Finding Multiple Solutions in Nonlinear Integer Programming with Algebraic Test-Sets

We explain how to compute all the solutions of a nonlinear integer problem using the algebraic test-sets associated to a suitable linear subproblem. These test-sets are obtained using Gröbner bases. The main advantage of this method, compared to other available alternatives, is its exactness within a quite good efficiency.Ministerio de Economía y Competitividad MTM2016-75024-PMinisterio de Economía y Competitividad MTM2016-74983-C2- 1-RJunta de Andalucía P12-FQM-269