Discrete Programming by the Filter Method

In this paper (section 1) a two-phase procedure, the filter method or accelerated additive algorithm, is proposed for solving linear programs with zero-one variables. In Phase I an auxiliary problem is constructed that, in Phase II, is used to “filter” the solutions to which the tests of the additive algorithm are to be applied. The filter method is then extended (section 2) by J. F. Benders’ partitioning procedure to the mixed-integer zero-one case, as well as to general integer and mixed-integer programs. Finally, a specialized version of this method is used (section 3) to tackle a general machine-sequencing model, formulated as the problem of finding a minimaximal path in a disjunctive graph.