Coefficient Strengthening: A Tool for Formulating Mixed Integer Programs

Formulating Integer Linear Programs: A Rogues' Gallery

The art of formulating linear and integer linear programs is, well, an art: It is hard to teach, and even harder to learn. To help demystify this art, we present a set of modeling building blocks that we call “formulettes.” Each formulette consists of a short verbal description that must be expressed in terms of variables and constraints in a linear or integer linear program. These formulettes ...

A Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs

We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables. Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems. For the mixed integer case where the leader’s variables are continuous, our algorithm also detects whether the infimum cost fail...

Formulating a Mixed Integer Programming Problem to Improve Solvability

Monoidal Cut Strengthening and Generalized Mixed-Integer Rounding for Disjunctive Programs∗

This article investigates cutting planes for mixed-integer disjunctive programs. In the early 1980s, Balas and Jeroslow presented monoidal disjunctive cuts exploiting the integrality of variables. For disjunctions arising from binary variables, it is known that these cutting planes are essentially the same as Gomory mixed-integer and mixed-integer rounding cuts. In this article, we investigate ...

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...