Constructing uniform designs: A heuristic integer programming method
In this paper, the wrap-around L-2-discrepancy (WD) of asymmetrical design is represented as a quadratic form, thus the problem of constructing a uniform design becomes a quadratic integer programming problem. By the theory of optimization, some theoretic properties are obtained. Algorithms for constructing uniform designs are then studied. When the number of runs n is smaller than the number of all level-combinations m, the construction problem can be transferred to a zero-one quadratic integer programming problem, and an efficient algorithm based on the simulated annealing is proposed. When n >= m, another algorithm is proposed. Empirical study shows that when n is large, the proposed algorithms can generate designs with lower WD compared to many existing methods. Moreover, these algorithms are suitable for constructing both symmetrical and asymmetrical designs. (C) 2011 Elsevier Inc. All rights reserved.
uniform design wrap-around l-2-discrepancy quadratic integer programming simulated annealing