Publication
Title
Symmetry breaking in mixed integer linear programming formulations for blocking two-level orthogonal experimental designs
Author
Abstract
Two-level orthogonal designs play an important role in industrial screening experiments, in which the primary goal is to identify the treatment factors with the largest main effects on the output of a process or the performance of a product. Often, the experimental tests suggested by the orthogonal designs cannot be performed on a single day or using a single batch of raw material. This causes day-to-day or batch-to-batch variation in the experimental results, and necessitates the use of orthogonal blocking patterns. These blocking patterns ensure that the factors' main effects can be estimated independently from the day-to-day or batch-to-batch variation. Finding an optimal orthogonal blocking pattern for an orthogonal design is a major challenge. Recently, mixed integer linear programming has been used for that purpose. While this approach is promising, computational experiments have indicated it is quite slow. We show how to speed up the mixed integer linear programming approach by adding symmetry breaking constraints to the formulation, and study the usefulness of an asymmetric representatives formulation. In other words, we introduce state-of-the-art symmetry breaking approaches in optimal experimental design. We perform extensive computational experiments to test which combinations of symmetry breaking constraints work best. Throughout, we consider two kinds of symmetry: symmetry due to the fact that the blocks can be relabeled without affecting the quality of the blocking pattern, and symmetry due to replicated test combinations. (C) 2018 Elsevier Ltd. All rights reserved.
Language
English
Source (journal)
Computers & operations research. - New York, N.Y.
Publication
New York, N.Y. : 2018
ISSN
0305-0548
Volume/pages
97(2018), p. 96-110
ISI
000435062500008
Full text (Publisher's DOI)
Full text (open access)
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UAntwerpen
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Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 10.07.2018
Last edited 17.09.2021
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