Abstract
Having in mind the idea that the computational effort and knowledge gained while solving a problem’s instance should be used to solve other ones, we present a new strategy that allows to take advantage of both aspects. The strategy is based on a set of operators and a basic learning process that is fed up with the information obtained while solving several instances. The output of the learning process is an adjustment of the operators. The instances can be managed sequentially or simultaneously by the strategy, thus varying the information available for the learning process. The method has been tested on different SAT instance classes and the results confirm that (a) the usefulness of the learning process and (b) that embedding problem specific algorithms into our strategy, instances can be solved faster than applying these algorithms instance by instance.
Notes
We had also considered to equally distribute those \(E - E^\prime\) evaluations not used by instance \(j\) among the remaining ones. However, as the results of this scheme were worse than the ones obtained by the scheme presented here we decided to omit them in the paper.
The reader should note that the computational time per evaluation or local search step is longer for gsat/tabu than for wsat and wsat/tabu. Nevertheless, we decide to use the number of local search steps as an efficiency measure since it has been used in very known works, as Hoos and Stützle (2000a) and Schuurmans and Southey (2001). A detailed study about the CPU time per step for these SAT solvers can be found in Hoos and Stützle (2000a).
References
Bäck T (1992) The interaction of mutation rate, selection, and self-adaptation within a genetic algorithm. In: Männer R, Manderick B (eds) Parallel problem solving from nature, pp 85–94
Barr RS, Golden BL, Kelly JP, Resende MGC, Stewart W (1995) Designing and reporting on computational experiments with heuristic methods. J Heuristics 1:9–32
Battiti R, Tecchiolli G (1994) The reactive tabu search. ORSA J Comput 6(2):126–140
Battiti R, Brunato M, Mascia F (2008) Reactive search and intelligent optimization, volume 45 of operations research/computer science interfaces. Springer-Verlag, Berlin
Birattari M (2005) The problem of tuning metaheuristics as seen from a machine learning perspective, volume 292 of Dissertations in artificial intelligence. IOS Press
Bouthillier AL, Crainic TG (2005) A cooperative parallel meta-heuristic for the vehicle routing problem with time windows. Comput Oper Res 32(7):1685–1708
Bräysy O (2003) A reactive variable neighborhood search for the vehicle-routing problem with time windows. INFORMS J Comput 15(4):347–368
Burke EK, Kendall G (2005) Search methodologies: introductory tutorials in optimization and decision support techniques. Springer, New York
Burke E, Kendall G, Newall J, Hart E, Ross P, Schulenburg S (2003) Handbook of metaheuristics. In: Hyper-heuristics: an emerging direction in modern search technology, pp 457–474
Cruz C, Pelta D (2009) Soft computing and cooperative strategies for optimization. Appl Soft Comput 9(1):30–38
Dorigo M, Stützle T (2004) Ant colony optimization. Bradford Book
Fleischer MA (1996) Cybernetic optimization by simulated annealing: accelerating convergence by parallel processing and probabilistic feedback control. J Heuristics 1(2):225–246
Gagliolo M, Schmidhuber J (2006) Learning dynamic algorithm portfolios. Ann Math Artif Intell 47(3–4):295–328
Gent I, Hoos HH, Prosser P, Walsh T (1999) Morphing: combining structure and randomness. In: Proceedings of the sixth national conference on artificial intelligence (AAAI’99), pp 654–660
Glover FW, Kochenberger GA (2003) Handbook of metaheuristics. International Series in Operations Research & Management Science. Springer, New York
Hart W, Krasnogor N, Smith J (eds) (2004) Recent advances in memetic algorithms. Studies in fuzziness and soft computing. Physica-Verlag
Hooker J (1995) Testing heuristics: we have it all wrong. J Heuristics 1:33–42
Hoos H, Stützle T (2000a) Local search algorithms for SAT: an empirical evaluation. J Autom Reason 24(4):421–481
Hoos H, Stützle T (2000b) SATLIB: an online resource for research on SAT. In: van Maaren H, Gent IP, Walsh T (eds) SAT2000, pp 283–292. IOS Press
Hoos HH, Stützle T (2004) Stochastic local search: foundations & applications. Elsevier, Amsterdam
Horvitz E, Ruan Y, Gomes CP, Kautz HA, Selman B, Chickering DM (2001) A bayesian approach to tackling hard computational problems. In: UAI ’01: Proceedings of the seventeenth conference in uncertainty in artificial intelligence, San Francisco, CA, USA. Morgan Kaufmann, Los Altos, pp 235–244
