Efficient reformulation for 0-1 programs: methods and computational results

作者: B.L. Dietrich , L.F. Escudero , F. Chance

DOI: 10.1016/0166-218X(93)90044-O

关键词:

摘要: Abstract We introduce two general methods for 0–1 program reformulation. Our first method generalizes coefficient reduction, our second lifting. Together they provide a unifying interpretation of many previously described automatic reformulation methods. The particular model structures that we consider are individual knapsack constraints, pairs clique and cover induced inequalities, variable upper bounding constraints capacity expansion constraints. describe several easy applications procedures. Some computational experience is reported, including the currently best known results on well-known 147 × 2655 benchmark problem.

参考文章(37)
George L Nemhauser, AHG Rinnooy Kan, MJ Todd, Handbooks in operations research and management science North-Holland , Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co. ,(1989)
D. Fayard, G. Plateau, An algorithm for the solution of the 0–1 knapsack problem Computing. ,vol. 28, pp. 269- 287 ,(1982) , 10.1007/BF02241754
E. Andrew Boyd, Polyhedral Results for the Precedence-Constrained Knapsack Problem integer programming and combinatorial optimization. pp. 85- 100 ,(1990)
J.M. Wilson, Generating cuts in integer programming with families of special ordered sets European Journal of Operational Research. ,vol. 46, pp. 101- 108 ,(1990) , 10.1016/0377-2217(90)90302-R
P. L. Hammer, E. L. Johnson, U. N. Peled, Facet of regular 0–1 polytopes Mathematical Programming. ,vol. 8, pp. 179- 206 ,(1975) , 10.1007/BF01580442
Laurence A. Wolsey, George L. Nemhauser, Integer and Combinatorial Optimization ,(1988)
Ferydoon Kianfar, Stronger Inequalities for 0, 1 Integer Programming Using Knapsack Functions Operations Research. ,vol. 19, pp. 1374- 1392 ,(1971) , 10.1287/OPRE.19.6.1374
A. Freville, G. Plateau, Heuristics and reduction methods for multiple constraints 0–1 linear programming problems European Journal of Operational Research. ,vol. 24, pp. 206- 215 ,(1986) , 10.1016/0377-2217(86)90042-1
Manfred W. Padberg, Technical Note-A Note on Zero-One Programming Operations Research. ,vol. 23, pp. 833- 837 ,(1975) , 10.1287/OPRE.23.4.833
Silvano Martello, Paolo Toth, A New Algorithm for the 0-1 Knapsack Problem Management Science. ,vol. 34, pp. 633- 644 ,(1988) , 10.1287/MNSC.34.5.633