Optimality Analysis on the Basis of Rectangular (Manhattan) Distance Measure for Maximin LHDs Obtained by the Iterated Local Search Heuristics Approach

Abstract

Design of Experiment (DoE) is an important issue for developing mathematical model of any physical problem especially when there exist large numbers of factors. Optimal Latin Hypercube Design (LHD) is one of the well-known and used tools among the experimental designs. For obtaining optimal LHD, Iterated Local Search (ILS) is one of the best way among the heuristic approaches. Grosso et al. (2009) showed that ILS approach has the ability to obtain a large number of maximin (Optimizations by maximizing minimum pairwise distance) LHD where distances are measured in terms of Euclidian distance measure. Several authors showed that rather than Euclidean distance measure other measures may suitable for good DoE. Manhattan distance measure is one of them [Morris and Mitchell (1995)]. In this research work, the main objective is to study the optimality of the maximin LHD obtained by ILS approach regarding Manhattan distance measure. For this purpose, ILS approach is implemented in windows environment (rather than Sun cluster, as Gross et al. (2009) done). Extensive experiments are performed to obtain maximin LHD measured in Euclidian distance measure. Then further experiments are reformed on those LHDs to find the minimum pair-wise distance of each LHD measured in Manhattan distance. Those values are compared with available one in the literature. It is noted that few values (maximin LHD measured in Manhattan distance measure) are available in the literature. It seems that the minimum pair-wise distance measured in Manhattan distance measure of the maximin LHDs obtained by ILS approach, optimized in Euclidian distance measure are comparable with those maximin LHDs obtained through other approaches but optimized in the Manhattan distance measure. Moreover some further experiments are performed to find out some new characteristics of those LHDs which may be used for further study. Some improved maximin LHDs are also obtained in this experimental arena and are presented in the thesis.