Optimal U—Type Designs
Designs with low discrepancy are of interest in many areas of statistical work. U—type designs are among the most widely studied design classes. In this paper a heuristic global optimization algorithm, Threshold Accepting, is used to find optimal U—type designs (uniform designs) or at least good approximations to uniform designs. As the evaluation of the discrepancy of a given point set is performed by an exact algorithm, the application presented here is restricted to small numbers of experiments in low dimensional spaces. The comparison with known optimal results for the two—factor uniform design and good designs for three to five factors shows a good performance of the algorithm.
Unable to display preview. Download preview PDF.
- Y. Fang (1995). Relationships between Uniform and Orthogonal Designs. The 3rd ICSA Statistical Conference, Beijing.Google Scholar
- B. L. Fox. Simulated Annealing: Folklore,Facts, and Directions. In: H. Niederreiter and P. J.-S. Shiue (eds.). Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing. Lecture Notes in Statistics 106, Springer, New York 1995.Google Scholar
- W. Li, and K.-T. Fang (1995). A Global Optimum Algorithm on Two Factor Uniform Design. In: K.-T. Fang and F. J. Hickernell (eds.). Proceedings Workshop on Quasi-Monte Carlo Methods and Their Applications. Hong Kong Baptist University, 189–201.Google Scholar
- H. Niederreiter, (1973). Application of diophantine approximations to numerical integration. In: C. F. Osgood (ed.). Diophantine Approximations and Its Applications. Academic Press, New York, 129–199.Google Scholar
- H. Niederreiter, (1992b). Lattice Rules for Multiple Integration. In: Marti, K. (ed.). Stochastic Optimization. Lecture Notes in Economics and Mathematical Systems 379, Springer-Verlag, Berlin.Google Scholar
- P. Winker, and K.-T. Fang (1997). Application of Threshold Accepting to the Evaluation of the Discrepancy of a Set of Points. SIAM Journal on Numerical Analysis, forthcoming.Google Scholar