ABSTRACT
Various optimization techniques have been employed for finding optimal LHDs, uniform designs, and other space-filling designs. In the previous chapter we introduced many useful methods for construction of UDs, each focusing on a specific structure of designs (e.g., Un(ns), Un(qs), and UDs with mixed levels). Alternatively, one may choose to employ a more general optimization approach that can be used to deal with any kind of UDs. This generality, though at the expense of computational complexity, is an attractive advantage of the optimization approach. In the past decades many powerful optimization algorithms have been developed. Park (1994) developed an algorithm for constructing optimal LHDs based on IMSE criterion and entropy criterion, Morris and Mitchell (1995) adapted a version of simulated annealing algorithm for construction of optimal LHDs based on φp criterion, and Ye (1998) employed the column-pairwise algorithm for constructing optimal symmetrical LHDs based on the φp criterion and entropy criterion. The threshold accepting heuristic has been used for construction of uniform designs under the star discrepancy (Winker and Fang (1998)), centered L2-discrepancy (Fang, Ma and Winker (2000), Fang, Lu and Winker (2003), and Fang, Maringer, Tang and Winker (2005)), and wrap-around L2-discrepancy (Fang and Ma (2001b), Fang, Lu and Winker (2003), and Fang, Tang and Yin (2005)). Jin, Chen and Sudjianto (2005) demonstrated the use of an evolutionary algorithm to efficiently generate optimal LHD, and uniform designs under various criteria. In this chapter we shall introduce some useful optimization algorithms and their applications to the construction of space-filling designs.
