Combined analytical and empirical learning framework for branch and bound algorithms: The knapsack problem

Artificial Intelligence in Engineering

Volumn 13, Issue 3, 1999, Pages 287-300

  Realff, M J ^a   Kvam, P H ^a   Taylor, W E ^b  

^a Georgia Institute of Technology   (United States)

^b LHS Communications Systems Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LEARNING ALGORITHMS; OPTIMIZATION; PROBLEM SOLVING; STATISTICAL TESTS;

KNAPSACK PROBLEM;

ARTIFICIAL INTELLIGENCE;

EID: 0032647533     PISSN: 09541810     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0954-1810(99)00004-7     Document Type: Article

References (39)

1. Garey M.R., Johnson D.S. Computers and intractability: a guide to the theory of NP-completeness. 1979;Freeman, New York.
2. Miller D.L., Pekny J.F. Exact solution of large asymmetric travelling salesman problems. Science. 251:1991;754-761.
3. Shah N., Pantelides C.C., Sargent R.W.H. General algorithm for short-term scheduling of batch operations. Part II - computational issues. Computers and Chemical Engineering. 17:1993;229-244.
4. Balas E. Disjunctive programming and a hierarchy of relaxations for discrete optimization problems. SIAM Journal of Algebraic Discrete Methods. 6:(3):1985;466-486.
5. Pekny JF, Reklaitis GV. Towards the convergence of theory and practice: a technology guide for scheduling/planning methodology. In Proceedings of Foundations in Computer-Aided Operations (FOCAPO), Snowbird, Utah, 1998.
6. Wolsey L.A. Integer programming. 1998;Wiley, New York.
7. Martello S., Toth P. Knapsack problems algorithms and computer implementations. 1990;Wiley, New York.
8. Kirschner KJ, Realff MJ. Process modeling of a waste volume reduction facility. An unpublished paper presented at the 1996 AIChE National Conference. Proceedings of the National Meeting of the AIChE, Chicago, 1996.
9. Crowder H., Johnson E.L., Padberg M.W. Solving large-scale zero-one linear programming problems. Operations Research. 1983;803-834.
10. Gilmore P.C., Gomory R.E. linear programming approach to the cutting stock problem. Operations Research. 1963;863-888.
11. Nemhauser G.L., Wolsey L.A. Integer and combinatorial optimization. Wiley interscience series in discrete mathematics and optimization. 1988;Wiley, New York.
12. Ibaraki T. The power of dominance relations in branch bound algorithms. Journal of the Association of Computing Machinery. 24:1977;264-279.
13. Horowitz E., Sahni S. Computing partitions with applications to the knapsack problem. Journal of ACM. 23:1974;277-292.
14. Minton S., Carbonell J., Knoblock C., Kuokka D., Etzioni O., Gil Y. Explanation based learning: a problem solving perspective. Machine learning, paradigms and methods. 1990;MIT Press, Cambridge, MA.
15. Glover F. Future paths for integer programming and links to artificial intelligence. Computers and Operations Research. 13:1986;533-549.
16. Glover F., Greenberg H.J. New approaches for heuristic search: A bilateral linkage with artificial intelligence. European Journal of Operations Research. 39:1989;119-130.
17. Fadlalla A., Evans J.R. Improving the performance of enumerative search methods part i. Computers and Operations Research. 22:1995;605-615.
18. Fadlalla A., Evans J.R., Levy M.S. Improving the performance of enumerative search methods part ii: Computational experiments. Computers and Operations Research. 22:1995;987-994.
19. Li D.-C., Lin H., Torng K. A strategy for evolution of algorithms to increase the computational effectiveness of np-hard scheduling problems. European Journal of Operations Research. 88:1996;404-412.
20. Breiman L. Classification and regression trees. 1984;Wadsworth, Belmont, CA.
21. Yu C.-F., Wu B.W. Learning dominance relations in combinatorial search problems. IEEE Transactions on Software Engineering. 14:1988;1155-1175.
22. Balas E., Zemel E. An algorithm for large zero-one knapsack problems. Operations Research. 28:1980;1130-1154.
23. Martello S., Toth P. Upper bounds and algorithms for hard 0-1 knapsack problems. Operations Research. 45:(5):1997;768-778.
24. Press W.H. Numerical recipes in C: the art of scientific computing. 2 :1992;Cambridge University Press, Cambridge.
25. Kearns M.J., Vazirani U.V. An introduction to computational learning theory. 1994;MIT Press, Cambridge, MA.
26. Shapiro S.C. Encyclopedia of artificial intelligence. 1990;Wiley, New York.
27. Clocksin W.F., Mellish C.S. Programming in prolog. 1984;Springer, Berlin.
28. Shavlik J.W. Extending explanation-based learning by generalizing the structure of explanations. Research notes in artificial intelligence. 1990;Morgan Kaufmann, Los Altos, CA.
29. Mooney R.J. A general explanation-based learning mechanism and its application to narrative understanding. Research notes in artificial intelligence. 1990;Morgan Kaufmann, Los Altos, CA.
30. Cormen T.H., Leiserson C.E., Rivest R.L. Introduction to algorithms. 1990;McGraw-Hill, New York.
31. Ibaraki B.R. Bound procedure and state-space representation of combinatorial optimization problems. Information and Control. 36:1978;1-27.
32. Kohler W.H. Steiglitz K. Characterization and theoretical comparison of branch and bound algorithm for permutation problem, JACM. 21:(1):1974;140-156.
33. Titterington D.M., Smith A.F.M., Makov U.E. Statistical analysis of finite mixture distributions. 1985;Wiley, New York.
34. Teicher H. Identifiability of mixtures. Annals of Mathematical Statistics. 31:1961;55-73.
35. Dempster A.P., Laird A., Rubin D.B. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society B. 1977;1-38.
36. Wu C.F.J. On the convergence properties of the em algorithm. The Annals of Statistics. 11:1983;95-103.
37. Lehmann E.L. Testing statistical hypotheses. 1959;Wiley, New York.
38. Mood A.M., Graybill I., Boes D.C. Introduction to the theory of statistics. 1974;McGraw Hill, New York.
39. Realff M.J., Stephanopoulos G. On the application of explanation-based learning to acquire control knowledge for branch and bound algorithms. INFORMS Journal on Computing. 10:(1):1998;56-71.