Abstract: In ordering problems, the goal is to find the optimal order. Each experimental run of an order problem is a permutation of m components. Because m! is typically large, it is necessary to select a subset of the m! sequences. Existing selection methods are based on parametric models. However, it is difficult to determine a good approximate model for an ordering problem before collecting the experimental data. With this in mind, we propose a method for choosing the subset for searching for the optimal order without assuming a prespecified model. The proposed method explores the inherent characteristics of the possible orders by using the distance between the positions of the components. We propose a systematic construction method for selecting a subset with a flexible run size, and also show its optimality. Compared with existing model-based methods, the proposed method is more appropriate when the model choice is not clear a priori.

Key words and phrases: Design of experiments, fractional order of addition design, pair-wise ordering distance.