Computational & Technology Resources
an online resource for computational,
engineering & technology publications 

CivilComp Proceedings
ISSN 17593433 CCP: 101
PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING Edited by:
Paper 18
Searching for Minimax Designs of Experiments: A Parallel Evolutionary Approach E. Myšáková and M. Lepš
Department of Mechanics, Faculty of Civil Engineering
, "Searching for Minimax Designs of Experiments: A Parallel Evolutionary Approach", in , (Editors), "Proceedings of the Third International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", CivilComp Press, Stirlingshire, UK, Paper 18, 2013. doi:10.4203/ccp.101.18
Keywords: design of experiments, spacefilling, minimax, Voronoi diagram, largest empty sphere problem, optimization, evolutionary algorithms, evolution strategy.
Summary
Spacefilling design strategies known as design of (computer) experiments (DoE) create an essential part of a surrogate
model. Two main objectives are usually placed on the resulting designs  orthogonality
and spacefilling properties. The last decade has witnessed the development
of several methods for the latter objective. One of the metrics, called minimax represents a very interesting research area. The authors think that this metric seems as the most suitable one for practical purposes, however its computation for higher dimensions is intractable and hence our paper presents new results on this subject.
Given a set of n points in a ddimensional hypercube, the minimax is the radius of the biggest sphere with its center inside the hypercube that does not contain any point of the set. This problem is also known as an empty sphere problem [1]. In other words, the minimax serves as an estimation of the spacefilling properties of the set of points showing the biggest unsampled space. One possible solution is to inspect all vertices forming a Voronoi diagram [2] of the given points. However, for the unbounded case the number of vertices grows exponentially and for the bounded case, i.e. the case of points inside a hypercube, the number is even higher. Although the boundary of the domain can be efficiently solved by mirroring [3], to reliably find the vertices of the Voronoi diagram in higher dimensions new algorithms are still needed. Our paper follows the earlier work [4], where an evolutionary strategy has been used to find the center of the biggest empty sphere. We show that this approach is able to find exact solutions only up to five dimensions and no more. Therefore, an improved algorithm is proposed, where the evolution strategy is run in parallel on subdivisions of the original hypercube. The results show that our procedure is more robust that the referenced one. However an extension to high dimensional spaces, e.g. hundreds, is still not satisfactorily solved and therefore future improvements are needed. References
purchase the fulltext of this paper (price £20)
go to the previous paper 
