Trace-Based Methods for Solving Nonlinear Global Optimization and Satisfiability Problems

Journal of Global Optimization

Volumn 10, Issue 2, 1997, Pages 107-141

  Wah, Benjamin W ^a   Chang, Yao Jen ^b  

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

^b CHUNG YUAN CHRISTIAN UNIVERSITY   (Taiwan)

Author keywords

Augmented lagrange multiplier method; Constraint satisfaction problems; Continuous nonlinear programming problems; Satisfiability problems; Trace function; Trajectory based method

Indexed keywords

EID: 0010835183     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008294209959     Document Type: Article

References (101)

1. E. Aarts and J. Korst. Simulated Annealing and Boltzmann Machines. J. Wiley and Sons, 1989.
2. E. H. L. Aarts and P. J. van Laarhoven. Simulated Annealing: Theory and Practice. Wiley, New York, 1987.
3. F. Aluffi-Pentini, V. Parisi, and F. Zirilli. Global optimization and stochastic differential equations. Journal of Optimization Theory and Applications, 47(1):1-16, September 1985.
4. N. Anderson and G. Walsh. A graphical method for a class of Branin trajectories. Journal of Optimization Theory and Applications, 49(3):367-374, June 1986.
5. D. H. Ballard, C. O. Jelinek, and R. Schinzinger. An algorithm for the solution of constrained polynomial programming problems. The Computer Journal, 17:261-266, 1974.
6. W. Baritompa. Accelerations for a variety of global optimization methods. Journal of Global Optimization, 4:37-45, 1994.
7. W. Baritompa and A. Cutler. Accelerations for global optimization covering methods using second derivatives. Journal of Global Optimization, 4:329-341, 1994.
8. B. Betrò and F. Schoen. Sequential stopping rules for the multistart algorithm in global optimization. Mathematical Programming, 38, 1987.
9. B. Betrò and F. Schoen. Optimal and sub-optimal stopping rules for the multistart algorithm in global optimization. Mathematical Programming, 57:445-458, 1992.
10. C. G. E. Boender and A. H. G. Rinnooy Kan. Bayesian stopping rules for multi-start global optimization methods, Mathematical Programming, 36, 1987.
11. C. G. E. Boender and A. H. G. Rinnooy Kan. On when to stop sampling for the maximum. Journal of Global Optimization, 1(4):331-340, 1991.
12. C. G. E. Boender, A. H. G. Rinnooy Kan, L. Stougie, and G. T. Timmer. A stochastic method for global optimization. Mathematical Programming, 22:125-140, 1982.
13. I. O. Bohachevsky, M. E. Johnson, and M. L. Stein. Generalized simulated annealing for function optimization. Technometrics, 28:209-217, 1986.
14. V. Cerny. Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm. Journal of Optimization Theory and Applications, 45:41-51, 1985.
15. B. C. Cetin, J. Barben, and J. W. Burdick. Terminal repeller unconstrained subenergy tunneling (TRUST) for fast global optimization. Journal of Optimization Theory and Applications, 77, April 1993.
16. A. Corana, M. Marchesi, C. Martini, and S. Ridella. Minimizing multimodal functions of continuous variables with the simulated annealing algorithm. ACM Trans. Math. Software, 13:2-280, 1987.
17. A. Davenport, E. Tsang, C. Wang, and K. Zhu, Genet: A connectionist architecture for solving constraint satisfaction problems by iterative improvement. In Proc. of the 12th National Conf. on Artificial Intelligence, pages 325-330, Seattle, WA, 1994.
18. M. Davis and H. Putnam. A computing procedure for quantification theory. J. Assoc. Comput. Mach., 7:201-215, 1960.
19. I. Diener and R. Schaback. An extended continuous Newton method. Journal of Optimization Theory and Applications, 67(1):57-77, October 1990.
20. L. C. W. Dixon and G. P. Szegö, editors. Towards global optimisation 2. North-Holland Pub. Co., Amsterdam, The Netherlands., 1978.
21. Y. G. Evtushenko, M. A. Potapov, and V. V. Korotkich. Numerical methods for global optimization. In C. A. Floudas and P. M. Pardalos, editors, Recent Advances in Global Optimization, pages 274-297, Princeton University Press, 1992.
