Bi-objective mathematical model for optimal sequencing of two-level factorial designs

Abstract

Conducting sequencing experiments with good statistical properties and low cost is a crucial challenge for both researchers and practitioners. The main reason for this challenge is the combinatorial nature of the problem and the possible conflicts among objectives. The problem was addressed by proposing a mathematical programming formulation aimed at generating minimum-cost run orders with the best statistical properties for $2^{k}$ full-factorial and fractional-factorial designs. The approach performance is evaluated using designs of up to 64 experiments with different levels of resolution. The results indicate that the approach can yield optimal or sub-optimal solutions, depending on the objectives established for a given design matrix.