# Integer Programming for Classifying Orthogonal Arrays

@article{Bulutoglu2015IntegerPF, title={Integer Programming for Classifying Orthogonal Arrays}, author={Dursun A. Bulutoglu and Kenneth Joseph Ryan}, journal={arXiv: Combinatorics}, year={2015} }

Classifying orthogonal arrays is a well known important class of problems that asks for finding all non-isomorphic, non-negative integer solutions to a class of systems of constraints. Solved instances are scarce. We develop two new methods based on finding all non-isomorphic solutions of two novel integer linear programming formulations for classifying all non-isomorphic OA(N,k,s,t) given a set of all non-isomorphic OA(N,k-1,s,t). We also establish the concept of orthogonal design equivalence…

## 9 Citations

### Finding the symmetry group of an LP with equality constraints and its application to classifying orthogonal arrays

- MathematicsDiscret. Optim.
- 2019

### The Linear Programming Relaxation Permutation Symmetry Group of an Orthogonal Array Defining Integer Linear Program

- Mathematics
- 2016

There is always a natural embedding of $S_{s}\wr S_{k}$
into the linear programming (LP) relaxation permutation symmetry group of an orthogonal array integer linear programming (ILP) formulation…

### On the orthogonal arrays of parameters OA(1536, 13, 2, 7) and related

- Mathematics, Computer ScienceArXiv
- 2019

It is proved that any orthogonal array OA$(N,n,2,t)$ with even $t attending the bound $N \ge 2^n(1-(n+1)/2(t+2)$ induces an equitable $3$-partition of the $n$-cube.

### On Unbalanced Boolean Functions with Best Correlation Immunity

- MathematicsElectron. J. Comb.
- 2020

It is proved that if a nonconstant unbalanced Boolean function attains the correlation-immunity bound and has ratio $C:B$ of the number of ones and zeros, then $CB$ is divisible by $3, which proves the nonexistence of equitable partitions for an infinite series of putative quotient matrices.

### On the OA(1536, 13, 2, 7) and related orthogonal arrays

- Mathematics, Computer ScienceDiscret. Math.
- 2020

### Uniform semi-Latin squares and their pairwise-variance aberrations

- MathematicsJournal of Statistical Planning and Inference
- 2021

### Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes

- MathematicsTechnometrics
- 2019

This article introduces a collection of strength-3 nonregular designs with large run sizes that, to the best of the knowledge, have not been explored before in the design literature and outperform many comparably sized benchmark designs in terms of the aliasing among the two-factor interactions.

### On unbalanced Boolean functions attaining the bound $2n/3-1$ on the correlation immunity

- Mathematics, Computer Science
- 2018

It is proved that if a nonconstant unbalanced Boolean function attains the correlation-immunity bound and has the ratio $C:B$ of the number of ones and zeros, gcd$(C,B)=1$, then $CB$ is divided by $3, which proves the nonexistence of equitable partitions for an infinite series of putative quotient matrices.

## References

SHOWING 1-10 OF 71 REFERENCES

### Symmetry in Integer Linear Programming

- Mathematics50 Years of Integer Programming
- 2010

This paper reviews techniques developed to take advantage of the symmetry in an ILP during its solution, and surveys related topics, such as symmetry detection, polyhedral studies of symmetric ILPs, and enumeration of all non isomorphic optimal solutions.

### Classification Algorithms for Codes and Designs

- Mathematics
- 2005

A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution…

### Complete enumeration of two-Level orthogonal arrays of strength d with d + 2 constraints

- Mathematics
- 2007

Enumerating nonisomorphic orthogonal arrays is an important, yet very difficult, problem. Although orthogonal arrays with a specified set of parameters have been enumerated in a number of cases,…

### Complete enumeration of pure‐level and mixed‐level orthogonal arrays

- Mathematics
- 2009

We specify an algorithm to enumerate a minimum complete set of combinatorially non‐isomorphic orthogonal arrays of given strength t, run‐size N, and level‐numbers of the factors. The algorithm is the…

### Isomorph-Free Exhaustive Generation

- MathematicsJ. Algorithms
- 1998

We describe a very general technique for generating families of combinatorial objects without isomorphs. It applies to almost any class of objects for which an inductive construction process exists.…

### Integrating Constraint and Integer Programming for the Orthogonal Latin Squares Problem

- Computer ScienceCP
- 2002

It is clearly illustrated that the integration of CP and IP is beneficial and that one hybrid algorithm exhibits the best performance as the problem size grows.

### A Branch-and-Cut Algorithm for the Resolution of Large-Scale Symmetric Traveling Salesman Problems

- Computer ScienceSIAM Rev.
- 1991

An algorithm is described for solving large-scale instances of the Symmetric Traveling Salesman Problem (STSP) to optimality. The core of the algorithm is a “polyhedral” cutting-plane procedure that…

### Dual Simplex

- Mathematics
- 2011

The dual simplex algorithm is an attractive alternative as a solution method for linear programming problems. Since the addition of new constraints to a problem typically breaks primal feasibility…