22. C. Fleurent and J. A. Ferland. Object-oriented implementation of heuristic search methods for graph coloring, maximum clique, and satisfiability. In M. A. Trick and D. S. Johnson, editors, The second DIMACS Challenge special issue, 1994.
23. C. A. Floudas and P. M. Pardalos. A Collection of Test Problems for Constrained Global Optimization Algorithms, volume 455 of Lecture Notes in Computer Science. Springer-Verlag, 1990.
24. C. A. Floudas and P. M. Pardalos, editors. Recent Advances in GLobal Optimization. Princeton University Press, 1992.
25. D. B. Fogel. An introduction to simulated evolutionary optimization. IEEE Trans. Neural Networks, 5(1):3-14, January 1994.
26. R. P. Ge and Y. F. Qin. A class of filled functions for finding global minimizers of a function of several variables. Journal of Optimization Theory and Applications, 54(2):241-252, 1987.
27. I. Gent and T. Walsh. Towards an understanding of hill-climbing procedures for SAT. In Proc. of the 11th National Conf. on Artificial Intelligence, pages 28-33, Washington, DC, 1993.
28. A. O. Griewank. Generalized descent for global optimization. Journal of Optimization Theory and Applications, 34:11-39, 1981.
29. J. Gu. Parallel Algorithms and Architectures for Very Fast AI Search. PhD thesis, Dept. of Computer Science, University of Utah, August 1989.
30. J. Gu. How to solve very large-scale satisfiability (VLSS) problems. Technical Report UCECE-TR-90-002, Univ. of Calgary, Canada, October 1990.
31. J. Gu. Efficient local search for very large-scale satisfiability problems. SIGART Bulletin, 3(1):8-12, January 1992.
32. J. Gu. On optimizing a search problem. In N. G. Bourbakis, editor, Artificial Intelligence Methods and Applications. World Scientific Publishers, 1992.
33. J. Gu. The UniSAT problem models (appendix). IEEE Trans. on Pattern Analysis and Machine Intelligence, 14(8):865, Aug 1992.
34. J. Gu. Local search for satisfiability (SAT) problems, IEEE Trans. on Systems, Man, and Cybernetics, 23(4):1108-1129, 1993.
35. J. Gu. Global optimization for satisfiability (SAT) problems. IEEE Trans. on Knowledge and Data Engineering, 6(3):361-381, Jun 1994.
36. J. Gu and Q.-P. Gu. Average time complexities of several local search algorithms for the satisfiability problem (sat). Technical Report UCECE-TR-91-004, Univ. of Calgary, Canada, 1991.
37. J. Gu and Q.-P. Gu. Average time complexity of the sat1.3 algorithm. Technical report, Tech. Rep., Univ. of Calgary, Canada, 1992.
38. J. Gu and W. Wang. A novel discrete relaxation architecture. IEEE Trans. on Pattern Analysis and Machine Intelligence, 14(8):857-865, August 1992.
39. E. Hansen. Bounding the set of solutions of a perturbed global optimization problem. Journal of Global Optimization, 1(4):359-374, 1991.
40. E. R. Hansen. Global optimization using interval analysis. M. Dekker, New York, 1992.
41. I. He and E. Polak. Multistart method with estimation scheme for global satisfying problems. Journal of Global Optimization, 3:130-156, 1993.
42. A. C. Hindmarsh. ODEPACK, a systematized collection of ode solvers. In R. S. Stepleman et al., editor, scientific computing, pages 55-64. north-holland, amsterdam, 1983.
43. J. H. Holland. Adaption in Natural and Adaptive Systems. University of Michigan Press, Ann Arbor, 1975.
44. J. J. Hopfield and D. W. Tank. Neural computation of decisions in optimization problems. Biological Cybernetics, 52:141-152, 1985.
45. R. Horst and H. Tuy. Global optimization: Deterministic approaches. Springer-Verlag, Berlin, 1993.
46. Reiner Horst and P. M. Pardalos, editors. Handbook of Global Optimization. Kluwer Academic Publishers, 1994.
47. L. Ingber. Adaptive Simulated Annealing (ASA). Lester Ingber Research, 1995.
48. A. E. W. Jones and G. W. Forbes, An adaptive simulated annealing algorithm for global optimization over continuous variables. Journal of Optimization Theory and Applications, 6:1-37, 1995.
49. A. P. Kamath, N. K. Karmarkar, K. G. Ramakrishnan, and M. G. C. Resende. A continuous approach to inductive inference. Mathematical Programming, 57:215-238, 1992.
50. S. Kirkpatrick, Jr. C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220(4598):671-680, 1983.
