A number theoretic reformulation and decomposition method for integer programming

Laurence A. Wolsey
1974 Discrete Mathematics  
Integer prcgramsning problems. and especially knapsack and finite abelian group problems, can be exactly replar.ed by equivalent problems of "smaller" size. This reformulation theoretically provides a new m :thod of solution for such problems, but the main advantages lie in reducing coeffitient magnierlldes and in removing selected constraints, while a disadvantage ;s the large increase in the number qf variables. By modifying the dyne mic programming approach S,I as effectively to avoid
more » ... in; a largl number of these neu variables, an algorithm to overcome this difficulty is.develaped. Ap plie;i to the solution of I:upe non-Erime group problems tiis provides an algorithm that appears on average to compare :a\ jurably with the deterministic L,.lgorithms of Hu and Gcmolry. * Origin21 vers,on rec+cd L May 1972.
doi:10.1016/0012-365x(74)90046-6 fatcat:abdc2viukbg7ljoqss5b4vlk3q