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Parameter Inequalities for Orthogonal Arrays with Mixed Levels

Wiebke S. Diestelkamp
2004 Designs, Codes and Cryptography  
We will also provide a new proof of Rao's inequalities for arbitrary orthogonal arrays with mixed levels based on the same method.  ...  We will utilize his algebraic approach to provide an analogous inequality for orthogonal arrays having mixed levels and show that the bound obtained in this fashion is often sharper than Rao's bounds.  ...  Acknowledgments I would like to thank the referees for a number of suggestions that greatly improved this paper. Thanks also to Jay Beder for his helpful comments.  ... 
doi:10.1023/b:desi.0000036245.92856.f0 fatcat:ggpz7sqhcjdatbo4d4sg4mlfta

The Lattice of N-Run Orthogonal Arrays [article]

E. M. Rains, N. J. A. Sloane, John Stufken
2002 arXiv   pre-print
If the number of runs in a (mixed-level) orthogonal array of strength 2 is specified, what numbers of levels and factors are possible?  ...  Using a new construction based on "mixed spreads", all parameter sets with 64 runs are determined. Four of these 64-run orthogonal arrays appear to be new.  ...  Acknowledgments We thank Michele Colgan for computing the properties of the lattices Λ ′ N shown in Table 3 . The research of John Stufken was supported by NSF grant DMS-9803684.  ... 
arXiv:math/0205299v1 fatcat:ahryhuoezrf3dlbozwgob6znsi

The lattice of N-run orthogonal arrays

E.M. Rains, N.J.A. Sloane, John Stufken
2002 Journal of Statistical Planning and Inference  
If the number of runs in a (mixed-level) orthogonal array of strength 2 is specified, what numbers of levels and factors are possible?  ...  Using a new construction based on "mixed spreads", all parameter sets with 64 runs are determined. Four of these 64-run orthogonal arrays appear to be new.  ...  Acknowledgments We thank Michele Colgan for computing the properties of the lattices Λ ′ N shown in Table 3 . The research of John Stufken was supported by NSF grant DMS-9803684.  ... 
doi:10.1016/s0378-3758(01)00119-7 fatcat:dwl4nouovreidadbv5mo3trtxu

Genuinely multipartite entangled states and orthogonal arrays

Dardo Goyeneche, Karol Życzkowski
2014 Physical Review A. Atomic, Molecular, and Optical Physics  
A pure quantum state of N subsystems with d levels each is called k-multipartite maximally entangled state, written k-uniform, if all its reductions to k qudits are maximally mixed.  ...  We establish a link between the combinatorial notion of orthogonal arrays and k-uniform states and prove the existence of several new classes of such states for N-qudit systems.  ...  In a combinatorial context we deal with 2×2 orthogonal array of d = 2 levels and strength k = 1.  ... 
doi:10.1103/physreva.90.022316 fatcat:d7po5f7l7jhwjfekku7flt7f6m

Page 4458 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
The proof of the inequalities adapts Rao’s original proof for symmetric arrays. The Erd6s-Ko-Rado theorem shows that the ‘odd’ inequality is the best one can get with this approach.  ...  The factors chosen by the experimenter are assigned to the rows of the array and the levels of the fac- tor are equated with the symbols in the array. Other questions arise.  ... 

A Novel Intelligent Multiobjective Simulated Annealing Algorithm for Designing Robust PID Controllers

Ming-Hao Hung, Li-Sun Shu, Shinn-Jang Ho, Shiow-Fen Hwang, Shinn-Ying Ho
2008 IEEE transactions on systems, man and cybernetics. Part A. Systems and humans  
An efficient existing multiobjective algorithm, the improved strength Pareto evolutionary algorithm, is also applied to the same example for comparison.  ...  The multiobjective generation mechanism operates on a highscore nondominated solution using a systematic reasoning method based on an orthogonal experimental design, which exploits its neighborhood to  ...  Orthogonal Experimental Design in IMOSA This section describes the orthogonal experimental design with three-level orthogonal arrays in IMOSA.  ... 
doi:10.1109/tsmca.2007.914793 fatcat:n6se5z7l25fklgpe6x4cpzt3tq

Orthogonal arrays of strength 3 and small run sizes

Andries E. Brouwer, Arjeh M. Cohen, Man V.M. Nguyen
2006 Journal of Statistical Planning and Inference  
All mixed (or asymmetric) orthogonal arrays of strength 3 with run size at most 64 are determined.  ...  Theorem 3 (Rao's generalized bounds for mixed orthogonal arrays).  ...  In Section 5, we give the non-existence proof for parameters not appearing in the table. 1 . Parameters of orthogonal arrays of strength 3 with N ≤ 64.  ... 
doi:10.1016/j.jspi.2004.12.012 fatcat:yfan3qrfivcerjo7dt5yddy7xi

OSA: Orthogonal Simulated Annealing Algorithm and Its Application to Designing Mixed$rm H_2 /rm H_infty$Optimal Controllers

