A hybrid elitist pareto-based coordinate exchange algorithm for constructing multi-criteria optimal experimental designs
- 217 Downloads
This paper presents a new Pareto-based coordinate exchange algorithm for populating or approximating the true Pareto front for multi-criteria optimal experimental design problems that arise naturally in a range of industrial applications. This heuristic combines an elitist-like operator inspired by evolutionary multi-objective optimization algorithms with a coordinate exchange operator that is commonly used to construct optimal designs. Benchmarking results from both a two-dimensional and three-dimensional example demonstrate that the proposed hybrid algorithm can generate highly reliable Pareto fronts with less computational effort than existing procedures in the statistics literature. The proposed algorithm also utilizes a multi-start operator, which makes it readily parallelizable for high performance computing infrastructures.
KeywordsMulti-criteria optimal experimental design Pareto front Hybrid algorithm
The authors would like to thank Drs. Christine Anderson-Cook, Lu Lu and You-jin Park for sharing their examples. We also wish to express gratitude to the reviewers and editor who reviewed this work and allowed us the opportunity to improve the paper. The first author is also grateful to Dr. Nancy Flournoy for her valuable suggestions and comments.
- Borkowski, J.J.: Using a genetic algorithm to generate small exact response surface designs. J. Probab. Stat. Sci. 1(1), 65–88 (2003)Google Scholar
- Farrell, R.H., Kiefer, J., Walbran, A.: Optimum multivariate designs. In LM LeCam and J. Neyman (eds.), Proceedings of the fifth Berkeley symposium on mathematical statistics and probability. University of California Press 1, 113–138 (1967)Google Scholar
- Fedorov, V.V.: Theory of Optimal Experiments. Elsevier Science, Philadelphia (1972)Google Scholar
- Gert van, V., Tommi, T.: “hit and run” and “shake and bake” for sampling uniformly from convex shapes. R Package (2015)Google Scholar
- Mashwani, W.K.: Hybrid multi-objective evolutionary algorithms: A survey of the state-of-the-art. Int. J. Comput. Sci. Issues 8, 374–392 (2011)Google Scholar
- Park, Y.J.: Multi-optimal designs for second-order response surface models. Commun. Korean Stat. Soc. 16(1), 195–208 (2009)Google Scholar
- Sambo, F., Borrotti, M., Mylona, K.: A coordinate-exchange two-phase local search algorithm for the d- and i-optimal designs of split-plot experiments. Comput. Stat. Data Anal. 71, 1193–1207 (2014)Google Scholar
- Scrucca, L.: R package ‘ga’ (2014)Google Scholar
- Sexton, C.J., Anthony, D.K., Lewis, S.M., Please, C.P., Keane, A.J.: Design of experiment algorithms for assembled products. J. Qual. Technol. 38, 298–308 (2006)Google Scholar
- Smith, N.A., Tromble, R.W.: Sampling uniformly from the unit simplex. Johns Hopkins University, Technical Report, pp. 1–6 (2004)Google Scholar