous reviewers of a previous version of this chapter whose detailed comments helped to greatly improve it. This work was supported by an EPSRC doctoral prize and EU FP7 FET project ICON. A shorter version of this chapter has appeared in AI Magazine [84].
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Kotthoff, L. (2016). Algorithm Selection for Combinatorial Search Problems: A Survey. In: Bessiere, C., De Raedt, L., Kotthoff, L., Nijssen, S., O'Sullivan, B., Pedreschi, D. (eds) Data Mining and Constraint Programming. Lecture Notes in Computer Science(), vol 10101. Springer, Cham. https://doi.org/10.1007/978-3-319-50137-6_7
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