Approximating the stability region for binary mixed-integer programs

Approximating the stability region for binary mixed-integer programs

We consider optimization problems with some binary variables, where the objective function is linear in these variables. The stability region of a given solution is the polyhedral set of objective coefficients for which the solution is optimal. Knowledge of this set provides valuable information for sensitivity analysis and re-optimization. An exact description of the stability region may requi...

Approximating Sparse Covering Integer Programs Online

A covering integer program (CIP) is a mathematical program of the form: min{cx | Ax ≥ 1, 0 ≤ x ≤ u, x ∈ Z}, where A ∈ R ≥0 , c, u ∈ R n ≥0. In the online setting, the constraints (i.e., the rows of the constraint matrix A) arrive over time, and the algorithm can only increase the coordinates of x to maintain feasibility. As an intermediate step, we consider solving the covering linear program (...

Approximating Covering Integer Programs with Multipli ityConstraintsStavros

Binary clutter inequalities for integer programs

We introduce a new class of valid inequalities for general integer linear programs, called binary clutter (BC) inequalities. They include the {0, 1 2 }-cuts of Caprara and Fischetti as a special case and have some interesting connections to binary matroids, binary clutters and Gomory corner polyhedra. We show that the separation problem for BC-cuts is strongly NPhard in general, but polynomiall...

Exploiting Solving Phases for Mixed-Integer Programs

Modern MIP solving software incorporates dozens of auxiliary algorithmic components for supporting the branch-and-bound search in finding and improving solutions and in strengthening the relaxation. Intuitively, a dynamic solving strategy with an appropriate emphasis on different solving components and strategies is desirable during the search process. We propose an adaptive solver behavior tha...