51. H. J. Kushner. A new method of locating the maximum of an arbitrary multipeak curve in the presence of noise. In Proc. Joint Automatic Control Conf., 1963.
52. R. W. Beckerand G. W. Lago. A global optimization algorithm. In Proc. of the 8th Allerton Conf. on Circuits and Systems Theory, pages 3-12, Monticello, Illinois, 1970.
53. S. Lucidi and M. Piccioni. Random tunneling by means of acceptance-rejection sampling for global optimization. Journal of Optimization Theory and Applications, 62:255-277, 1989.
54. D. G. Luenberger. Linear and Nonlinear Programming. Addison-Wesley Publishing Company, 1984.
55. Z. Michalewicz. Genetic Algorithms + Data Structure = Evolution Programs. Springer-Verlag, 1994.
56. S. Minton, M. D. Johnson, A. B. Philips, and P. Laird. Minimizing conflicts: a heuristic repair method for constraint, satisfaction and scheduling problems. Artificial Intelligence, 58:161-205, Dec 1992.
57. D. Mitchell, B. Selman, and H. Levesque. Hard and easy distributions of SAT problems. In Proc. of the 10th National Conf. on Artificial Intelligence, pages 459-465, 1992.
58. J. Mockus. Bayesian Approach to Global Optimization. Kluwer Academic Publishers, Dordrecht-London-Boston, 1989.
59. J. Mockus. Application of bayesian approach to numerical methods of global and stochastic optimization. Journal of Global Optimization, 4:347-365, 1994.
60. R. Moore and E. Hansen amd A. Leclerc. Rigorous methods for global optimization. In C. A. Floudas and P. M. Pardalos, editors, Recent Advances in Global Optimization, pages 321-342. Princeton University Press, 1992.
61. P. Morris. The breakout method for escaping from local minima. In Proc. of the 11th National Conf. on Artificial Intelligence, pages 40-45, Washington, DC, 1993.
62. P. M. Pardalos. Complexity in numerical optimization. World Scientific, Singapore and River Edge, N .I , 1993.
63. P. M. Pardalos and J. B. Rosen. Constrained Global Optimization: Algorithms and Applications, volume 268 of Lecture Notes in Computer Science. Springer-Verlag, 1987.
64. N. R. Patel, R. L. Smith, and Z. B. Zabinsky. Pure adaptive search in Monte Carlo optimization. Mathematical Programming, 43:317-328, 1988.
65. M. Piccioni. A combined multistart-annealing algorithm for continuous global optimization. Technical Report 87-45, Systems and Research Center, The University of Maryland, College Park MD, 1987.
66. D. Powell and M. M. Skolnick. Using genetic algorithms in engineering design optimization with nonlinear constraints. In S. Forrest, editor, Proc. of the Fifth Int'l Conf. on Genetic Algorithms, pages 424-431. Morgan Kaufmann, 1993.
67. H. E. Romeijn and R. L. Smith. Simulated annealing for constrained global optimization. Journal of Global Optimization, 5(2):101-126, September 1994.
68. R. Rotondi. A new method for global optimization based on the k-th nearest neighbor. Technical report, CNR-IAMI, Milano, 1987.
69. M. S. Sarma. On the convergence of the Baba and Dorea random optimization methods. Journal of Optimization Theory and Applications, 66:337-343, 1990.
70. S. Schäffler and H. Warsitz. A trajectory-following method for unconstrained optimization. Journal of Optimization Theory and Applications, 67(1):133-140, October 1990.
71. I. P. Schagen. Internal modeling of objective functions tor global optimization. Journal of Optimization Theory and Applications, 51(2), 1986.
72. F. Schoen. Stochastic techniques for global optimization: A survey on recent advances. Journal of Global Optimization, 1(3):207-228, 1991.
73. R. Sebastiani, Applying GSAT to non-clausal formulas. Journal of Artificial Intelligence Research, 1:309-314, 1994.
74. B. Selman, 1995. private communication.
75. D. Selman and H. Kautz. Domain-independent extensions to GSAT: Solving large structured satisfiability problems. In Proc. of the 13th Int'l Joint Conf. on Artificial Intelligence, pages 290-295, 1993.
76. B. Selman, H. Kautz, and B. Cohen. Local search strategics for satisfiability testing. In Proc. of the Second DIMACS Challenge Workshop on Cliques, Coloring, and Satisfiability, Rutgers University, pages 290-295, oct 1993.