S.-J. Ho, S.-Y. Ho, L.-S. Shu
2004 IEEE transactions on systems, man and cybernetics. Part A. Systems and humans  
This paper proposes a novel orthogonal simulated annealing (OSA) algorithm for solving intractable large-scale engineering problems and its application to designing mixed H 2 H optimal structure-specified  ...  controllers with robust stability and disturbance attenuation.  ...  THE UNDERLINED NUMBERS OF H CORRESPOND TO A WELL-BALANCED SUBSET WHICH FORMS AN ORTHOGONAL ARRAY L (3 ) TABLE II II ORTHOGONAL ARRAY L (3 ) TABLE III A III CONCISE EXAMPLE OF IGM USING L (3 )  ... 
doi:10.1109/tsmca.2004.832834 fatcat:d46xuykejjgkbdhvftrwztdasi

Designing structure-specified mixed H/sub 2//H/sub /spl infin// optimal controllers using an intelligent genetic algorithm IGA

Shinn-Jang Ho, Shinn-Ying Ho, Ming-Hao Hung, Li-Sun Shu, Hui-Ling Huang
2005 IEEE Transactions on Control Systems Technology  
The newly-developed IGA with intelligent crossover based on orthogonal experimental design (OED) is efficient for solving intractable engineering problems with lots of design parameters.  ...  This brief proposes an efficient method for designing accurate structure-specified mixed H 2 H optimal controllers for systems with uncertainties and disturbance using an intelligent genetic algorithm  ...  Used OED An efficient way to study the effect of several factors simultaneously is to use OED with both orthogonal array (OA) and factor analysis [14] , [15] .  ... 
doi:10.1109/tcst.2005.857403 fatcat:3q3mlzpoxvdt5ndmnszjueslpa

Multipartite entanglement in heterogeneous systems

Dardo Goyeneche, Jakub Bielawski, Karol Życzkowski
2016 Physical Review A  
Such states are related to quantum error correction codes over mixed alphabets and mixed orthogonal arrays.  ...  Heterogeneous bipartite quantum pure states, composed of two subsystems with a different number of levels, cannot have both reductions maximally mixed.  ...  For this state, the reductions to the second and third party are maximally mixed for any value of the parameters {α j }.  ... 
doi:10.1103/physreva.94.012346 fatcat:je3qja2bzvd57jkalsyigxdj5m

Solving multi-contingency transient stability constrained optimal power flow problems with an improved GA

K.Y. Chan, K.W. Chan, S.H. Ling, H.H.C. Iu, G.T.Y. Pong
2007 2007 IEEE Congress on Evolutionary Computation  
for genetic algorithms to deal with, using a penalty function.  ...  The improved genetic algorithm is proposed by incorporating an orthogonal design in exploring solution spaces.  ...  Aydin for many useful discussions and valuable suggestions to the proposed crossover operator.  ... 
doi:10.1109/cec.2007.4424840 dblp:conf/cec/ChanLCIP07 fatcat:ne5yyisbxfbx7ajsf3uhp25v2q

Hybrid inner-outer algorithm for solving real-world mechanical optimization problems

Omnia Osman Fadel Abouhabaga, Mohamed Hassan Gadallah, Hanan Kamel Kouta, Mohamed Abass Zaghloul
2021 Journal of Engineering and Applied Science (Cairo) (Online)  
Accordingly, a novel algorithm called inner-outer array is proposed in this paper. It depends on the design of parameters and then tolerance design as one of design of experiment stages.  ...  The authors would like to thank the reviewers for their suggestions that have enhanced the article presentation.  ...  Acknowledgements This article is made possible with the assistance and encouragement of both the Faculty of Engineering at Port Said University and Cairo University.  ... 
doi:10.1186/s44147-021-00004-0 fatcat:yuc4rvgdbrbcbkxr3jqnis2odu

Approximation of Bounds on Mixed Level Orthogonal Arrays [article]

Ferruh Ozbudak, Ali Devin Sezer
2009 arXiv   pre-print
Mixed level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao and Gilbert-Varshamov type bounds for mixed level orthogonal arrays.  ...  The computational complexity of the terms involved in these bounds can grow fast as the parameters of the arrays increase and this justifies the construction of these algorithms.  ...  Mixed level orthogonal arrays (OAs, for short) are fundamental to experimental design.  ... 
arXiv:0903.3438v2 fatcat:p7ypz2bm2reejlxhwoigam4zf4

Arrays for combinatorial interaction testing: a review on constructive approaches

Xiao-Nan Lu, Masakazu Jimbo
2019 Japanese Journal of Statistics and Data Science  
Finally, we propose two improved bounds for studying the optimality of locating arrays.  ...  This paper presents a review of the brief history, essential problems, and significant results on arrays for combinatorial interaction testing, including covering arrays, locating arrays, detecting arrays  ...  More generally, various factors may have different numbers of levels; such OAs are called mixed orthogonal arrays.  ... 
doi:10.1007/s42081-019-00056-w fatcat:iysolo3sevc3bpxdtisiz6ispu

Approximation of bounds on mixed-level orthogonal arrays

Ali Devin Sezer, Ferruh Özbudak
2011 Advances in Applied Probability  
Mixed-level orthogonal arrays are basic structures in experimental design. We develop three algorithms that compute Rao- and Gilbert-Varshamov-type bounds for mixed-level orthogonal arrays.  ...  The computational complexity of the terms involved in the original combinatorial representations of these bounds can grow fast as the parameters of the arrays increase and this justifies the construction  ...  Acknowledgements We are grateful to the associate editor and the anonymous referee for valuable suggestions, whose incorporation improved the paper.  ... 
doi:10.1017/s0001867800004912 fatcat:njqc5dijunfmfbnz3iitidlv6y
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