Hybrid Entropy–Decimal Approaches for Isomorphism Detection of Factorial Designs
DOI:
https://doi.org/10.66279/8tdx3m87Keywords:
Entropy, Decimal system, Isomorphic designs, Regular design, Non‑regular designAbstract
In experimental design, selecting an optimal design from a vast space of candidates is a fundamental challenge. Many candidate designs are isomorphic-structurally equivalent under relabeling factors, reordering runs, or switching levels and thus statistically indistinguishable. Retaining such redundant designs wastes computational resources and obscures truly distinct experimental strategies. Existing criteria for detecting non-isomorphic designs fail to distinguish all non‑isomorphic classes (e.g., the 68 classes of 27-run three-level designs). More powerful projection‑based methods achieve perfect discrimination but are computationally expensive. This paper bridges the gap by introducing simple yet powerful hybrid methods that combine entropy with a decimal‑system transformation. The approach converts the structural information of a design into a compact decimal vector and then computes an enhanced entropy that incorporates the magnitude of the values, producing a scalar signature invariant under isomorphism. The proposed algorithms work seamlessly for both regular and irregular factorial designs. Extensive experiments on three challenging families-18-run three‑level designs (3 non‑isomorphic classes), 27‑run three-level designs (68 non‑isomorphic classes), and 32‑run four‑level designs (20 non‑isomorphic classes) show that the method achieves perfect discrimination at low computational cost. The framework is simple, universal, and efficient, making it a valuable tool for design theorists and practitioners.
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