77. B. Selman, H. Kautz, and B. Cohen. Noise strategies for improving local search. In Proc. of the 12th National Conf. on Artificial Intelligence, pages 337-343, Seattle, WA, 1994.
78. B. Selman and H. A. Kautz. An empirical study of greedy local search for satisfiability testing. In Proc. of the 11th National Conf. on Artificial Intelligence, pages 46-51, Washington, DC, 1993.
79. B. Selman, H. J. Levesque, and D. G. Mitchell. A new method for solving hard satisfiability problems. In Proc. of AAAI-92, pages 440-446, San Jose, CA, 1992.
80. Y. Shang and B. W. Wah. Global optimization for neural network training. IEEE Computer, 29:45-54, March 1996
81. J. A. Snyman and L. P. Fatti. A multi-start global minimization algorithm with dynamic search trajectories. Journal of Optimization Theory and Applications, 54(1):121-141, July 1987.
82. R. Socic and J. Gu. Fast search algorithms for the N-queen problem. IEEE Trans. on Systems, Man, and Cybernetics, 21(6):1572-1576, November 1991.
83. R. Sosič and J. Gu. A polynomial time algorithm for the n-queens problem. SIGART Bulletin, 1(3):7-11, October 1990.
84. R. Sosić and J. Gu. 3,000,000 queens in less than one minute. SIGART Bulletin, 2(2):22-24, April 1991.
85. R. Sosič and J. Gu. Efficient local search with conflict minimization: A case study of the n-queens problem. IEEE Trans. on Knowledge and Data Engineering, 6(5):661-668, 1994.
86. R. Spaans and R. Luus. Importance of search-domain reduction in random optimization. Journal of Optimization Theory and Applications, 75(3):635-638, December 1992.
87. H. S. Stone and J. M. Stone, Efficient search techniques - an empirical study of the n-queens problem. IBM J. Res. Dev., 31:464-174, 1987.
88. B. E. Stuckman. A global search method for optimizing nonlinear systems. IEEE Trans. on Systems, Man, and Cybernetics, 18(6):965-977, 1988.
89. E. G. Sturua and S. K. Zavriev. A trajectory algorithm based on the gradient method I. the search on the quasioptimal trajectories. Journal of Global Optimization, 1991(4);375-388, 1991.
90. G. T. Timmer. Global Optimization: A Stochastic Approach. PhD thesis, Erasmus University, Rotterdam, 1984.
91. A. Törn. Global optimization as a combination of global and local search. Gothenburg Business Adm. Studies, 17:191-206, 1973.
92. A. Törn. Cluster analysis using seed points and density determined hyperspheres as an aid to global optimization. IEEE Trans. Syst. Men and Cybernetics, 7:610-616, 1977.
93. A. Törn and S. Viitanen. Topographical global optimization. In C. A. Floudas and P. M. Pardalos, editors, Recent Advances in Global Optimization, pages 385-398. Princeton University Press, 1992.
94. A. Törn and A. Žilinskas. Global Optimization. Springer-Verlag, 1989.
95. D. Vanderbilt and S. G. Louie. A Monte Carlo simulated annealing approach to optimization over continuous variables. Journal of Computational Physics, 56:259-271, 1984.
96. T. L. Vincent, B. S. Goh, and K. L. Teo. Trajectory-following algorithms for min-max optimization problems. Journal of Optimization Theory and Applications, 75(3):501-519, December 1992.
97. A. Žilinskas. A review of statistical models for global optimization. Journal of Global Optimization, 2:145-153, 1992.
98. B. W. Wah and Y. Shang. A discrete lagrangian-based global-search method for solving satisfiability problems. In Ding-Zhu Du, Jun Gu, and Panos Pardalos, editors, Proc. DIMACS Workshop on Satisfiability Problem: Theory and Applications. American Mathematical Society, March 1996.
99. B. W. Wah, Y. Shang, T. Wang, and T. Yu. Global optimization design of QMF filter banks. In Proc. IEEE Midwest Symposium on Circuits and Systems, Iowa City, Iowa, (accepted to appear) Aug. 1996. IEEE.
100. Z. B. Zabinsky and R. L. Smith. Pure adaptive search in global optimization. Mathematical Programming, 53:323-338, 1992.
101. Z. B. Zabinsky, et al. Improving hit-and-run for global optimization. Journal of Global Optimization, 3:171-192, 1993.