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Merging variables: one technique of search in pseudo-Boolean optimization. (English) Zbl 1429.90100
Bykadorov, Igor (ed.) et al., Mathematical optimization theory and operations research. 18th international conference, MOTOR 2019, Ekaterinburg, Russia, July 8–12, 2019. Revised selected papers. Cham: Springer. Commun. Comput. Inf. Sci. 1090, 86-102 (2019).
Summary: In the present paper, we describe new heuristic technique, which can be applied to the optimization of pseudo-Boolean functions including Black-Box functions. This technique is based on a simple procedure which consists in transition from the optimization problem over Boolean hypercube to the optimization problem of auxiliary function in a specially constructed metric space. It is shown that there is a natural connection between the points of the original Boolean hypercube and points from new metric space. For a Boolean hypercube with fixed dimension it is possible to construct a number of such metric spaces. The proposed technique can be considered as a special case of Variable Neighborhood Search, which is focused on pseudo-Boolean optimization. Preliminary computational results show high efficiency of the proposed technique on some reasonably hard problems. Also it is shown that the described technique in combination with the well-known \((1+1)\)-Evolutionary Algorithm allows to decrease the upper bound on the runtime of this algorithm for arbitrary pseudo-Boolean functions.
For the entire collection see [Zbl 1428.90004].
MSC:
90C59 Approximation methods and heuristics in mathematical programming
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[1] Boros, E., Hammer, P.L.: Pseudo-boolean optimization. Discrete Appl. Math. 123(1-3), 155-225 (2002) · Zbl 1076.90032
[2] Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, vol. 185. IOS Press, Amsterdam (2009) · Zbl 1183.68568
[3] Burke, E., Kendall, G. (eds.): Search Methodologies, 2nd edn. Springer, New York (2014). https://doi.org/10.1007/978-1-4614-6940-7
[4] McWilliams, F., Sloan, N.: The Theory of Error-Correcting Codes. North Holland, Amsterdam (1983)
[5] Luke, S.: Essentials of Metaheuristics, 2nd edn. George Mason University, Fairfax (2015)
[6] Rudolph, G.: Convergence properties of evolutionary algorithms. Ph.D. thesis, Hamburg (1997) · Zbl 0891.93089
[7] Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theor. Comput. Sci. 276(1-2), 51-81 (2002) · Zbl 1002.68037
[8] Stanley, R.: Enumerative Combinatorics. Cambridge University Press, Cambridge (2011) · Zbl 1247.05003
[9] Feller, W.: An Introduction to Probability Theory and its Applications, 3rd edn. Wiley, Hoboken (1970) · Zbl 0158.34902
[10] Mladenović, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097-1100 (1997) · Zbl 0889.90119
[11] Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. Eur. J. Oper. Res. 130(3), 449-467 (2001) · Zbl 0981.90063
[12] Hansen, P., Mladenović, N., Todosijević, R., Hanafi, S.: Variable neighborhood search: basics and variants. EURO J. Comput. Optim. 5(3), 423-454 (2016) · Zbl 1390.90586
[13] Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers, Dordrecht (1997) · Zbl 0930.90083
[14] Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into SAT. JSAT 2(1-4), 1-26 (2006) · Zbl 1116.68083
[15] Rivest, R.L.: The MD4 message digest algorithm. In: Menezes, A.J., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 303-311. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-38424-3_22 · Zbl 0800.68418
[16] Otpuschennikov, I., Semenov, A., Gribanova, I., Zaikin, O., Kochemazov, S.: Encoding cryptographic functions to SAT using TRANSALG system. In: The 22nd European Conference on Artificial Intelligence (ECAI 2016). Frontiers in Artificial Intelligence and Applications, vol. 285, pp. 1594-1595. IOS Press (2016)
[17] Marques-Silva, J.P., Lynce, I., Malik, S.: Conflict-driven clause learning SAT solvers. In: Biere et al. [2], pp. 131-153
[18] Williams, R., Gomes, C.P., Selman, B.: Backdoors to typical case complexity. In: The 18th International Joint Conference on Artificial Intelligence (IJCAI 2003), pp. 1173-1178 (2003)
[19] Soos, M., Nohl, K., Castelluccia, C.: Extending SAT solvers to cryptographic problems. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 244-257. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02777-2_24
[20] Biere, A.: CaDiCaL, Lingeling, Plingeling, Treengeling, YalSAT entering the SAT competition 2017. In: Balyo, T., Heule, M.J.H., Järvisalo, M. (eds.) SAT Competition 2017, vol. B-2017-1, pp. 14-15 (2017)
[21] Ahuja, R.K., Ergun, O., Orlin, J.B., Punnen, A.P.: A survey of very large-scale neighborhood search techniques. Discrete Appl. Math. 123(1-3), 75-102 (2002) · Zbl 1014.68052
[22] Avella, P., D’Auria, B., Salerno, S., Vasil’ev, I.: A computational study of local search algorithms for italian high-school timetabling. J. Heuristics 13(6), 543-556 (2007) · Zbl 1144.90451
[23] Doerr, B.: Analyzing randomized search heuristics via stochastic domination. Theor. Comput. Sci. 773, 115-137 (2019) · Zbl 07057289
[24] Li, C., Manya, F.: MaxSAT. In: Biere et al. [2], pp. 613-632
[25] Ansótegui, C., Heymann, B., Pon, J., Sellmann, M., Tierney, K.: Hyper-reactive tabu search for MaxSAT. In: Battiti, R., Brunato, M., Kotsireas, I., Pardalos, P.M. (eds.) LION 12 2018. LNCS, vol. 11353, pp. 309-325. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-05348-2_27
[26] Bouhmala, N., Øvergård, K.I.: Combining genetic algorithm with variable neighborhood search for MAX-SAT. In: Zelinka, I., Vasant, P., Duy, V.H., Dao, T.T. (eds.) Innovative Computing, Optimization and Its Applications. SCI, vol. 741, pp. 73-92. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-66984-7_5
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