Abstract
Integer Linear Programs are widely used in areas such as routing problems, scheduling analysis and optimization, logic synthesis, and partitioning problems. As many of these problems have a Boolean nature, i.e., the variables are restricted to 0 and 1, so called Pseudo-Boolean solvers have been proposed. They are mostly based on SAT solvers which took continuous improvements over the past years. However, Pseudo-Boolean solvers are only able to optimize a single linear function while fulfilling several constraints. Unfortunately many real-world optimization problems have multiple objective functions which are often conflicting and have to be optimized simultaneously, resulting in general in a set of optimal solutions. As a consequence, a single-objective Pseudo-Boolean solver will not be able to find this set of optimal solutions. As a remedy, we propose three different algorithms for solving multi-objective Pseudo-Boolean problems. Our experimental results will show the applicability of these algorithms on the basis of several test cases.
Supported in part by the German Science Foundation (DFG), SFB 694.
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References
Barth, P.: A Davis-Putnam based enumeration algorithm for linear pseudo-Boolean optimization. Research Report MPI-I-95-2-003, Max-Planck-Institut für Informatik, Saarbrücken, Germany (1995)
Cook, S.A.: The complexity of theorem-proving procedures. In: STOC ’71: Proceedings of the third annual ACM symposium on Theory of computing, Shaker Heights, Ohio, United States, pp. 151–158. ACM Press, New York (1971), doi:10.1145/800157.805047
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press, New York (1972)
Marques-Silva, J.P., Sakallah, K.A.: Boolean satisfiability in electronic design automation. In: DAC ’00: Proceedings of the 37th conference on Design automation, Los Angeles, California, United States, pp. 675–680. ACM Press, New York (2000), doi:10.1145/337292.337611
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Commun. ACM 5(7), 394–397 (1962), doi:10.1145/368273.368557
Marques-Silva, J.P., Sakallah, K.A.: Grasp - a new search algorithm for satisfiability. In: ICCAD ’96: Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design, San Jose, California, United States, pp. 220–227. IEEE Computer Society, Washington (1996)
Moskewicz, M.W., et al.: Chaff: engineering an efficient sat solver. In: DAC ’01: Proceedings of the 38th conference on Design automation, Las Vegas, Nevada, United States, pp. 530–535. ACM Press, New York (2001), doi:10.1145/378239.379017
Zhang, L., et al.: Efficient conflict driven learning in a boolean satisfiability solver. In: ICCAD ’01: Proc. of the 2001 IEEE/ACM international conference on Computer-aided design, San Jose, California, pp. 279–285. IEEE Press, Piscataway (2001)
Aloul, F.A., et al.: Generic ilp versus specialized 0-1 ilp: an update. In: ICCAD ’02: Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design, San Jose, California, pp. 450–457. ACM Press, New York (2002), doi:10.1145/774572.774638
Teich, J., Blickle, T., Thiele, L.: An evolutionary approach to system-level synthesis. In: CODES ’97: Proceedings of the 5th International Workshop on Hardware/Software Co-Design, Washington, DC, USA, p. 167. IEEE Computer Society Press, Los Alamitos (1997)
Sheini, H.M., Sakallah, K.A.: Pueblo: A modern pseudo-boolean sat solver. In: DATE ’05: Proc. of the conf. on Design, Automation and Test in Europe, Washington, DC, USA, pp. 684–685. IEEE Computer Society Press, Los Alamitos (2005)
Chai, D., Kuehlmann, A.: A fast pseudo-boolean constraint solver. In: DAC ’03: Proc. of the 40th conference on Design automation, Anaheim, CA, USA, pp. 830–835. ACM Press, New York (2003), doi:10.1145/775832.776041
Eén, N., Sörensson, N.: Translating Pseudo-Boolean Constraints into SAT. Journal on Satisfiability, Boolean Moelding and Computation 2, 1–25 (2006)
Eén, N., Sörensson, N.: An Extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Tseitin, G.S.: On the Complexity of Derivations in Propositional Calculus. Studies in Contr. Math. and Math. Logic (1968)
Zitzler, E., et al.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evolutionary Computation 7(2), 117–132 (2003)
Manquinho, V.M., Marques-Silva, J.: Effective lower bounding techniques for pseudo-boolean optimization. In: DATE ’05: Proceedings of the conference on Design, Automation and Test in Europe, Washington, DC, USA, pp. 660–665. IEEE Computer Society Press, Los Alamitos (2005)
Berre, D.L., Simon, L.: Sat competition 2005. Website (2005), Available online at http://www.satcompetition.org/2005/
Manquinho, V., Roussel, O.: Pseudo boolean evaluation 2006. Website (2006), Available online at http://www.cril.univ-artois.fr/PB06/
Haubelt, C., et al.: SAT-Based Techniques in System Design. In: Wehn, N., Verkest, D. (eds.) Proceedings of Design, Automation and Test in Europe, Munich, Germany, March 2003, pp. 1168–1169. IEEE Computer Society Press, Los Alamitos (2003)
Deb, K. (ed.): Optimization for Engineering Design. Prentice-Hall of India Pvt.Ltd., New Delhi (1995)
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Lukasiewycz, M., Glaß, M., Haubelt, C., Teich, J. (2007). Solving Multi-objective Pseudo-Boolean Problems. In: Marques-Silva, J., Sakallah, K.A. (eds) Theory and Applications of Satisfiability Testing – SAT 2007. SAT 2007. Lecture Notes in Computer Science, vol 4501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72788-0_9
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DOI: https://doi.org/10.1007/978-3-540-72788-0_9
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