Almost Orthogonal Arrays: Search Three Ways
Provides practical tools for constructing near-orthogonal arrays, benefiting researchers and practitioners in experimental design and related fields who need flexible array parameters.
The paper addresses the difficulty of constructing orthogonal arrays by exploring three methods (integer programming, local search, algebraic methods) to find almost orthogonal arrays, achieving competitive results and improving existing arrays for many non-orthogonality measures.
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.