Optimality Analysis of Maximin LHDs Obtaining by Iterated Local Search Heuristics Approach Regarding Audze-Eglais Criterion

Abstract

The design of experiments (DoEs) have much recent interest and this is likely to grow as more and more simulation models are used to carry out research. A good experimental design should have at least two important properties namely projective property (non-collapsing) and Space-filling (design points should be evenly spread over the entire design space) property. Any Latin Hyper-cube design (LHD) is inherently preserve projective property. But randomly generated LHDs have poor space-filling property. In consequence, in sense of space-filling, Optimal LHDs are required for good DoEs. Several optimal LHDs are available in the literature; Maximin LHD is one of the most frequently used among such optimal LHDs. It is also noted that researchers implement different type of methods to find out maximin LHDs. But the performances of the approaches are not same. In this study, we consider maximin LHDs obtained by Iterated Local search (ILS) heuristic approach in which inter-site distances are measured in Euclidean distance measure. We have compared the performance and effectiveness of ILS approach with some well-known approaches available in the literature regarding maximin LHDs in Euclidean distance measure. The experimental study agrees that ILS approach outperforms regarding maximin LHDs measured in Euclidean distance measure. We perform further extensive experiments in perspective of Audze-Eglais values. We compare Audze-Eglais values of maximin LHDs, which are optimized regarding ɸp optimal criterion and obtained by ILS approach, with Audze-Eglais value of Audze-Eglais LHDs, which are optimized regarding Audze-Eglais optimal criterion and obtained by Enhanced Stochastic Evolutionary (ESE) algorithm. In the experimental results show that the Audze-Eglais value of Maximin LHDs are comparable. We have also compared the performance of ILS approach with other approaches regarding various characteristics of the optimal designs by considering a typical design namely (k, N) = (4, 9). The comparison study reveals that ILS approach is one of the best approaches for finding maximin LHDs.