A revised Taha's algorithm for polynomial 0–1 programming

Polynomial 0–1 programming has been undoubtedly playing a central role in nonlinear integer programming. There is, however, a clear need to develop more efficient exact algorithms for general polynomial 0–1 programming. The original version of the Taha's implicit enumeration method can only deal with polynomial 0–1 programming problems with coefficients in the objective function being all nonnegative. This article considers an extended version of the Taha's method for general polynomial 0–1 programming problems and presents an efficient implicit enumeration algorithm by systematically investigating schemes for ‘fathoming’, ‘consistency checking’ and ‘augmenting’. Promising computational results are reported.