Penalty formulations and trap-avoidance strategies for solving hard satisfiability problems

Journal of Computer Science and Technology

Volumn 20, Issue 1, 2005, Pages 3-17

  Wah, Benjamin W ^a   Wu, Zhe ^b  

^a University of Illinois at Urbana Champaign   (United States)

^b ORACLE CORPORATION   (United States)

Author keywords

Boolean satisfiability; Constraint satisfaction; Knowledge representation and reasoning; Penalty formulation; Saddle point; Search; Techniques of algorithms

Indexed keywords

ALGORITHMS; BENCHMARKING; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; HEURISTIC METHODS; KNOWLEDGE REPRESENTATION; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS);

BOOLEAN SATISFIABILITY; CONSTRAINT SATISFACTION; KNOWLEDGE REPRESENTATION AND REASONING; PENALTY FORMULATION; SADDLE POINT; SEARCH; TECHNIQUES OF ALGORITHMS;

PROBLEM SOLVING;

EID: 18544364055     PISSN: 10009000     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11390-005-0002-8     Document Type: Article

References (53)

1. Shang Y, Wah B W. A discrete Lagrangian based global search method for solving satisfiability problems. J. Global Optimization, January 1998, 12(1): 61-99.
2. Barth P. A Davis-Putnam based enumeration algorithm for linear pseudo-Boolean optimization. Technical Report MPI-I-95-2-003, Max-Planck-Institute fur Informatik, 1995.
3. Robinson J A. A machine-oriented logic based on the resolution principle. J. Assoc. Comput. Mach., 1965, pp.23-41.
4. Genesereth M R, Nilsson N J. Logical Foundation of Artificial Intelligence. Morgan Kaufmann, 1987.
5. Davis M, Putnam H. A computing procedure for quantification theory. J. Assoc, Comput. Mach., 1960, 7: 201-215.
6. Purdom P W. Search rearrangement backtracking and polynomial average time. Artificial Intelligence, 1983, 21: 117-133.
7. Gu J, Wang W. A novel discrete relaxation architecture. IEEE Trans. PAMI, August 1992, 14(8): 857-865.
8. Gu J. The UniSAT problem models (appendix). IEEE Trans. PAMI, Aug 1992, 14(8): 865.
9. Gu J. Efficient local search for very large-scale satisfiability problems. SIGART Bulletin, January 1992, 3(1): 8-12.
10. Gu J. Local search for satisfiability (SAT) problems. IEEE Trans. Systems, Man, and Cybernetics, 1993, 23(4): 1108-1129.
11. Gu J. Global optimization for satisfiability (SAT) problems. IEEE Trans. Knowledge and Data Engineering, Jun 1994, 6(3): 361-381.
12. Selman B et al. A new method for solving hard satisfiability problems. In Proc. AAAI-98, San Jose, 1992, pp.440-446.
13. Selman B, Kautz H, Cohen B. Noise strategies for improving local search. In Proc. 12th National Conf. Artificial Intelligence, Seattle, WA, 1964, pp.337-343.
14. Selman B, Kautz H. Domain-independent extensions to GSAT: Solving large structured satisfiability problems. In Proc. 13th Int. Joint Conf. Artificial Intelligence, 1993, pp.290-295.
15. Selman B et al. Local search strategies for satisfiability testing. In Proc. 2nd DIMACS Challenge Workshop on Cliques, Coloring, and Satisfiability, Rutgers University, 1993, pp.290-295.
16. Hoos H H. On the run-time behaviour of stochastic local search algorithms for SAT. In Proc. Sixteenth National Conf. Artificial Intelligence, 1999, pp.661-666.
17. Gent I P, Walsh T. An empirical analysis of search in GSAT. Journal of Artificial Intelligence Research, 1993, 1: 25-37.
18. Glover F. Tabu search - Part I. ORSA J. Computing, 1989, 1(3): 190-206.
19. Battiti R, Tecchiolli G. The reactive tabu search. ORSA Journal on Computing, 1994, 6(2): 126-140.
20. Morris P. The breakout method for escaping from local minima. In Proc. 11th National Conf. Artificial Intelligence, Washington DC, 1993, pp.40-45.
21. Frank J. Learning short-term weights for GSAT. In Proc. 15th Int. Joint Conf. AI, 1997, pp.384-391.
22. Fukunaga A. Efficient implementations of SAT local search. In Proc. 7th Int. Conf. Theory and Applications of Satisfiability Testing, 2004.
23. Van Hentenryck P, Michel L. Control abstractions for local search. In Proc. the Ninth Int. Conf. Principles and Practice of Constraint Programming, LNCS 2833, 2003, pp.65-80.
24. Zhang L, Malik S. Towards symmetric treatment of conflicts and satisfaction in quantified Boolean satisfiability solver. In Proc. 8th Int. Conf. Principles and Practice of Constraint Programming. Springer Verlag, 2002.
25. Moskewicz M et al. Chaff: Engineering an efficient SAT solver. In Proc. 39th Design Automation Conf., 2001.
