Iterated Local Search Approaches for Maximin Latin Hypercube Designs

Abstract

Many scientific phenomena are now investigated by experimental design. In the field of experimental design problems we consider maximin Latin Hypercube Designs (LHDs). Problems are formulated as optimization ones. Optimal Latin Hypercube designs has good space-filling as well as non-collapsing properties, is widely used experimental design. Here, we consider Iterated Local search (ILS) heuristic approach to obtain optimized (maximin) LHD in Euclidian distance measure. There is another important property required in experimental design is the multicollinearity. Since if two factors are correlated then it will not be possible to distinguish between the effects of the two factors based on this experiment. There are procedures to find good LHDs by minimizing the pair-wise correlation or maximizing the intersite distances. Several experiments are performed to compare our results with available ones in the literature. Many improvements, regarding maximin LHD, are obtained. Extensive experiments have been also performed to analyze the multicollinearity of the optimal LHDs. Some other structural information of the optimal (maximin) LHDs obtained by the ILS approach are analyzed. Finally experimentally it has been shown that the maximin LHDs obtained by ILS is the state of arts regarding space-filling as well as non-collapsing properties and comparable regarding multicollinearity property. Moreover the dependency among the factors of the experimental design obtained by ILS approach is negligible for large value of design points.