Integer programming approaches to find row–column arrangements of two-level orthogonal experimental designs

New Approaches to Integer Programming

Optimal Foldover Plans for Two-Level Nonregular Orthogonal Designs

This article considers optimal foldover plans for nonregular designs. By using the indicator function, we deŽ ne words with fractional lengths. The extended word-length pattern is then used to select among nonregular foldover designs. Some general properties of foldover designs are obtained using the indicator function. We prove that the full-foldover plan that reverses the signs of all factors...

Polyhedral Approaches to Mixed Integer Linear Programming

This survey presents tools from polyhedral theory that are used in integer programming. It applies them to the study of valid inequalities for mixed integer linear sets, such as Gomory’s mixed integer cuts.

Non-standard approaches to integer programming

In this survey we address three of the principal algebraic approaches to integer programming. After introducing lattices and basis reduction, we 0rst survey their use in integer programming, presenting among others Lenstra’s algorithm that is polynomial in 0xed dimension, and the solution of diophanine equations using basis reduction. The second topic concerns augmentation algorithms and test s...

Classification of Orthogonal Arrays by Integer Programming

The problem of classifying all isomorphism classes of OA(N, k, s, t)s is shown to be equivalent to finding all isomorphism classes of non-negative integer solutions to a system of linear equations under the symmetry group of the system of equations. A branch-and-cut algorithm developed by Margot (2002, 2003a, 2003b, 2005) for solving integer programming problems with large symmetry groups is us...