Abstract
The classical group approach to integer linear programming problems (IP) can be generalized in order to obtain group minimization problems with different computational load and different relaxation.
The aim of this work is to analyze some group problems, associated to the same (IP), both from the point of view of the relaxation of the (IP) and of the complexity of the group solution algorithm; evaluation criteria for these group problems are pointed out.
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DER-SAN CHEN, ZIONTS: Comparison of some algorithms for solving the Group Theoretic Integer Programming Problem. Operations Research, vol. 24, n.6. Nov–Dec. 1976.
J.F. SHAPIRO: Group theoretic algorithms for the integer programming problem II: extension to a general algorithm — Operations Research, vol. 16, pp.928–947, 1968.
G.A.GORRY, J.F.SHAPIRO: An adaptive group theoretic algorithm for integer programming problems. Management Science vol. 17 n. 5 Gen. 1971.
J.F. SHAPIRO: Dynamic programming algorithms for the integer programming problem I: the integer programming problem as a knapsack type problem. Operations Research vol. 16, pp. 103–121, 1968.
D.E.BELL: Constructive group relaxation for integer programs. Siam Journal on Applied Mathematics, vol. 30, n. 4, June 1976.
G.A.GORRY, J.F.SHAPIRO, L.A.WOLSEY: Relaxation methods for pure and mixed integer programming problems. Management Science vol. 18, n. 5, Jan. 1972.
R.JEROSLOW: Cutting plane theory: algebraic methods. Discrete Mathematics, vol. 23, n. 2, Aug. 1978.
E.V.DENARDO, B.L.FOX: "Shortest Route Methods: 1. Reaching, Pruning and Buckets" Op. Res., Jan. 1979.
E.V.DENARDO, B.L.FOX: "Shortest Route Methods: 2. Group knapsacks, Expanded Networks and branch and bound" Univ. of Montreal, Pub. 263-2, March 1978.
H.M.SALKIN: "Integer programming" Addition Wesley 1975.
F.R.GANTMACHER: "The theory of matrices" Chelsea Pub. Comp. 1959.
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Bertolazzi, P., Leporelli, C., Lucertini, M. (1980). Alternative group relaxation of integer programming problems. In: Iracki, K., Malanowski, K., Walukiewicz, S. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006599
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DOI: https://doi.org/10.1007/BFb0006599
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