Almost Orthogonal Arrays: Search Three Ways

TL;DR

This paper explores three methods—integer programming, local search, and algebraic techniques—to find almost orthogonal arrays, improving existing arrays and providing a public repository of results.

Contribution

It introduces three novel approaches for constructing almost orthogonal arrays and demonstrates their effectiveness compared to existing methods.

Findings

All search results are competitive with existing literature.

The methods improve many non-orthogonality measures.

Found arrays are publicly available in a repository.

Abstract

Orthogonal arrays play a fundamental role in many applications. However, constructing orthogonal arrays with the required parameters for an application usually is extremely difficult and, sometimes, even impossible. Hence there is an increasing need for a relaxation of orthogonal arrays to allow a wider flexibility. The latter has lead to various types of arrays under the name of ``nearly-orthogonal arrays'', and less often ``almost orthogonal arrays''. In this paper, we explore how to find almost orthogonal arrays three ways: using integer programming, local search meta-heuristics and algebraic methods. We compare all our search results with the ones existing in the literature, and we show that they are competitive, improving some of the existing arrays for many non-orthogonality measures. All our found almost orthogonal arrays are available at a public repository.