Huberman BA, Lukose RM, Hogg T (1997) An economics approach to hard computational problems. Science 275:51–54
Hutter F, Hoos HH, Stützle T (2007) Automatic algorithm configuration based on local search. In: Proceedings of the twenty-second national conference on artificial intelligence (AAAI’07), pp 1152–1157
Kennedy J, Eberhart RC (2001) Swarm intelligence. Morgan Kaufmann, Los Altos
Lagoudakis MG, Littman ML (2000) Algorithm selection using reinforcement learning. In: ICML ’00: Proceedings of the seventeenth international conference on machine learning, San Francisco, CA, USA. Morgan Kaufmann, Los Altos, pp 511–518
Lin L, Mitsuo G (2008) Auto-tuning strategy for evolutionary algorithms: balancing between exploration and exploitation. Soft Comput 13(2):157–168
Lobo FG, Lima CF, Michalewicz Z (2007) Parameter setting in evolutionary algorithms, volume 54 of studies in computational intelligence. Springer, New York
Masegosa AD, Royo AS, Pelta D (2008) Nature-inspired cooperative strategies, volume 129 of studies in computational sciences. In: An adaptive metaheuristic for the simultaneous resolution of a set of instances. Springer, New York, pp 125–137
Mateo J, de la Ossa L (2006) LiO: tool for metaheuristics. http://www.info-ab.uclm.es/simd/SOFTWARE/LIO/
Mazure B, Sais L, Grégoire E (1997) Tabu search for SAT. In: Proceedings of the fourteenth national conference on artificial intelligence (AAAI’97), pp 281–285
McAllester D, Selman B, Kautz H (1997) Evidence for invariants in local search. In: Proceedings of the fourteenth national conference on artificial intelligence (AAAI’97), pp 321–326
Ong Y-S, Lim M-H, Zhu N, Wong K-W (2006) Classification of adaptive memetic algorithms:a comparative study. IEEE Trans Syst Man Cybern B: Cybern 36(1):141–152
Pelta D, Krasnogor N (2004) Multimeme algorithms using fuzzy logic based memes for protein structure prediction. In: Hart W, Krasnogor N, Smith J (eds) Recent advances in memetic algorithms, volume 166 of studies in fuzziness and soft computing. Physica-Verlag, Berlin, pp 49–54
Pelta D, Blanco A, Verdegay J (2002) A fuzzy valuation-based local search framework for combinatorial optimization problems. J Fuzzy Optim Decis Mak 1(2):177–193
Pelta D, Cruz C, Gonzalez J (2009) A study on diversity and cooperation in a multiagent strategy for dynamic optimization problems. Int J Intell Syst 24(7):844–861
Pelta D, Cruz C, Sancho-Royo A, Verdegay J (2006) Using memory and fuzzy rules in a co-operative multi-thread strategy for optimization. Inf Sci 176(13):1849–1868
Petrik M, Zilberstein S (2006) Learning parallel portfolios of algorithms. Ann Math Artif Intell 48(1–2):85–106
Schuurmans D, Southey F (2001) Local search characteristics of incomplete SAT procedures. Artif Intell 132(2):121–150
Selman B, Levesque H, Mitchell D (1992) A new method for solving hard satisfiability problems. In: Proceedings of the ninth national conference on artificial intelligence (AAAI’92), pp 440–446
Selman B, Kautz H, Cohen B (1994) Noise strategies for improving local search. In: Proceedings of the twelfth national conference on artificial intelligence (AAAI’95). MIT Press, Cambridge, pp 337–343
Singer J, Gent IP, Smaill A (2000) Backbone fragility and the local search cost peak. J Artif Intell Res 12:235–270
Smith J (2007a) Coevolving memetic algorithms: a review and progress report. IEEE Trans Syst Man Cybern B: Cybern 37(1):6–17
Smith J (2007b) Credit assignment in adaptive memetic algorithms. In: Proceedings of GECCO 2007, pp 1412–1419
Smith J, Fogarty T (1997) Operator and parameter adaptation in genetic algorithms. Soft Comput 1(2):81–87
White T, Oppacher F (1994) Adaptive crossover using automata. Lect Notes Comput Sci 866:229–238
Wong Y-Y, Lee K-H, Leung K-S, Ho C-W (2003) A novel approach in parameter adaptation and diversity maintenance for genetic algorithms. Soft Comput 7(8):506–515
Xu L, Hutter F, Hoos HH, Leyton-Brown K (2008) SATzilla: portfolio-based algorithm selection for SAT. J Artif Intell Res 32:565–606
Acknowledgments
A.D. Masegosa is supported by the scholarship program FPI from the Spanish Ministry of Science and Innovation. This work has been partially funded by the project TIN2008-01948 from the Spanish Ministry of Science and Innovation and P07-TIC-02970 from the Andalusian Government. The authors wish to thank the anonymous reviewers for their useful comments.
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Masegosa, A.D., Pelta, D.A. & González, J.R. Solving multiple instances at once: the role of search and adaptation. Soft Comput 15, 233–250 (2011). https://doi.org/10.1007/s00500-010-0564-4
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DOI: https://doi.org/10.1007/s00500-010-0564-4