Abstract
A substantial connection exists between supervised learning from data represented in logic form and the solution of the Minimum Cost Satisfiability Problem (MinCostSAT). Methods based on such connection have been developed and successfully applied in many contexts. The deployment of such methods to large-scale learning problem is often hindered by the computational challenge of solving MinCostSAT, a problem well known to be NP-complete. In this paper, we propose a GRASP-based metaheuristic designed for such problem, that proves successful in leveraging the very distinctive structure of the MinCostSAT problems arising in supervised learning. The algorithm is equipped with an original stopping criterion based on probabilistic assumptions which results very effective for deciding when the search space has been explored enough. Although the proposed solver may approach MinCostSAT of general form, in this paper we limit our analysis to some instances that have been created from artificial supervised learning problems, and show that our method outperforms more general purpose well established solvers.
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Notes
- 1.
For missing values, the algorithm was not able to find the optimal solution in 24 h.
References
Arisi, I., D’Onofrio, M., Brandi, R., Felsani, A., Capsoni, S., Drovandi, G., Felici, G., Weitschek, E., Bertolazzi, P., Cattaneo, A.: Gene expression biomarkers in the brain of a mouse model for alzheimer’s disease: Mining of microarray data by logic classification and feature selection. J. Alzheimer’s Dis. 24(4), 721–738 (2011)
Bertolazzi, P., Felici, G., Festa, P., Fiscon, G., Weitschek, E.: Integer programming models for feature selection: new extensions and a randomized solution algorithm. Eur. J. Oper. Res. 250(2), 389–399 (2016)
Bertolazzi, P., Felici, G., Weitschek, E.: Learning to classify species with barcodes. BMC Bioinform. 10(14), S7 (2009)
Cestarelli, V., Fiscon, G., Felici, G., Bertolazzi, P., Weitschek, E.: CAMUR: knowledge extraction from RNA-seq cancer data through equivalent classification rules. Bioinformatics 32(5), 697–704 (2016)
Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into SAT. J. Satisf. Boolean Model. Comput. 2, 1–26 (2006)
Felici, G., Truemper, K.: A minsat approach for learning in logic domains. INFORMS J. Comput. 14(1), 20–36 (2002)
Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6(2), 109–133 (1995)
Festa, P., Resende, M.G.C.: An annotated bibliography of GRASP - part I: algorithms. Int. Trans. Oper. Res. 16(1), 1–24 (2009)
Festa, P., Resende, M.G.C.: An annotated bibliography of GRASP - part II: applications. Int. Trans. Oper. Res. 16(2), 131–172 (2009)
Fu, Z., Malik, S.: Solving the minimum-cost satisfiability problem using SAT based branch-and-bound search. In: 2006 IEEE/ACM International Conference on Computer Aided Design, pp. 852–859, November 2006
Garey, M.R., Johnson, D.S.: Computers and Intractability, vol. 29. W.H. Freeman, New York (2002)
Manquinho, V.M., Marques-Silva, J.P.: Search pruning techniques in SAT-based branch-and-bound algorithms for the binate covering problem. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 21(5), 505–516 (2002)
Manquinho, V.M., Flores, P.F., Silva, J.P.M., Oliveira, A.L.: Prime implicant computation using satisfiability algorithms. In: Ninth IEEE International Conference on Tools with Artificial Intelligence, 1997 Proceedings, pp. 232–239. IEEE (1997)
Marques-Silva, J.P., Sakallah, K.A.: GRASP: a search algorithm for propositional satisfiability. IEEE Trans. Comput. 48(5), 506–521 (1999)
Martins, R., Manquinho, V., Lynce, I.: Clause sharing in deterministic parallel maximum satisfiability. In: RCRA International Workshop on Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion (2012)
Martins, R., Manquinho, V.M., Lynce, I.: Clause sharing in parallel MaxSAT. In: Hamadi, Y., Schoenauer, M. (eds.) LION 2012. LNCS, pp. 455–460. Springer, Heidelberg (2012). doi:10.1007/978-3-642-34413-8_44
Martins, R., Manquinho, V.M., Lynce, I.: Parallel search for maximum satisfiability. AI Commun. 25(2), 75–95 (2012)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Proceedings of the 38th Annual Design Automation Conference, DAC 2001, pp. 530–535. ACM, New York (2001)
de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). doi:10.1007/978-3-540-78800-3_24
Pipponzi, M., Somenzi, F.: An iterative algorithm for the binate covering problem. In: Proceedings of the European Design Automation Conference, EDAC 1990, pp. 208–211, March 1990
Ribeiro, C.C., Rosseti, I., Souza, R.C.: Probabilistic stopping rules for GRASP heuristics and extensions. Int. Trans. Oper. Res. 20(3), 301–323 (2013)
Scholz, F.W.: Maximum likelihood estimation (2004)
Servit, M., Zamazal, J.: Heuristic approach to binate covering problem. In: Proceedings The European Conference on Design Automation, pp. 123–129, March 1992
Sorensson, N., Een, N.: Minisat v1.13 - a sat solver with conflict-clause minimization. Technical report (2005(53))
Truemper, K.: Design of Logic-Based Intelligent Systems. Wiley-Interscience Publication, Wiley (2004)
Villa, T., Kam, T., Brayton, R.K., Sangiovanni-Vincenteili, A.L.: Explicit and implicit algorithms for binate covering problems. IEEE Trans. Comput. Aided Des. Integr. Circ. Syst. 16(7), 677–691 (1997)
Weitschek, E., Felici, G., Bertolazzi, P.: MALA: a microarray clustering and classification software. In: 2012 23rd International Workshop on Database and Expert Systems Applications, pp. 201–205, September 2012
Weitschek, E., Fiscon, G., Felici, G.: Supervised DNA barcodes species classification: analysis, comparisons and results. BioData Min. 7(1), 4 (2014)
Weitschek, E., Lo Presti, A., Drovandi, G., Felici, G., Ciccozzi, M., Ciotti, M., Bertolazzi, P.: Human polyomaviruses identification by logic mining techniques. Virol. J. 9(1), 58 (2012)
Acknowledgements
This work has been realized thanks to the use of the S.Co.P.E. computing infrastructure at the University of Napoli FEDERICO II.
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Felici, G., Ferone, D., Festa, P., Napoletano, A., Pastore, T. (2017). A GRASP for the Minimum Cost SAT Problem. In: Battiti, R., Kvasov, D., Sergeyev, Y. (eds) Learning and Intelligent Optimization. LION 2017. Lecture Notes in Computer Science(), vol 10556. Springer, Cham. https://doi.org/10.1007/978-3-319-69404-7_5
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