26. Wah B W, Wang T. Simulated annealing with asymptotic convergence for nonlinear constrained global optimization. In Proc. Principles and Practice of Constraint Programming, Springer-Verlag, October 1999, pp.461-475.
27. Folino G et al. Combining cellular genetic algorithms and local search for solving satisfiability problems. In Proc. 10th IEEE Int. Conf. Tools with AI, 1998, pp.192-198.
28. Blair C E, Jeroslow R G, Lowe J K. Some results and experiments in programming techniques for prepositional logic. Computers and Operations Research, 1986, 13(5): 633-645.
29. Hooker J N. Resolution vs. cutting plane solution of inference problems: Some computational results. Operations Research Letters, 1988, 7: 1-7.
30. Kamath A P, Karmarkar N K, Ramakrishnan K G, Resende M G C. Computational experience with an interior point algorithm on the satisfiability problem. Annals of Operations Research, 1990, 25: 43-58.
31. Shi R C J, Vannelli A, Vlach J. An improvement on Karmarkar's algorithm for integer programming. COAL Bulletin of the Mathematical Programming Society, 1992, 21: 23-28.
32. Wah B W, Shang Y. A discrete Lagrangian-based global-search method for solving satisfiability problems. In Satisfiability Problem: Theory and Applications, Ding-Zhu Du, Jun Gu, Panos Pardalos (eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, 1997, pp.365-392.
33. Wah B W, Chang Y-J. Trace-based methods for solving nonlinear global optimization problems. J. Global Optimization, March 1997, 10(2): 107-141.
34. Shang Y, Wah B W. Global optimization for neural network training. IEEE Computer, March 1996, 29(3): 45-54.
35. Luenberger D G. Linear and Nonlinear Programming. Addison-Wesley, Reading, MA, 1984.
36. Spellucci P. An SQP method for general nonlinear programs using only equality constrained subproblems. Mathematical Programming, 1998, 82: 413-448.
37. Wah B W, Wang T. Constrained simulated annealing with applications in nonlinear constrained global optimization. In Proc. Int. Conf. Tools with AI, IEEE, Nov. 1999, pp.381-388.
38. Chang Y J et al. Lagrangian techniques for solving a class of zero-one integer linear programs. In Proc. Computer Software and Applications Conf., Dallas, Aug. 1995, IEEE, pp.156-161.
39. Wah B, Chen Y X. Fast temporal planning using the theory of extended saddle points for mixed nonlinear optimization. Artificial Intelligence, (accepted for publication) 2005.
40. Wu Z. Discrete Lagrangian methods for solving nonlinear discrete constrained optimization problems [Thesis]. Dept. Computer Science, Univ. Illinois, Urbana, IL, May 1998.
41. Wah B W, Wu Z. The theory of discrete Lagrange multipliers for nonlinear discrete optimization. In Proc. Principles and Practice of Constraint Programming, Springer-Verlag, October 1999, pp.28-42.
42. Aarts E, Korst J. Simulated Annealing and Boltzmann Machines. J. Wiley and Sons, 1989.
43. Wu Z. The theory and applications of nonlinear constrained optimization using Lagrange multipliers [Dissertation], Dept. Computer Science, Univ. Illinois, Urbana, IL, May 2001.
44. Gent I P et al. Morphing: Combining structure and randomness. In Proc. 16th National Conf. AI, 1999, pp.654-660
45. Marques-Silva J P, Sakalla K A. GRASP: A search algorithm for propositional satisfiability. IEEE Trans. Computers, May 1999, 48(5): 506-521.
46. Wu Z, Wah B W. Trap escaping strategies in discrete Lagrangian methods for solving hard satisfiability and maximum satisfiability problems. In Proc. 1999 National Conf. Artificial Intelligence, AAAI, July 1999, pp.673-678.
47. Selman B. Private communcation, 1995.
48. Kautz H, Selman B. Pushing the envelope: Planning, propositional logic, and stochastic search. In Proc. the AAAI National Conf. AI, 1996, pp.1194-1201.
49. SATLIB suite. http://www.informatik.tu-darmstadt.de/AI/SATLIB.
50. Choi K F M et al. A Lagrangian reconstruction of a class of local search methods. In Proc. 10th Int. Conf. Artificial Intelligence Tools, IEEE Computer Society, 1998.
51. Freeman J W. Improvements to propositional satisfiability search algorithms [Dissertation]. Dept. Computer and Information Science, Univ. Pennsylvania, May 1995.
52. Dubois O et al. SAT versus UNSAT. In DIMACS Workshop on Satisfiability Testing, New Brunswick, NJ, 1993.
53. Pretolani D. Efficiency and stability of hypergraph SAT algorithms. In Second DIMACS Implementation Challenge, Johnson D S, Trick M A (eds.), Volume 26, American Mathematical Society, 1993, pp.479-498.